mirror of
https://github.com/InternLM/InternBootcamp.git
synced 2026-04-19 12:58:04 +00:00
155 lines
4.6 KiB
Python
Executable file
155 lines
4.6 KiB
Python
Executable file
"""#
|
|
|
|
### 谜题描述
|
|
Arkady decides to observe a river for n consecutive days. The river's water level on each day is equal to some real value.
|
|
|
|
Arkady goes to the riverside each day and makes a mark on the side of the channel at the height of the water level, but if it coincides with a mark made before, no new mark is created. The water does not wash the marks away. Arkady writes down the number of marks strictly above the water level each day, on the i-th day this value is equal to mi.
|
|
|
|
Define di as the number of marks strictly under the water level on the i-th day. You are to find out the minimum possible sum of di over all days. There are no marks on the channel before the first day.
|
|
|
|
Input
|
|
|
|
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of days.
|
|
|
|
The second line contains n space-separated integers m1, m2, ..., mn (0 ≤ mi < i) — the number of marks strictly above the water on each day.
|
|
|
|
Output
|
|
|
|
Output one single integer — the minimum possible sum of the number of marks strictly below the water level among all days.
|
|
|
|
Examples
|
|
|
|
Input
|
|
|
|
6
|
|
0 1 0 3 0 2
|
|
|
|
|
|
Output
|
|
|
|
6
|
|
|
|
|
|
Input
|
|
|
|
5
|
|
0 1 2 1 2
|
|
|
|
|
|
Output
|
|
|
|
1
|
|
|
|
|
|
Input
|
|
|
|
5
|
|
0 1 1 2 2
|
|
|
|
|
|
Output
|
|
|
|
0
|
|
|
|
Note
|
|
|
|
In the first example, the following figure shows an optimal case.
|
|
|
|
<image>
|
|
|
|
Note that on day 3, a new mark should be created because if not, there cannot be 3 marks above water on day 4. The total number of marks underwater is 0 + 0 + 2 + 0 + 3 + 1 = 6.
|
|
|
|
In the second example, the following figure shows an optimal case.
|
|
|
|
<image>
|
|
|
|
Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
|
|
```python
|
|
n = int(raw_input())
|
|
nums = list(map(int,raw_input().split()))
|
|
cur = 1
|
|
ans = 0
|
|
arr = [0 for x in range(n)]
|
|
for i in range(1,n):
|
|
arr[i] = max(nums[i],arr[i-1])
|
|
for i in range(n-1,-1,-1):
|
|
cur = max(cur-1,arr[i])
|
|
ans += cur-nums[i]
|
|
print ans
|
|
```
|
|
|
|
|
|
请完成上述谜题的训练场环境类实现，包括所有必要的方法。
|
|
"""
|
|
|
|
from bootcamp import Basebootcamp
|
|
import random
|
|
import re
|
|
from typing import Dict, Any
|
|
|
|
from bootcamp import Basebootcamp
|
|
|
|
class Criversidecuriobootcamp(Basebootcamp):
|
|
def __init__(self, **params):
|
|
self.n = params.get('n', 5) # Default to 5 days if not provided
|
|
# Ensure that 'm' is provided and has the correct length
|
|
self.m = params.get('m', None)
|
|
if self.m is None:
|
|
self.m = [0] * self.n # Default to all zeros if not provided
|
|
else:
|
|
# Ensure that 'm' has the correct length
|
|
if len(self.m) != self.n:
|
|
raise ValueError("Length of 'm' must be equal to 'n'")
|
|
# Additional parameters can be added if needed
|
|
|
|
def case_generator(self) -> Dict[str, Any]:
|
|
n = random.randint(1, 100) # Random number of days between 1 and 100
|
|
m = []
|
|
m.append(0) # On day 1, m[0] must be 0
|
|
for i in range(1, n):
|
|
mi = random.randint(0, i-1) # Valid values for m[i] are 0 <= mi < i
|
|
m.append(mi)
|
|
|
|
# Now compute the correct answer using the reference solution logic
|
|
arr = [0] * n
|
|
for i in range(1, n):
|
|
arr[i] = max(m[i], arr[i-1])
|
|
cur = 1
|
|
correct_ans = 0
|
|
for i in range(n-1, -1, -1):
|
|
cur = max(cur - 1, arr[i])
|
|
correct_ans += cur - m[i]
|
|
|
|
return {
|
|
'n': n,
|
|
'm': m,
|
|
'correct_ans': correct_ans
|
|
}
|
|
|
|
@staticmethod
|
|
def prompt_func(question_case: Dict[str, Any]) -> str:
|
|
n = question_case['n']
|
|
m = question_case['m']
|
|
# Create a string representation of the problem
|
|
prompt = f"Arkady观察了一条河流{n}天。每天他记录了严格高于水位的标记数，分别为：{m}。" \
|
|
f"现在，请你计算每天严格低于水位的标记数的最小总和。" \
|
|
f"请将答案放在[answer]标签中，格式为：[answer]数字[/answer]"
|
|
return prompt
|
|
|
|
@staticmethod
|
|
def extract_output(output: str) -> int:
|
|
# Extract the last answer in the format [answer]x[/answer]
|
|
matches = re.findall(r'\[answer\](.*?)\[\/answer\]', output, re.DOTALL)
|
|
if not matches:
|
|
return None
|
|
ans_str = matches[-1].strip()
|
|
# Check if the extracted string is a valid integer
|
|
if not ans_str.isdigit():
|
|
return None
|
|
return int(ans_str)
|
|
|
|
@classmethod
|
|
def _verify_correction(cls, solution: int, identity: Dict[str, Any]) -> bool:
|
|
# Compare the extracted solution with the correct answer
|
|
correct_ans = identity['correct_ans']
|
|
return solution == correct_ans
|