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import string_insertion, minor whitespace fixes, gallery update
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Andreas Koepf
parent
d60d608192
commit
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4 changed files with 648 additions and 141 deletions
781
GALLERY.md
781
GALLERY.md
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@ -26,6 +26,7 @@ This gallery shows examples from all available datasets using their default conf
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- [fraction_simplification](#fraction_simplification)
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- [fraction_simplification](#fraction_simplification)
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- [game_of_life](#game_of_life)
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- [game_of_life](#game_of_life)
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- [gcd](#gcd)
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- [gcd](#gcd)
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- [graph_color](#graph_color)
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- [group_anagrams](#group_anagrams)
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- [group_anagrams](#group_anagrams)
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- [gsm_symbolic](#gsm_symbolic)
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- [gsm_symbolic](#gsm_symbolic)
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- [intermediate_integration](#intermediate_integration)
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- [intermediate_integration](#intermediate_integration)
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@ -46,8 +47,10 @@ This gallery shows examples from all available datasets using their default conf
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- [palindrome](#palindrome)
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- [palindrome](#palindrome)
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- [polynomial_equations](#polynomial_equations)
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- [polynomial_equations](#polynomial_equations)
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- [polynomial_multiplication](#polynomial_multiplication)
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- [polynomial_multiplication](#polynomial_multiplication)
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- [pool_matrix](#pool_matrix)
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- [power_function](#power_function)
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- [power_function](#power_function)
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- [prime_factorization](#prime_factorization)
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- [prime_factorization](#prime_factorization)
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- [products](#products)
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- [propositional_logic](#propositional_logic)
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- [propositional_logic](#propositional_logic)
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- [quantum_lock](#quantum_lock)
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- [quantum_lock](#quantum_lock)
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- [ransom_note](#ransom_note)
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- [ransom_note](#ransom_note)
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@ -63,6 +66,9 @@ This gallery shows examples from all available datasets using their default conf
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- [sokoban](#sokoban)
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- [sokoban](#sokoban)
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- [spell_backward](#spell_backward)
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- [spell_backward](#spell_backward)
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- [spiral_matrix](#spiral_matrix)
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- [spiral_matrix](#spiral_matrix)
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- [string_insertion](#string_insertion)
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- [string_manipulation](#string_manipulation)
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- [string_synthesis](#string_synthesis)
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- [sudoku](#sudoku)
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- [sudoku](#sudoku)
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- [syllogism](#syllogism)
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- [syllogism](#syllogism)
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- [time_intervals](#time_intervals)
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- [time_intervals](#time_intervals)
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@ -1488,8 +1494,8 @@ Generates Game of Life games with configurable parameters
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Default configuration:
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Default configuration:
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```python
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```python
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grid_size_x = 20
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grid_size_x = 10
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grid_size_y = 20
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grid_size_y = 10
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filled_cells = 100
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filled_cells = 100
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simulation_steps = 1
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simulation_steps = 1
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seed = 42
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seed = 42
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@ -1499,139 +1505,52 @@ size = 500
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Example tasks:
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Example tasks:
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````
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````
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Example 1:
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Example 1:
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Question: What will this Game of Life board look like after 1 steps of simulation?
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Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])
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[[0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0]
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[[0,1,0,1,1,0,0,0,1,0],
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[0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
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[1,0,0,1,0,1,1,1,1,1],
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[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0]
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[0,0,1,1,1,1,1,1,1,0],
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[1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0]
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[1,1,1,1,0,0,0,0,1,1],
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[0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0]
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[1,1,1,1,0,0,1,0,1,1],
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[0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0]
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[1,1,0,1,1,0,1,1,0,1],
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[0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0]
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[1,0,0,1,1,0,0,0,0,1],
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[1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
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[1,1,1,0,0,1,1,0,1,1],
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[1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0]
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[1,1,1,1,1,0,0,1,0,1],
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[0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1]
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[0,1,1,1,0,1,1,0,1,0]].
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[1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0]
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Answer: [[0,1,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,1,0]]
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[0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1]
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Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}
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[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
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[0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
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[0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0]
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[1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0]
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[1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1]
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[0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0]
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[0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0]]
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Answer: [[0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0]
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[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0]
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[0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0]
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[0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0]
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[0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0]
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[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
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[1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
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[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
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[0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1]
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[1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0]
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[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1]
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[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
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[1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1]
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[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1]
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[1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
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[1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
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[0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0]
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[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
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Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
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Example 2:
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Example 2:
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Question: What will this Game of Life board look like after 1 steps of simulation?
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Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])
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[[1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0]
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[[1,1,1,1,1,1,0,1,1,1],
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[0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0]
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[0,0,1,1,1,1,1,1,1,1],
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[0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0]
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[0,1,0,0,0,0,0,1,1,1],
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[0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1]
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[1,0,0,1,1,1,1,0,0,1],
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[0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
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[0,1,0,1,1,0,0,1,1,0],
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
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[1,1,1,1,0,1,1,0,1,1],
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[0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0]
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[0,1,1,0,1,1,1,0,0,1],
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[1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0]
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[0,0,1,0,1,1,0,0,1,1],
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[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0]
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[0,1,1,0,1,0,1,0,1,1],
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[0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0]
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[1,1,1,0,1,1,1,0,0,1]].
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[0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0]
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Answer: [[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,1,0,1,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0]]
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[0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
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Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}
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[0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1]
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[0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1]
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[0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1]
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[0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1]
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[0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
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[0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
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[0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
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[0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0]]
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Answer: [[0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1]
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[0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0]
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[0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1]
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[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1]
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[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]
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[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
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[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0]
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[0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0]
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[1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1]
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[1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0]
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[1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
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[0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1]
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[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
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[0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]]
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Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
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Example 3:
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Example 3:
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Question: What will this Game of Life board look like after 1 steps of simulation?
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Question: What will this Game of Life board look like after 1 steps of simulation? Reply as array of array representing rows in the grid from top to bottom in JSON format. (An empty 3x3 grid would look like this: [[0,0,0],[0,0,0],[0,0,0]])
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[[0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1]
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[[0,1,0,1,1,1,1,0,0,1],
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[0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1]
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[0,1,0,0,1,1,1,0,1,1],
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[0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0]
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[0,1,1,1,1,0,1,0,1,0],
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[0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0]
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[1,0,0,1,1,0,1,1,1,1],
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[0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
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[1,1,1,0,0,1,1,0,1,1],
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[0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0]
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[0,1,0,0,1,1,0,1,0,1],
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[0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0]
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[0,1,1,0,0,0,1,0,1,1],
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[0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1]
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[0,1,1,0,1,1,1,1,0,1],
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[0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0]
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[1,1,1,1,1,1,0,1,1,0],
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[1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1]
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[1,1,1,0,0,1,1,0,1,0]].
