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270 lines
7.4 KiB
Python
Executable file
270 lines
7.4 KiB
Python
Executable file
"""#
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### 谜题描述
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Your classmate, whom you do not like because he is boring, but whom you respect for his intellect, has two strings: s of length n and t of length m.
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A sequence p_1, p_2, …, p_m, where 1 ≤ p_1 < p_2 < … < p_m ≤ n, is called beautiful, if s_{p_i} = t_i for all i from 1 to m. The width of a sequence is defined as max_{1 ≤ i < m} \left(p_{i + 1} - p_i\right).
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Please help your classmate to identify the beautiful sequence with the maximum width. Your classmate promised you that for the given strings s and t there is at least one beautiful sequence.
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Input
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The first input line contains two integers n and m (2 ≤ m ≤ n ≤ 2 ⋅ 10^5) — the lengths of the strings s and t.
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The following line contains a single string s of length n, consisting of lowercase letters of the Latin alphabet.
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The last line contains a single string t of length m, consisting of lowercase letters of the Latin alphabet.
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It is guaranteed that there is at least one beautiful sequence for the given strings.
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Output
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Output one integer — the maximum width of a beautiful sequence.
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Examples
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Input
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5 3
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abbbc
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abc
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Output
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3
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Input
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5 2
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aaaaa
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aa
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Output
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4
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Input
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5 5
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abcdf
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abcdf
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Output
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1
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Input
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2 2
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ab
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ab
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Output
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1
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Note
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In the first example there are two beautiful sequences of width 3: they are \{1, 2, 5\} and \{1, 4, 5\}.
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In the second example the beautiful sequence with the maximum width is \{1, 5\}.
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In the third example there is exactly one beautiful sequence — it is \{1, 2, 3, 4, 5\}.
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In the fourth example there is exactly one beautiful sequence — it is \{1, 2\}.
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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from collections import Counter
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import math
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if __name__==\"__main__\":
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n,m= map(int,raw_input().split(\" \"))
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s1=raw_input().strip()
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s2=raw_input().strip()
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ans1=[0 for k in s2]
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ans2=[0 for k in s2]
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b2=0
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for i in range(0,len(s1)):
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if s1[i]==s2[b2]:
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ans1[b2]=i
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b2+=1
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if b2==len(s2):
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break
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b2=len(s2)-1
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for i in range(len(s1)-1,-1,-1):
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if s1[i]==s2[b2]:
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ans2[b2]=i
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b2-=1
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if b2<0:
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break
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ans=0
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for i in range(0,len(s2)-1):
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ans=max(ans,ans2[i+1]-ans1[i])
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print ans
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```
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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。
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"""
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from bootcamp import Basebootcamp
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import random
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from bootcamp import Basebootcamp
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class Cmaximumwidthbootcamp(Basebootcamp):
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def __init__(self, min_n=2, max_n=20, min_m=2, max_m=15):
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self.params = {
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'min_n': min_n,
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'max_n': max_n,
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'min_m': min_m,
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'max_m': max_m,
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}
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def case_generator(self):
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max_retry = 5
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for _ in range(max_retry):
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try:
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m = random.randint(
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max(self.params['min_m'], 2),
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min(self.params['max_m'], self.params['max_n'])
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)
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n = random.randint(
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max(m, self.params['min_n']),
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self.params['max_n']
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)
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# 生成策略优化
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gen_strategy = random.choices(
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['direct_insert', 'reverse_insert', 'balanced'],
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weights=[0.3, 0.3, 0.4],
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k=1
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)[0]
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t = []
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s = []
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# 生成逻辑优化
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if gen_strategy == 'direct_insert':
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t = [chr(97 + random.randint(0, 25)) for _ in range(m)]
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ptr = 0
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for i in range(m):
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gap = random.randint(0, n - m - ptr) if i < m-1 else 0
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s += [chr(97 + random.randint(0, 25)) for _ in range(gap)]
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s.append(t[i])
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ptr += gap + 1
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s += [chr(97 + random.randint(0, 25)) for _ in range(n - len(s))]
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elif gen_strategy == 'reverse_insert':
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t = [chr(97 + random.randint(0, 25)) for _ in range(m)]
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remaining_space = n - m
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gaps = [random.randint(0, remaining_space) for _ in range(m-1)]
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total_gaps = sum(gaps)
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if total_gaps > remaining_space:
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scale = remaining_space / total_gaps
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gaps = [int(g*scale) for g in gaps]
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for i in range(m):
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s.append(t[i])
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if i < m-1:
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s += [chr(97 + random.randint(0,25)) for _ in range(gaps[i])]
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s += [chr(97 + random.randint(0,25)) for _ in range(n - len(s))]
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else: # balanced strategy
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t = [chr(97 + random.randint(0, 25)) for _ in range(m)]
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pos = sorted(random.sample(range(n), m))
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s = [chr(97 + random.randint(0,25)) for _ in range(n)]
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for i,p in enumerate(pos):
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s[p] = t[i]
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s = ''.join(s[:n]) # 长度强制对齐
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t = ''.join(t)
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# 验证子序列
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def is_subsequence(s, t):
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it = iter(s)
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return all(c in it for c in t)
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if not is_subsequence(s, t):
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continue # 重试
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# 计算正确答案
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ans1 = []
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ptr = 0
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for c in t:
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while ptr < len(s) and s[ptr] != c:
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ptr += 1
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ans1.append(ptr)
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ptr += 1
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ans2 = []
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ptr = len(s) - 1
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for c in reversed(t):
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while ptr >= 0 and s[ptr] != c:
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ptr -= 1
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ans2.append(ptr)
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ptr -= 1
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ans2.reverse()
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max_width = max(ans2[i+1] - ans1[i] for i in range(m-1))
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return {
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'n': n,
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'm': m,
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's': s,
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't': t,
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'correct_answer': max_width
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}
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except Exception as e:
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continue
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raise RuntimeError("生成有效案例失败")
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@staticmethod
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def prompt_func(question_case) -> str:
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return f"""请解决以下字符串序列问题：
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输入格式：
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第一行：n m（2 ≤ m ≤ n）
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第二行：s（长度n）
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第三行：t（长度m）
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问题描述：
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寻找s中满足s[p_i] = t[i]的严格递增下标序列p_1 < p_2 < ... < p_m。
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定义序列宽度为相邻下标差的最大值，即max(p_{{i+1}} - p_i)。
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求所有可能序列中的最大宽度。
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输入数据：
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{question_case['n']} {question_case['m']}
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{question_case['s']}
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{question_case['t']}
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将答案用[answer]标签包裹，例如：[answer]3[/answer]"""
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@staticmethod
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def extract_output(output):
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import re
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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return int(matches[-1].strip()) if matches else None
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@classmethod
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def _verify_correction(cls, solution, identity):
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return solution == identity['correct_answer']
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