init-commit

internbootcamp/bootcamp/dmahmoudandehabandanotherarrayconstructiontask/dmahmoudandehabandanotherarrayconstructiontask.py

@@ -0,0 +1,212 @@
+"""# 
+
+### 谜题描述
+Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
+
+  * b is lexicographically greater than or equal to a. 
+  * bi ≥ 2. 
+  * b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z. 
+
+
+
+Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
+
+An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
+
+Input
+
+The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
+
+The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
+
+Output
+
+Output n space-separated integers, the i-th of them representing bi.
+
+Examples
+
+Input
+
+5
+2 3 5 4 13
+
+
+Output
+
+2 3 5 7 11 
+
+Input
+
+3
+10 3 7
+
+
+Output
+
+10 3 7 
+
+Note
+
+Note that in the second sample, the array is already pairwise coprime so we printed it.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+MAX_NUM = 2000000
+prime_str = ('2      3      5      7     11     13     17     19     23     29 '
+        +   '31     37     41     43     47     53     59     61     67     71 '
+        +   '73     79     83     89     97    101    103    107    109    113 '
+        +  '127    131    137    139    149    151    157    163    167    173 '
+        +  '179    181    191    193    197    199    211    223    227    229 '
+        +  '233    239    241    251    257    263    269    271    277    281 '
+        +  '283    293    307    311    313    317 '
+)
+prime_list = [int(p) for p in prime_str.split()]
+used = [False] * MAX_NUM
+n = input()
+a = list(map(int,raw_input().split()))
+def record(x):
+    t = []
+    for p in prime_list:
+        if x % p == 0:
+            while x % p == 0:
+                x = x // p
+            t.append(p)
+            if x == 1:
+                break
+    if x != 1:
+        t.append(x)
+
+    for ti in t:
+        for i in range(ti, MAX_NUM, ti):
+            used[i] = True
+b = []
+for ai in a:
+    if not used[ai]:
+        b.append(ai)
+        record(ai)
+    else:
+        temp = ai + 1
+        while used[temp]:
+            temp += 1
+        b.append(temp)
+        record(temp)
+        break
+temp = 2
+while len(b) < len(a):
+    while used[temp]:
+        temp += 1
+    b.append(temp)
+    record(temp)
+print(' '.join(str(x) for x in b))
+```
+
+
+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
+from bootcamp import Basebootcamp
+
+class Dmahmoudandehabandanotherarrayconstructiontaskbootcamp(Basebootcamp):
+    def __init__(self, max_n=10, max_ai=100):
+        self.max_n = max_n
+        self.max_ai = max_ai
+
+    @staticmethod
+    def generate_b(a):
+        MAX_NUM = 2000000
+        prime_str = ('2 3 5 7 11 13 17 19 23 29 '
+                     '31 37 41 43 47 53 59 61 67 71 '
+                     '73 79 83 89 97 101 103 107 109 113 '
+                     '127 131 137 139 149 151 157 163 167 173 '
+                     '179 181 191 193 197 199 211 223 227 229 '
+                     '233 239 241 251 257 263 269 271 277 281 '
+                     '283 293 307 311 313 317')
+        prime_list = [int(p) for p in prime_str.split()]
+        used = [False] * (MAX_NUM + 1)
+        n = len(a)
+        b = []
+
+        def record(x):
+            t = []
+            tmp_x = x
+            for p in prime_list:
+                if tmp_x % p == 0:
+                    while tmp_x % p == 0:
+                        tmp_x = tmp_x // p
+                    t.append(p)
+                    if tmp_x == 1:
+                        break
+            if tmp_x != 1:
+                t.append(tmp_x)
+            for ti in t:
+                if ti > MAX_NUM:
+                    continue
+                for i in range(ti, MAX_NUM + 1, ti):
+                    used[i] = True
+
+        for ai in a:
+            if ai <= MAX_NUM and not used[ai]:
+                b.append(ai)
+                record(ai)
+            else:
+                temp = ai + 1
+                while temp <= MAX_NUM and used[temp]:
+                    temp += 1
+                if temp > MAX_NUM:
+                    temp = ai + 1
+                b.append(temp)
+                record(temp)
+                break  # Break after first replacement
+        
+        temp = 2
+        while len(b) < len(a):
+            while temp <= MAX_NUM and used[temp]:
+                temp += 1
+            if temp > MAX_NUM:
+                break
+            b.append(temp)
+            record(temp)
+            temp += 1
+        
+        return b
+
+    def case_generator(self):
+        n = random.randint(1, self.max_n)
+        a = [random.randint(2, self.max_ai) for _ in range(n)]
+        expected_b = self.generate_b(a)
+        return {
+            'n': n,
+            'a': a,
+            'expected_b': expected_b
+        }
+
+    @staticmethod
+    def prompt_func(question_case):
+        a_str = ' '.join(map(str, question_case['a']))
+        return (
+            f"You are given an array a of {question_case['n']} integers. Your task is to construct the lexicographically smallest array b that meets the following conditions:\n\n"
+            "1. The array b is lexicographically greater than or equal to a.\n"
+            "2. Each element in b is at least 2.\n"
+            "3. All elements in b are pairwise coprime (their GCD must be 1).\n\n"
+            f"Input array a: {a_str}\n\n"
+            "Output the space-separated elements of array b. Enclose your answer within [answer] and [/answer] tags."
+        )
+
+    @staticmethod
+    def extract_output(output):
+        import re
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        last_answer = matches[-1].strip()
+        try:
+            return list(map(int, last_answer.split()))
+        except:
+            return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        expected_b = identity.get('expected_b', [])
+        return solution == expected_b