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[0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0]
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Answer: [[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,1],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0]]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0]
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Metadata: {'grid_size_x': 10, 'grid_size_y': 10, 'filled_cells': 100, 'simulation_steps': 1}
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[0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0]
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[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
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[0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0]
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[0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0]
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[0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0]
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[1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0]
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[0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
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[0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0]]
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Answer: [[1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1]
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[0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0]
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[0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0]
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[0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0]
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[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0]
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[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1]
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[0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0]
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[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1]
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[0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
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[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
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[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0]
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[0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0]
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[0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0]
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[0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0]
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[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
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[0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0]
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[0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0]]
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Metadata: {'grid_size_x': 20, 'grid_size_y': 20, 'filled_cells': 100, 'simulation_steps': 1}
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````
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````
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@ -1667,6 +1586,58 @@ Metadata: {'numbers': [297, 30], 'result': 3}
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````
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````
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### graph_color
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Generates graph coloring problems with configurable parameters
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Default configuration:
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```python
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num_colors = 4
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num_vertices = 10
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edge_probability = 0.4
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seed = 42
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size = 500
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```
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Example tasks:
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````
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Example 1:
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Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:
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Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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||||||
|
Edges: [(0, 2), (0, 3), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 8), (2, 9), (3, 5), (3, 6), (3, 7), (4, 9), (6, 9), (7, 8), (7, 9), (8, 9)]
|
||||||
|
Possible colors: [1, 2, 3, 4]
|
||||||
|
|
||||||
|
Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})
|
||||||
|
|
||||||
|
Answer: None
|
||||||
|
Metadata: {'possible_answer': {0: 1, 1: 1, 2: 2, 3: 2, 4: 2, 5: 3, 6: 3, 7: 1, 8: 3, 9: 4}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 2), (0, 3), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 8), (2, 9), (3, 5), (3, 6), (3, 7), (4, 9), (6, 9), (7, 8), (7, 9), (8, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:
|
||||||
|
|
||||||
|
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
|
||||||
|
Edges: [(0, 1), (0, 3), (0, 9), (1, 3), (1, 8), (2, 4), (2, 5), (3, 6), (3, 7), (3, 8), (4, 6), (4, 9), (6, 7), (7, 9)]
|
||||||
|
Possible colors: [1, 2, 3, 4]
|
||||||
|
|
||||||
|
Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})
|
||||||
|
|
||||||
|
Answer: None
|
||||||
|
Metadata: {'possible_answer': {0: 1, 1: 2, 2: 1, 3: 3, 4: 2, 5: 2, 6: 1, 7: 2, 8: 1, 9: 3}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 1), (0, 3), (0, 9), (1, 3), (1, 8), (2, 4), (2, 5), (3, 6), (3, 7), (3, 8), (4, 6), (4, 9), (6, 7), (7, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:
|
||||||
|
|
||||||
|
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
|
||||||
|
Edges: [(0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 9), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (4, 8), (5, 8), (6, 9)]
|
||||||
|
Possible colors: [1, 2, 3, 4]
|
||||||
|
|
||||||
|
Return your solution as a JSON map of verteces to colors. (For example: {0: 1, 1: 2, 2: 3})
|
||||||
|
|
||||||
|
Answer: None
|
||||||
|
Metadata: {'possible_answer': {0: 1, 1: 1, 2: 1, 3: 1, 4: 2, 5: 3, 6: 3, 7: 3, 8: 4, 9: 2}, 'puzzle': {'vertices': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [(0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 9), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (4, 8), (5, 8), (6, 9)], 'num_colors': 4, 'color_options': [1, 2, 3, 4]}}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
### group_anagrams
|
### group_anagrams
|
||||||
Generates Group Anagrams exercises with configurable difficulty
|
Generates Group Anagrams exercises with configurable difficulty
|
||||||
|
|
||||||
|
|
@ -1790,16 +1761,28 @@ Example tasks:
|
||||||
````
|
````
|
||||||
Example 1:
|
Example 1:
|
||||||
Question: Find the indefinite integral: ∫ -3*exp(3*x + 9) dx
|
Question: Find the indefinite integral: ∫ -3*exp(3*x + 9) dx
|
||||||
|
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: -exp(3*x + 9) + C
|
Answer: -exp(3*x + 9) + C
|
||||||
Metadata: {'integrand': '-3*exp(3*x + 9)', 'problem_type': 'substitution', 'variable': 'x', 'type': 'exponential', 'expected_answer_expression': -exp(3*x + 9)}
|
Metadata: {'integrand': '-3*exp(3*x + 9)', 'problem_type': 'substitution', 'variable': 'x', 'type': 'exponential', 'expected_answer_expression': -exp(3*x + 9)}
|
||||||
|
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: Evaluate the indefinite integral: ∫ -6*sin(2*X + 10)*cos(2*X + 10)**4 dx
|
Question: Evaluate the indefinite integral: ∫ -6*sin(2*X + 10)*cos(2*X + 10)**4 dx
