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3138. 同位字符串连接的最小长度

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题目描述

https://leetcode.cn/problems/minimum-length-of-anagram-concatenation/description/?envType=daily-question&envId=2024-12-20

给你一个字符串 s,已知它是某个字符串 t 的若干个同位字符串的串联。

返回字符串 t 的最小可能长度。

同位字符串是由重新排列字母形成的字符串。例如,"aab"、"aba" 和 "baa" 都是 "aab" 的同位字符串。

示例 1:

输入:s = "abba"

输出:2

解释:

t 的一个可能的字符串是 "ba"。

示例 2:

输入:s = "cdef"

输出:4

解释:

t 的一个可能的字符串是 "cdef",注意 t 可以等于 s。

思路

由于题意很容易联想到这道题要进行计数(Counter),我们需要找到每个字符串的最小子串。例如 abba 的最小子串是 abcdefcdef

我们从长度 1(即单个字符)开始遍历,通过切片获取当前子串。

最开始对原始字符串进行 Counter,得到字符数量字典。接下来只需判断当前子串中某个字符的计数乘以 n/k 是否等于原始字符串的计数(即当前子串乘以 x 倍是否等于原始字符串)。

Since the problem naturally suggests using a counting method (Counter), we need to find the minimum substring for each string. For example, for abba, the result is ab; for cdef, it's cdef. We iterate from length 1 (a single character) onwards, slicing the string to get the current substring.

Initially, we compute the character count for the original string using Counter, which gives us a dictionary of character frequencies. Next, we only need to check if the count of each character in the current substring multiplied by n/k equals the count in the original string (i.e., whether repeating the current substring x times equals the original string).

代码

import collections
class Solution:
    def minAnagramLength(self, s: str) -> int:
        def check(k: int) -> bool:
            # 遍历字符串 s,每次取长度为 k 的子串
            # Iterate over the string `s`, taking substrings of length `k`
            for i in range(0, n, k):
                # 统计每个字符出现的次数
                # Count the occurrences of each character in the current substring
                cnt1 = collections.Counter(s[i: i + k])
                for c, v in cnt.items():
                    # 如果每个字符出现的次数乘以 n/k != cnt[] return False
                    # If the count of any character multiplied by (n // k) != the original count, return False
                    if cnt1[c] * (n // k) != v:
                        return False
            return True

        cnt = collections.Counter(s)
        n = len(s)
        for i in range(1, n+1):
            if n % i == 0 and check(i):
                return i

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