|
||||||
|
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: 3*cos(2*X + 10)**5/5 + C
|
Answer: 3*cos(2*X + 10)**5/5 + C
|
||||||
Metadata: {'integrand': '-6*sin(2*X + 10)*cos(2*X + 10)**4', 'problem_type': 'substitution', 'variable': 'X', 'type': 'trigonometric', 'expected_answer_expression': 3*cos(2*X + 10)**5/5}
|
Metadata: {'integrand': '-6*sin(2*X + 10)*cos(2*X + 10)**4', 'problem_type': 'substitution', 'variable': 'X', 'type': 'trigonometric', 'expected_answer_expression': 3*cos(2*X + 10)**5/5}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Find the indefinite integral: ∫ 2*asin(x) dx
|
Question: Find the indefinite integral: ∫ 2*asin(x) dx
|
||||||
|
In addition, when doing calculation, use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: 2*Integral(asin(x), x) + C
|
Answer: 2*Integral(asin(x), x) + C
|
||||||
Metadata: {'integrand': '2*asin(x)', 'problem_type': 'by_parts', 'variable': 'x', 'type': 'log_inverse_trig', 'expected_answer_expression': 2*Integral(asin(x), x)}
|
Metadata: {'integrand': '2*asin(x)', 'problem_type': 'by_parts', 'variable': 'x', 'type': 'log_inverse_trig', 'expected_answer_expression': 2*Integral(asin(x), x)}
|
||||||
|
|
||||||
|
|
@ -2636,16 +2619,28 @@ Example tasks:
|
||||||
````
|
````
|
||||||
Example 1:
|
Example 1:
|
||||||
Question: Sort these numbers in ascending order: 48, -51, -72, -80
|
Question: Sort these numbers in ascending order: 48, -51, -72, -80
|
||||||
|
Please follow the instruction below:
|
||||||
|
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
|
||||||
|
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']
|
||||||
|
|
||||||
Answer: ['-80', '-72', '-51', '48']
|
Answer: ['-80', '-72', '-51', '48']
|
||||||
Metadata: {'original_numbers': ['48', '-51', '-72', '-80'], 'direction': 'ascending', 'sorted_numbers': ['-80', '-72', '-51', '48']}
|
Metadata: {'original_numbers': ['48', '-51', '-72', '-80'], 'direction': 'ascending', 'sorted_numbers': ['-80', '-72', '-51', '48']}
|
||||||
|
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: Sort these numbers in ascending order: 39.2, -71.2, -7.5
|
Question: Sort these numbers in ascending order: 39.2, -71.2, -7.5
|
||||||
|
Please follow the instruction below:
|
||||||
|
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
|
||||||
|
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']
|
||||||
|
|
||||||
Answer: ['-71.2', '-7.5', '39.2']
|
Answer: ['-71.2', '-7.5', '39.2']
|
||||||
Metadata: {'original_numbers': ['39.2', '-71.2', '-7.5'], 'direction': 'ascending', 'sorted_numbers': ['-71.2', '-7.5', '39.2']}
|
Metadata: {'original_numbers': ['39.2', '-71.2', '-7.5'], 'direction': 'ascending', 'sorted_numbers': ['-71.2', '-7.5', '39.2']}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Sort these numbers in descending order: 8.39, 72.41, -64.67, -54.97, -94.18, -76.67, -98.24, -68.66, 2.74
|
Question: Sort these numbers in descending order: 8.39, 72.41, -64.67, -54.97, -94.18, -76.67, -98.24, -68.66, 2.74
|
||||||
|
Please follow the instruction below:
|
||||||
|
## 1. Let all your answers be a list of numbers. Instead of reporting your answer as -69, -13, 1, 7, 11, 43, 59, 61, use ['-69', '-13', '1', '7', '11', '43', '59', '61'] instead
|
||||||
|
## 2. Convert all numbers in the square brackets as strings. For example, ['-69', '-13', '1', '7', '11', '43', '59', '61']
|
||||||
|
|
||||||
Answer: ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']
|
Answer: ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']
|
||||||
Metadata: {'original_numbers': ['8.39', '72.41', '-64.67', '-54.97', '-94.18', '-76.67', '-98.24', '-68.66', '2.74'], 'direction': 'descending', 'sorted_numbers': ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']}
|
Metadata: {'original_numbers': ['8.39', '72.41', '-64.67', '-54.97', '-94.18', '-76.67', '-98.24', '-68.66', '2.74'], 'direction': 'descending', 'sorted_numbers': ['72.41', '8.39', '2.74', '-54.97', '-64.67', '-68.66', '-76.67', '-94.18', '-98.24']}
|
||||||
|
|
||||||
|
|
@ -2721,19 +2716,40 @@ size = 500
|
||||||
Example tasks:
|
Example tasks:
|
||||||
````
|
````
|
||||||
Example 1:
|
Example 1:
|
||||||
Question: Find the real value(s) of u in the equation: -127*u = 0
|
Question: Find the real value(s) of w in the equation: -127*w = 0
|
||||||
Answer: [0.0]
|
In solving the equations, please abide by the following instruction:
|
||||||
Metadata: {'polynomial_expr': '-127*u', 'variable': 'u', 'degree': 1, 'real_solutions': [0.0]}
|
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
|
||||||
|
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
|
||||||
|
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
|
||||||
|
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
|
||||||
|
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.
|
||||||
|
|
||||||
|
Answer: 0.0
|
||||||
|
Metadata: {'polynomial_expr': '-127*w', 'variable': 'w', 'degree': 1, 'real_solutions': [0.0]}
|
||||||
|
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: Determine the real value(s) of b that satisfies: 86*b**2 - 2*b - 13 = 0
|
Question: Determine the real value(s) of b that satisfies: 86*b**2 - 2*b - 13 = 0
|
||||||
Answer: [-0.3773425275273891, 0.4005983414808775]
|
In solving the equations, please abide by the following instruction:
|
||||||
Metadata: {'polynomial_expr': '86*b**2 - 2*b - 13', 'variable': 'b', 'degree': 2, 'real_solutions': [-0.3773425275273891, 0.4005983414808775]}
|
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
|
||||||
|
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
|
||||||
|
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
|
||||||
|
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
|
||||||
|
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.
|
||||||
|
|
||||||
|
Answer: -0.3773, 0.4006
|
||||||
|
Metadata: {'polynomial_expr': '86*b**2 - 2*b - 13', 'variable': 'b', 'degree': 2, 'real_solutions': [-0.3773, 0.4006]}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Determine the real value(s) of n that satisfies: 71*n**3 - 2*n - 29 = 0
|
Question: Determine the real value(s) of p that satisfies: 71*p**3 - 2*p - 29 = 0
|
||||||
Answer: [0.7546129960163634]
|
In solving the equations, please abide by the following instruction:
|
||||||
Metadata: {'polynomial_expr': '71*n**3 - 2*n - 29', 'variable': 'n', 'degree': 3, 'real_solutions': [0.7546129960163634]}
|
## 1. All answers should be comma-separated. For example "-0.3773, 0.4005" etc.
|
||||||
|
## 2. In cases where your answer is b = 2 + sqrt(4560) / 172 and b = 2 - sqrt(4560) / 172. Since b can be 2 numbers, resolve your answer like this instead, "-0.3773, 0.4005".
|
||||||
|
## 3. If there are no real values of i that satisfy the equation, report your answer as empty string, "".
|
||||||
|
## 4. If there are 2 answers, resolve the answers as comma-separated floats of 2 numbers, if 3 answers, make it comma-separated floats of 3 numbers.
|
||||||
|
## 5. Resolve all numbers as floats in the string of comma-separated numbers. Round the floats higher than 4 decimal place(d.p) down to 4 d.p.
|
||||||
|
|
||||||
|
Answer: 0.7546
|
||||||
|
Metadata: {'polynomial_expr': '71*p**3 - 2*p - 29', 'variable': 'p', 'degree': 3, 'real_solutions': [0.7546]}
|
||||||
|
|
||||||
````
|
````
|
||||||
|
|
||||||
|
|
@ -2762,21 +2778,153 @@ Example tasks:
|
||||||
````
|
````
|
||||||
Example 1:
|
Example 1:
|
||||||
Question: Calculate the following: (65*x - 72)*(105*x - 125)
|
Question: Calculate the following: (65*x - 72)*(105*x - 125)
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.
|
||||||
|
|
||||||
Answer: 6825*x**2 - 15685*x + 9000
|
Answer: 6825*x**2 - 15685*x + 9000
|
||||||
Metadata: {'polynomial_expr': '(65*x - 72)*(105*x - 125)', 'single_variable': True, 'result': '6825*x**2 - 15685*x + 9000'}
|
Metadata: {'polynomial_expr': '(65*x - 72)*(105*x - 125)', 'single_variable': True, 'result': '6825*x**2 - 15685*x + 9000'}
|
||||||
|
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: Calculate the following: (-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)
|
Question: Calculate the following: (-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.
|
||||||
|
|
||||||
Answer: -774*x**4 - 2390*x**3 + 173*x**2 + 364*x
|
Answer: -774*x**4 - 2390*x**3 + 173*x**2 + 364*x
|
||||||
Metadata: {'polynomial_expr': '(-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)', 'single_variable': True, 'result': '-774*x**4 - 2390*x**3 + 173*x**2 + 364*x'}
|
Metadata: {'polynomial_expr': '(-9*x**2 - 28*x)*(86*x**2 - 2*x - 13)', 'single_variable': True, 'result': '-774*x**4 - 2390*x**3 + 173*x**2 + 364*x'}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Calculate the following: (43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)
|
Question: Calculate the following: (43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps and even in reporting answers.
|
||||||
|
|
||||||
Answer: -19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x
|
Answer: -19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x
|
||||||
Metadata: {'polynomial_expr': '(43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)', 'single_variable': True, 'result': '-19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x'}
|
Metadata: {'polynomial_expr': '(43 - 91*x)*(3*x**2 - 10*x)*(71*x**3 - 2*x - 29)', 'single_variable': True, 'result': '-19383*x**6 + 73769*x**5 - 29984*x**4 + 5839*x**3 - 29271*x**2 + 12470*x'}
|
||||||
|
|
||||||
````
|
````
|
||||||
|
|
||||||
|
### pool_matrix
|
||||||
|
Generates Pool Matrix exercises with configurable difficulty
|
||||||
|
|
||||||
|
Default configuration:
|
||||||
|
```python
|
||||||
|
min_rows = 2
|
||||||
|
min_cols = 2
|
||||||
|
max_rows = 10
|
||||||
|
max_cols = 10
|
||||||
|
max_pool_size = 3
|
||||||
|
size = 500
|
||||||
|
seed = 42
|
||||||
|
```
|
||||||
|
|
||||||
|
Example tasks:
|
||||||
|
````
|
||||||
|
Example 1:
|
||||||
|
Question: Your job is to perform max/average pooling on the given matrix.
|
||||||
|
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.
|
||||||
|
|
||||||
|
Example 1:
|
||||||
|
- Input: Perform max pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
6 8
|
||||||
|
14 16
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
- Input: Perform average pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
3.5 5.5
|
||||||
|
11.5 13.5
|
||||||
|
|
||||||
|
Perform max pooling on the following matrix with a kernel size of 3:
|
||||||
|
6 3
|
||||||
|
7 4
|
||||||
|
6 9
|
||||||
|
|
||||||
|
Answer: 9
|
||||||
|
Metadata: {'matrix': [[6, 3], [7, 4], [6, 9]], 'pool_type': 'max', 'pool_size': 3, 'solution': [[9]]}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: Your job is to perform max/average pooling on the given matrix.
|
||||||
|
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.
|
||||||
|
|
||||||
|
Example 1:
|
||||||
|
- Input: Perform max pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
6 8
|
||||||
|
14 16
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
- Input: Perform average pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
3.5 5.5
|
||||||
|
11.5 13.5
|
||||||
|
|
||||||
|
Perform average pooling on the following matrix with a kernel size of 3:
|
||||||
|
4 0 1 5 0 3
|
||||||
|
1 2 7 0 3 2
|
||||||
|
|
||||||
|
Answer: 2.5 2.17
|
||||||
|
Metadata: {'matrix': [[4, 0, 1, 5, 0, 3], [1, 2, 7, 0, 3, 2]], 'pool_type': 'average', 'pool_size': 3, 'solution': [[2.5, 2.1666666666666665]]}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: Your job is to perform max/average pooling on the given matrix.
|
||||||
|
The stride is equal to the kernel size, meaning there is no overlap between the pooling regions.
|
||||||
|
|
||||||
|
Example 1:
|
||||||
|
- Input: Perform max pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
6 8
|
||||||
|
14 16
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
- Input: Perform average pooling on the following matrix with a kernel size of 2:
|
||||||
|
1 2 3 4
|
||||||
|
5 6 7 8
|
||||||
|
9 10 11 12
|
||||||
|
13 14 15 16
|
||||||
|
- Output:
|
||||||
|
3.5 5.5
|
||||||
|
11.5 13.5
|
||||||
|
|
||||||
|
Perform average pooling on the following matrix with a kernel size of 3:
|
||||||
|
4 3 1 3 0 4 3 8 7 7
|
||||||
|
6 9 3 7 3 3 6 5 4 5
|
||||||
|
9 1 8 7 4 5 3 0 4 9
|
||||||
|
2 8 8 6 2 0 3 4 8 3
|
||||||
|
2 2 1 2 2 9 8 1 8 9
|
||||||
|
4 2 4 6 7 5 5 6 2 5
|
||||||
|
1 8 9 1 8 0 9 3 5 9
|
||||||
|
5 0 8 0 4 2 9 7 6 6
|
||||||
|
|
||||||
|
Answer: 4.89 4.0 4.44 7.0
|
||||||
|
3.67 4.33 5.0 5.67
|
||||||
|
5.17 2.5 6.5 7.5
|
||||||
|
Metadata: {'matrix': [[4, 3, 1, 3, 0, 4, 3, 8, 7, 7], [6, 9, 3, 7, 3, 3, 6, 5, 4, 5], [9, 1, 8, 7, 4, 5, 3, 0, 4, 9], [2, 8, 8, 6, 2, 0, 3, 4, 8, 3], [2, 2, 1, 2, 2, 9, 8, 1, 8, 9], [4, 2, 4, 6, 7, 5, 5, 6, 2, 5], [1, 8, 9, 1, 8, 0, 9, 3, 5, 9], [5, 0, 8, 0, 4, 2, 9, 7, 6, 6]], 'pool_type': 'average', 'pool_size': 3, 'solution': [[4.888888888888889, 4.0, 4.444444444444445, 7.0], [3.6666666666666665, 4.333333333333333, 5.0, 5.666666666666667], [5.166666666666667, 2.5, 6.5, 7.5]]}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
### power_function
|
### power_function
|
||||||
Generates Power Function exercises with configurable difficulty
|
Generates Power Function exercises with configurable difficulty
|
||||||
|
|
||||||
|
|
@ -2839,6 +2987,38 @@ Metadata: {'number': 420, 'factors': [2, 2, 3, 5, 7]}
|
||||||
|
|
||||||
````
|
````
|
||||||
|
|
||||||
|
### products
|
||||||
|
Generates multiplication tasks with configurable number of terms
|
||||||
|
|
||||||
|
Default configuration:
|
||||||
|
```python
|
||||||
|
min_terms = 2
|
||||||
|
max_terms = 2
|
||||||
|
min_digits = 1
|
||||||
|
max_digits = 5
|
||||||
|
seed = 42
|
||||||
|
size = 500
|
||||||
|
```
|
||||||
|
|
||||||
|
Example tasks:
|
||||||
|
````
|
||||||
|
Example 1:
|
||||||
|
Question: 4 * 3 =
|
||||||
|
Answer: 12
|
||||||
|
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 1}, 'expression': '4 * 3'}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: 812 * 880 =
|
||||||
|
Answer: 714560
|
||||||
|
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 3}, 'expression': '812 * 880'}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: 81037 * 25290 =
|
||||||
|
Answer: 2049425730
|
||||||
|
Metadata: {'difficulty': {'num_terms': 2, 'num_digits': 5}, 'expression': '81037 * 25290'}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
### propositional_logic
|
### propositional_logic
|
||||||
Generates propositional logic reasoning tasks
|
Generates propositional logic reasoning tasks
|
||||||
|
|
||||||
|
|
@ -3874,16 +4054,28 @@ Example tasks:
|
||||||
````
|
````
|
||||||
Example 1:
|
Example 1:
|
||||||
Question: Find the indefinite integral: ∫ 70*x**6 + 12*x**2/5 dx
|
Question: Find the indefinite integral: ∫ 70*x**6 + 12*x**2/5 dx
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: 10*x**7 + 4*x**3/5 + C
|
Answer: 10*x**7 + 4*x**3/5 + C
|
||||||
Metadata: {'integrand': '70*x**6 + 12*x**2/5', 'variable': 'x', 'expected_answer_expression': 10*x**7 + 4*x**3/5}
|
Metadata: {'integrand': '70*x**6 + 12*x**2/5', 'variable': 'x', 'expected_answer_expression': 10*x**7 + 4*x**3/5}
|
||||||
|
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: Find the indefinite integral: ∫ 49*x**6/10 + 48*x**5 - 4*x - 10/9 dx
|
Question: Find the indefinite integral: ∫ 49*x**6/10 + 48*x**5 - 4*x - 10/9 dx
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9 + C
|
Answer: 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9 + C
|
||||||
Metadata: {'integrand': '49*x**6/10 + 48*x**5 - 4*x - 10/9', 'variable': 'x', 'expected_answer_expression': 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9}
|
Metadata: {'integrand': '49*x**6/10 + 48*x**5 - 4*x - 10/9', 'variable': 'x', 'expected_answer_expression': 7*x**7/10 + 8*x**6 - 2*x**2 - 10*x/9}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Find the indefinite integral: ∫ -28*X**3 + 8*X dx
|
Question: Find the indefinite integral: ∫ -28*X**3 + 8*X dx
|
||||||
|
In addition, When doing calculation, Use the following instructions together with your mathematical ingenuity to solve the integral problems
|
||||||
|
## 1. Use ** instead ^ to represent powers. For example 7*X**2 instead of 7*X^2.
|
||||||
|
## 2. Always use * when doing all sorts of multiplcation in your reasoning steps. For example Use [-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C] instead of [-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C].
|
||||||
|
|
||||||
Answer: -7*X**4 + 4*X**2 + C
|
Answer: -7*X**4 + 4*X**2 + C
|
||||||
Metadata: {'integrand': '-28*X**3 + 8*X', 'variable': 'X', 'expected_answer_expression': -7*X**4 + 4*X**2}
|
Metadata: {'integrand': '-28*X**3 + 8*X', 'variable': 'X', 'expected_answer_expression': -7*X**4 + 4*X**2}
|
||||||
|
|
||||||
|
|
@ -4094,6 +4286,321 @@ Metadata: {'matrix': [[6, 4, 1, 8, 2, 6, 2], [9, 5, 1, 3, 4, 8, 0], [1, 2, 1, 4,
|
||||||
|
|
||||||
````
|
````
|
||||||
|
|
||||||
|
### string_insertion
|
||||||
|
Generates String Insertion exercises with configurable difficulty
|
||||||
|
|
||||||
|
Default configuration:
|
||||||
|
```python
|
||||||
|
min_string_length = 5
|
||||||
|
max_string_length = 20
|
||||||
|
size = 500
|
||||||
|
seed = 42
|
||||||
|
```
|
||||||
|
|
||||||
|
Example tasks:
|
||||||
|
````
|
||||||
|
Example 1:
|
||||||
|
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
|
||||||
|
1. If there is a substring ABCD in the string, insert the character A after the substring.
|
||||||
|
2. If there is a substring BCDE in the string, insert the character B after the substring.
|
||||||
|
3. If there is a substring CDEA in the string, insert the character C after the substring.
|
||||||
|
4. If there is a substring DEAB in the string, insert the character D after the substring.
|
||||||
|
5. If there is a substring EABC in the string, insert the character E after the substring.
|
||||||
|
|
||||||
|
Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.
|
||||||
|
|
||||||
|
Example
|
||||||
|
- Input: DDABCDEEDEAB
|
||||||
|
- Output: DDABCDAEEDEABD
|
||||||
|
- Explanation:
|
||||||
|
- Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
|
||||||
|
- First, we insert A after ABCD.
|
||||||
|
- Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
|
||||||
|
- Lastly, we insert D after DEAB.
|
||||||
|
|
||||||
|
Given the following string, provide the answer after inserting the characters according to the pattern: ['A', 'C', 'B', 'B', 'B', 'A', 'E', 'A']
|
||||||
|
|
||||||
|
Answer: ACBBBAEA
|
||||||
|
Metadata: {'string': ['A', 'C', 'B', 'B', 'B', 'A', 'E', 'A'], 'solution': 'ACBBBAEA'}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
|
||||||
|
1. If there is a substring ABCD in the string, insert the character A after the substring.
|
||||||
|
2. If there is a substring BCDE in the string, insert the character B after the substring.
|
||||||
|
3. If there is a substring CDEA in the string, insert the character C after the substring.
|
||||||
|
4. If there is a substring DEAB in the string, insert the character D after the substring.
|
||||||
|
5. If there is a substring EABC in the string, insert the character E after the substring.
|
||||||
|
|
||||||
|
Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.
|
||||||
|
|
||||||
|
Example
|
||||||
|
- Input: DDABCDEEDEAB
|
||||||
|
- Output: DDABCDAEEDEABD
|
||||||
|
- Explanation:
|
||||||
|
- Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
|
||||||
|
- First, we insert A after ABCD.
|
||||||
|
- Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
|
||||||
|
- Lastly, we insert D after DEAB.
|
||||||
|
|
||||||
|
Given the following string, provide the answer after inserting the characters according to the pattern: ['C', 'B', 'D', 'C', 'A', 'D']
|
||||||
|
|
||||||
|
Answer: CBDCAD
|
||||||
|
Metadata: {'string': ['C', 'B', 'D', 'C', 'A', 'D'], 'solution': 'CBDCAD'}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: Given a string consisting of characters A, B, C, D, and E, your job is to insert a character according to the following pattern:
|
||||||
|
1. If there is a substring ABCD in the string, insert the character A after the substring.
|
||||||
|
2. If there is a substring BCDE in the string, insert the character B after the substring.
|
||||||
|
3. If there is a substring CDEA in the string, insert the character C after the substring.
|
||||||
|
4. If there is a substring DEAB in the string, insert the character D after the substring.
|
||||||
|
5. If there is a substring EABC in the string, insert the character E after the substring.
|
||||||
|
|
||||||
|
Once you have inserted a character, you have to skip over the substring and the inserted character and continue the search from the next character.
|
||||||
|
|
||||||
|
Example
|
||||||
|
- Input: DDABCDEEDEAB
|
||||||
|
- Output: DDABCDAEEDEABD
|
||||||
|
- Explanation:
|
||||||
|
- Theere are two inserted characters: DDABCD[A]EEDEAB[D] (shown in square brackets)
|
||||||
|
- First, we insert A after ABCD.
|
||||||
|
- Even though with the newly inserted 'A' we can obtain the substring BCD[A], we can't use it to insert another character.
|
||||||
|
- Lastly, we insert D after DEAB.
|
||||||
|
|
||||||
|
Given the following string, provide the answer after inserting the characters according to the pattern: ['E', 'E', 'A', 'B', 'D', 'B', 'C', 'A', 'B', 'A', 'E', 'A', 'A', 'B', 'E', 'C', 'D', 'E']
|
||||||
|
|
||||||
|
Answer: EEABDBCABAEAABECDE
|
||||||
|
Metadata: {'string': ['E', 'E', 'A', 'B', 'D', 'B', 'C', 'A', 'B', 'A', 'E', 'A', 'A', 'B', 'E', 'C', 'D', 'E'], 'solution': 'EEABDBCABAEAABECDE'}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
|
### string_manipulation
|
||||||
|
Generates String Insertion exercises with configurable difficulty
|
||||||
|
|
||||||
|
Default configuration:
|
||||||
|
```python
|
||||||
|
min_string_length = 5
|
||||||
|
max_string_length = 20
|
||||||
|
min_num_rules = 3
|
||||||
|
max_num_rules = 8
|
||||||
|
size = 500
|
||||||
|
seed = 42
|
||||||
|
```
|
||||||
|
|
||||||
|
Example tasks:
|
||||||
|
````
|
||||||
|
Example 1:
|
||||||
|
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.
|
||||||
|
|
||||||
|
Evaluate the following rules in order, and apply the first applicable rule to the string:
|
||||||
|
1. If the string contains an even number of 'b's (and at least one 'b'), append 'ab' at the end.
|
||||||
|
2. If the string prefix is 'bc', delete the first two characters and append 'aa' to the end.
|
||||||
|
3. If the string ends with 'ca', remove the last character.
|
||||||
|
4. If the string suffix is 'ac', replace it with 'cb'.
|
||||||
|
5. If the string prefix is 'ab', replace it with 'ca'.
|
||||||
|
6. If the string contains 'ca' (not at the start), remove the first occurrence found after the first character.
|
||||||
|
7. If the string suffix is 'bb', delete the last two characters.
|
||||||
|
8. If the string starts with 'ac', replace the first two characters with 'zz'.
|
||||||
|
|
||||||
|
Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
|
||||||
|
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input:
|
||||||
|
- String: abbac
|
||||||
|
- Rules:
|
||||||
|
1. If the string prefix is 'ab', replace it with 'ca'.
|
||||||
|
2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
|
||||||
|
3. If the string ends with 'aa', replace it with 'cc'.
|
||||||
|
- Output: bbbacc
|
||||||
|
- Explanation:
|
||||||
|
- In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
|
||||||
|
- In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
|
||||||
|
- In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc
|
||||||
|
|
||||||
|
Transform the following string according to the above list of rules:
|
||||||
|
acbaaaca
|
||||||
|
|
||||||
|
Answer: zzbaacbab
|
||||||
|
Metadata: {'string': 'acbaaaca', 'solution': 'zzbaacbab', 'states': ['acbaaaca', 'acbaaac', 'acbaacb', 'acbaacbab', 'zzbaacbab'], 'selected_rules': ["If the string contains an even number of 'b's (and at least one 'b'), append 'ab' at the end.", "If the string prefix is 'bc', delete the first two characters and append 'aa' to the end.", "If the string ends with 'ca', remove the last character.", "If the string suffix is 'ac', replace it with 'cb'.", "If the string prefix is 'ab', replace it with 'ca'.", "If the string contains 'ca' (not at the start), remove the first occurrence found after the first character.", "If the string suffix is 'bb', delete the last two characters.", "If the string starts with 'ac', replace the first two characters with 'zz'."]}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.
|
||||||
|
|
||||||
|
Evaluate the following rules in order, and apply the first applicable rule to the string:
|
||||||
|
1. If the string suffix is 'bb', delete the last two characters.
|
||||||
|
2. If the string starts with 'bb', remove the second character.
|
||||||
|
3. If the string ends with 'aa', replace it with 'cc'.
|
||||||
|
4. If the string prefix is 'ab', replace it with 'ca'.
|
||||||
|
5. If the string ends with 'ca', remove the last character.
|
||||||
|
6. If the string contains 'bca', delete the first occurrence entirely.
|
||||||
|
7. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
|
||||||
|
8. If the string length is greater than 15, remove the middle character.
|
||||||
|
|
||||||
|
Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
|
||||||
|
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input:
|
||||||
|
- String: abbac
|
||||||
|
- Rules:
|
||||||
|
1. If the string prefix is 'ab', replace it with 'ca'.
|
||||||
|
2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
|
||||||
|
3. If the string ends with 'aa', replace it with 'cc'.
|
||||||
|
- Output: bbbacc
|
||||||
|
- Explanation:
|
||||||
|
- In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
|
||||||
|
- In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
|
||||||
|
- In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc
|
||||||
|
|
||||||
|
Transform the following string according to the above list of rules:
|
||||||
|
bcabbc
|
||||||
|
|
||||||
|
Answer: bc
|
||||||
|
Metadata: {'string': 'bcabbc', 'solution': 'bc', 'states': ['bcabbc', 'bbc', 'bc'], 'selected_rules': ["If the string suffix is 'bb', delete the last two characters.", "If the string starts with 'bb', remove the second character.", "If the string ends with 'aa', replace it with 'cc'.", "If the string prefix is 'ab', replace it with 'ca'.", "If the string ends with 'ca', remove the last character.", "If the string contains 'bca', delete the first occurrence entirely.", "If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.", 'If the string length is greater than 15, remove the middle character.']}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: Your job is to repeatedly transform a string according to a set of rules until no further transformations can be performed, or a state is repeated.
|
||||||
|
|
||||||
|
Evaluate the following rules in order, and apply the first applicable rule to the string:
|
||||||
|
1. If the string contains 'acb', replace the first occurrence with its reverse ('bca').
|
||||||
|
2. If the string length is greater than 15, remove the middle character.
|
||||||
|
3. If the string starts with 'ac', replace the first two characters with 'zz'.
|
||||||
|
4. If the string ends with 'ba', replace it with 'ab'.
|
||||||
|
5. If the string starts with 'cc', remove the first two characters.
|
||||||
|
6. If the string suffix is 'ac', replace it with 'cb'.
|
||||||
|
7. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
|
||||||
|
8. If the string prefix is 'cb', replace it with 'aa' and delete the last character.
|
||||||
|
|
||||||
|
Once you have applied a rule, repeat the process with the new string until no further transformations can be performed (i.e. the string doesn't change), or a state is repeated.
|
||||||
|
If a state is repeated, the process is terminated, and the repeated state is discarded (i.e. is not considered as the final answer) and the state before the repeated state is considered as the final answer.
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input:
|
||||||
|
- String: abbac
|
||||||
|
- Rules:
|
||||||
|
1. If the string prefix is 'ab', replace it with 'ca'.
|
||||||
|
2. If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.
|
||||||
|
3. If the string ends with 'aa', replace it with 'cc'.
|
||||||
|
- Output: bbbacc
|
||||||
|
- Explanation:
|
||||||
|
- In the first iteration, rule 1 is applied to the string abbac, resulting in cabac
|
||||||
|
- In the second interation, rule 1 doesn't apply, but rule 2 is applied to the string cabac, resulting in bbbacc
|
||||||
|
- In the third iteration, none of the rules (1, 2, 3) apply, so the process is terminated, and the final answer is bbbacc
|
||||||
|
|
||||||
|
Transform the following string according to the above list of rules:
|
||||||
|
cccaababaaacaaaccb
|
||||||
|
|
||||||
|
Answer: bbababcaaaccbc
|
||||||
|
Metadata: {'string': 'cccaababaaacaaaccb', 'solution': 'bbababcaaaccbc', 'states': ['cccaababaaacaaaccb', 'cccaababaacaaaccb', 'cccaababacaaaccb', 'cccaababcaaaccb', 'caababcaaaccb', 'bbababcaaaccbc'], 'selected_rules': ["If the string contains 'acb', replace the first occurrence with its reverse ('bca').", 'If the string length is greater than 15, remove the middle character.', "If the string starts with 'ac', replace the first two characters with 'zz'.", "If the string ends with 'ba', replace it with 'ab'.", "If the string starts with 'cc', remove the first two characters.", "If the string suffix is 'ac', replace it with 'cb'.", "If the string prefix is 'ca', replace it with 'bb' and append 'c' to the end.", "If the string prefix is 'cb', replace it with 'aa' and delete the last character."]}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
|
### string_synthesis
|
||||||
|
Generates String Synthesis exercises with configurable difficulty
|
||||||
|
|
||||||
|
Default configuration:
|
||||||
|
```python
|
||||||
|
min_initial_blocks = 0
|
||||||
|
max_initial_blocks = 5
|
||||||
|
max_iterations = 1000
|
||||||
|
size = 500
|
||||||
|
seed = 42
|
||||||
|
```
|
||||||
|
|
||||||
|
Example tasks:
|
||||||
|
````
|
||||||
|
Example 1:
|
||||||
|
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
|
||||||
|
1. One [A], one [B], and one [C] can be combined to form one {A}.
|
||||||
|
2. One [A] and one [B] can be combined to form one {C}.
|
||||||
|
3. One [B] and one [C] can be combined to form one {B}.
|
||||||
|
4. Two [C] can be combined to form one {C}.
|
||||||
|
5. One {A} and one {C} can be combined to form one (A) and one (B).
|
||||||
|
6. Two {B} can be combined to form one (C).
|
||||||
|
|
||||||
|
Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
|
||||||
|
In the case a state is repeated the answer is the state before the repetition!
|
||||||
|
|
||||||
|
The output should be the count of each block type after the rules have been applied in the order they are listed above.
|
||||||
|
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input: You have 2 [A], 3 [B], and 3 [C].
|
||||||
|
- Output: 0 0 0 2 1 0 0 0 0
|
||||||
|
- Explanation:
|
||||||
|
0. Initial state: 2 3 3 0 0 0 0 0 0
|
||||||
|
1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
|
||||||
|
2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
|
||||||
|
3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
|
||||||
|
4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0
|
||||||
|
|
||||||
|
Now, you have 5 [A], 0 [B], and 0 [C] blocks. Provide the count of each block type after applying the above rules.
|
||||||
|
|
||||||
|
Answer: 5 0 0 0 0 0 0 0 0
|
||||||
|
Metadata: {'states': [[5, 0, 0, 0, 0, 0, 0, 0, 0]], 'solution': [5, 0, 0, 0, 0, 0, 0, 0, 0]}
|
||||||
|
|
||||||
|
Example 2:
|
||||||
|
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
|
||||||
|
1. One [A], one [B], and one [C] can be combined to form one {A}.
|
||||||
|
2. One [A] and one [B] can be combined to form one {C}.
|
||||||
|
3. One [B] and one [C] can be combined to form one {B}.
|
||||||
|
4. Two [C] can be combined to form one {C}.
|
||||||
|
5. One {A} and one {C} can be combined to form one (A) and one (B).
|
||||||
|
6. Two {B} can be combined to form one (C).
|
||||||
|
|
||||||
|
Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
|
||||||
|
In the case a state is repeated the answer is the state before the repetition!
|
||||||
|
|
||||||
|
The output should be the count of each block type after the rules have been applied in the order they are listed above.
|
||||||
|
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input: You have 2 [A], 3 [B], and 3 [C].
|
||||||
|
- Output: 0 0 0 2 1 0 0 0 0
|
||||||
|
- Explanation:
|
||||||
|
0. Initial state: 2 3 3 0 0 0 0 0 0
|
||||||
|
1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
|
||||||
|
2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
|
||||||
|
3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
|
||||||
|
4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0
|
||||||
|
|
||||||
|
Now, you have 0 [A], 2 [B], and 5 [C] blocks. Provide the count of each block type after applying the above rules.
|
||||||
|
|
||||||
|
Answer: 0 0 1 0 0 1 0 0 1
|
||||||
|
Metadata: {'states': [[0, 2, 5, 0, 0, 0, 0, 0, 0], [0, 1, 4, 0, 1, 0, 0, 0, 0], [0, 0, 3, 0, 2, 0, 0, 0, 0], [0, 0, 1, 0, 2, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 1]], 'solution': [0, 0, 1, 0, 0, 1, 0, 0, 1]}
|
||||||
|
|
||||||
|
Example 3:
|
||||||
|
Question: There are nine different blocks [A] [B] [C] {A} {B} {C} (A) (B) (C)
|
||||||
|
1. One [A], one [B], and one [C] can be combined to form one {A}.
|
||||||
|
2. One [A] and one [B] can be combined to form one {C}.
|
||||||
|
3. One [B] and one [C] can be combined to form one {B}.
|
||||||
|
4. Two [C] can be combined to form one {C}.
|
||||||
|
5. One {A} and one {C} can be combined to form one (A) and one (B).
|
||||||
|
6. Two {B} can be combined to form one (C).
|
||||||
|
|
||||||
|
Given a certain number of initial blocks, your job is to cycle through the rules 1-6 above, synthesizing new blocks until no more rules can be applied, or until a state (counts of each block type) is repeated.
|
||||||
|
In the case a state is repeated the answer is the state before the repetition!
|
||||||
|
|
||||||
|
The output should be the count of each block type after the rules have been applied in the order they are listed above.
|
||||||
|
For example 1 0 3 0 2 0 0 0 1 means that you have 1 [A] 0 [B] 3 [C] 0 {A} 2 {B} 0 {C} 0 (A) 0 (B) 1 (C).
|
||||||
|
|
||||||
|
Example:
|
||||||
|
- Input: You have 2 [A], 3 [B], and 3 [C].
|
||||||
|
- Output: 0 0 0 2 1 0 0 0 0
|
||||||
|
- Explanation:
|
||||||
|
0. Initial state: 2 3 3 0 0 0 0 0 0
|
||||||
|
1. We can apply Rule 1 and obtain 1 {A}. New state: 1 2 2 1 0 0 0 0 0
|
||||||
|
2. We can apply Rule 1 again and obtain 1 {A}. New state 0 1 1 2 0 0 0 0 0
|
||||||
|
3. We can apply Rule 3 and obtain 1 {B}. New state 0 0 0 2 1 0 0 0 0
|
||||||
|
4. No more rules can be applied. The answer is 0 0 0 2 1 0 0 0 0
|
||||||
|
|
||||||
|
Now, you have 3 [A], 4 [B], and 4 [C] blocks. Provide the count of each block type after applying the above rules.
|
||||||
|
|
||||||
|
Answer: 0 0 0 3 1 0 0 0 0
|
||||||
|
Metadata: {'states': [[3, 4, 4, 0, 0, 0, 0, 0, 0], [2, 3, 3, 1, 0, 0, 0, 0, 0], [1, 2, 2, 2, 0, 0, 0, 0, 0], [0, 1, 1, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 1, 0, 0, 0, 0]], 'solution': [0, 0, 0, 3, 1, 0, 0, 0, 0]}
|
||||||
|
|
||||||
|
````
|
||||||
|
|
||||||
### sudoku
|
### sudoku
|
||||||
Generates sudoku puzzles with configurable difficulty
|
Generates sudoku puzzles with configurable difficulty
|
||||||
|
|
||||||
|
|
@ -4253,7 +4760,7 @@ Metadata: {'task_type': 'datetime_tz', 'start_time': datetime.datetime(2964, 6,
|
||||||
Example 2:
|
Example 2:
|
||||||
Question: A video call started at 09:44 and ended at 12:22. How long was the call? Answer in HH:MM.
|
Question: A video call started at 09:44 and ended at 12:22. How long was the call? Answer in HH:MM.
|
||||||
Answer: 02:38
|
Answer: 02:38
|
||||||
Metadata: {'task_type': 'time', 'start_time': datetime.datetime(2025, 2, 11, 9, 44), 'end_time': datetime.datetime(2025, 2, 11, 12, 22), 'format': '%H:%M', 'expected_format': 'HH:MM'}
|
Metadata: {'task_type': 'time', 'start_time': datetime.datetime(2025, 2, 14, 9, 44), 'end_time': datetime.datetime(2025, 2, 14, 12, 22), 'format': '%H:%M', 'expected_format': 'HH:MM'}
|
||||||
|
|
||||||
Example 3:
|
Example 3:
|
||||||
Question: Calculate the time difference between Sat Dec 22 2677 and Thu Mar 21 2678. Express the result in D days.
|
Question: Calculate the time difference between Sat Dec 22 2677 and Thu Mar 21 2678. Express the result in D days.
|
||||||
|
|
|
||||||
|
|
@ -27,6 +27,7 @@ from .rotate_matrix import RotateMatrixConfig, RotateMatrixDataset
|
||||||
from .sentence_reordering import SentenceReorderingConfig, SentenceReorderingDataset
|
from .sentence_reordering import SentenceReorderingConfig, SentenceReorderingDataset
|
||||||
from .spell_backward import SpellBackwardConfig, SpellBackwardDataset
|
from .spell_backward import SpellBackwardConfig, SpellBackwardDataset
|
||||||
from .spiral_matrix import SpiralMatrixConfig, SpiralMatrixDataset
|
from .spiral_matrix import SpiralMatrixConfig, SpiralMatrixDataset
|
||||||
|
from .string_insertion import StringInsertionConfig, StringInsertionDataset
|
||||||
from .string_manipulation import StringManipulationConfig, StringManipulationDataset
|
from .string_manipulation import StringManipulationConfig, StringManipulationDataset
|
||||||
from .string_synthesis import StringSynthesisConfig, StringSynthesisDataset
|
from .string_synthesis import StringSynthesisConfig, StringSynthesisDataset
|
||||||
from .word_ladder import WordLadderConfig, WordLadderDataset
|
from .word_ladder import WordLadderConfig, WordLadderDataset
|
||||||
|
|
|
||||||
|
|
@ -67,7 +67,7 @@ class GameOfLifeDataset(ProceduralDataset):
|
||||||
)
|
)
|
||||||
|
|
||||||
rows = [json.dumps(board[0, i].tolist(), separators=(",", ":")) for i in range(board.shape[1])]
|
rows = [json.dumps(board[0, i].tolist(), separators=(",", ":")) for i in range(board.shape[1])]
|
||||||
board_str = "[" + ", \n ".join(rows) + "]"
|
board_str = "[" + ",\n ".join(rows) + "]"
|
||||||
|
|
||||||
final_step = evolved[-1]
|
final_step = evolved[-1]
|
||||||
final_step_list = final_step.tolist()
|
final_step_list = final_step.tolist()
|
||||||
|
|
|
||||||
|
|
@ -194,15 +194,14 @@ class GraphColorDataset(ProceduralDataset):
|
||||||
solution = greedy_graph_coloring(puzzle)
|
solution = greedy_graph_coloring(puzzle)
|
||||||
|
|
||||||
edges = str(puzzle["edges"])
|
edges = str(puzzle["edges"])
|
||||||
question = f"""
|
question = f"""Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:
|
||||||
Please provide a coloring for this graph such that every vertex is not connected to a vertex of the same color. The graph has these properties:
|
|
||||||
|
|
||||||
Vertices: {puzzle["vertices"]}
|
Vertices: {puzzle["vertices"]}
|
||||||
Edges: {edges}
|
Edges: {edges}
|
||||||
Possible colors: {puzzle["color_options"]}
|
Possible colors: {puzzle["color_options"]}
|
||||||
|
|
||||||
Return your solution as a JSON map of verteces to colors. (For example: {{0: 1, 1: 2, 2: 3}})
|
Return your solution as a JSON map of verteces to colors. (For example: {{0: 1, 1: 2, 2: 3}})
|
||||||
"""
|
"""
|
||||||
|
|
||||||
return {
|
return {
|
||||||
"question": question,
|
"question": question,
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue