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‎Problemset/1278-Palindrome Partitioning III/README.md

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# 1278. Palindrome Partitioning III
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You are given a string `s` containing lowercase letters and an integer `k`. You need to :
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* First, change some characters of `s` to other lowercase English letters.
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* Then divide `s` into `k` non-empty disjoint substrings such that each substring is a palindrome.
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Return *the minimal number of characters that you need to change to divide the string*.
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#### Example 1:
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<pre>
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<strong>Input:</strong> s = "abc", k = 2
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> You can split the string into "ab" and "c", and change 1 character in "ab" to make it palindrome.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> s = "aabbc", k = 3
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> You can split the string into "aa", "bb" and "c", all of them are palindrome.
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</pre>
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#### Example 3:
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<pre>
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<strong>Input:</strong> s = "leetcode", k = 8
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<strong>Output:</strong> 0
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</pre>
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#### Constraints:
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* `1 <= k <= s.length <= 100`.
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* `s` only contains lowercase English letters.
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## Solutions (Python)
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### 1. Solution
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```Python
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from functools import cache
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class Solution:
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def palindromePartition(self, s: str, k: int) -> int:
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@cache
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def palindromeChange(i: int, j: int) -> int:
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if i >= j:
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return 0
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return palindromeChange(i + 1, j - 1) + (s[i] != s[j])
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@cache
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def subPartition(i: int, k: int) -> int:
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if k == 1:
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return palindromeChange(i, len(s) - 1)
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return min(palindromeChange(i, j) + subPartition(j + 1, k - 1) for j in range(i, len(s) - k + 1))
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return subPartition(0, k)
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```

‎Problemset/1278-Palindrome Partitioning III/README_CN.md

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# 1278. 分割回文串 III
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给你一个由小写字母组成的字符串 `s`，和一个整数 `k`。
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请你按下面的要求分割字符串：
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* 首先，你可以将 `s` 中的部分字符修改为其他的小写英文字母。
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* 接着，你需要把 `s` 分割成 `k` 个非空且不相交的子串，并且每个子串都是回文串。
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请返回以这种方式分割字符串所需修改的最少字符数。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> s = "abc", k = 2
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<strong>输出:</strong> 1
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<strong>解释:</strong> 你可以把字符串分割成 "ab" 和 "c"，并修改 "ab" 中的 1 个字符，将它变成回文串。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> s = "aabbc", k = 3
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<strong>输出:</strong> 0
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<strong>解释:</strong> 你可以把字符串分割成 "aa"、"bb" 和 "c"，它们都是回文串。
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</pre>
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#### 示例 3:
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<pre>
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<strong>输入:</strong> s = "leetcode", k = 8
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<strong>输出:</strong> 0
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</pre>
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#### 提示:
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* `1 <= k <= s.length <= 100`
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* `s` 中只含有小写英文字母。
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## 题解 (Python)
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### 1. 题解
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```Python
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from functools import cache
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class Solution:
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def palindromePartition(self, s: str, k: int) -> int:
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@cache
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def palindromeChange(i: int, j: int) -> int:
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if i >= j:
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return 0
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return palindromeChange(i + 1, j - 1) + (s[i] != s[j])
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@cache
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def subPartition(i: int, k: int) -> int:
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if k == 1:
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return palindromeChange(i, len(s) - 1)
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return min(palindromeChange(i, j) + subPartition(j + 1, k - 1) for j in range(i, len(s) - k + 1))
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return subPartition(0, k)
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```

‎Problemset/1278-Palindrome Partitioning III/Solution.py

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from functools import cache
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class Solution:
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def palindromePartition(self, s: str, k: int) -> int:
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@cache
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def palindromeChange(i: int, j: int) -> int:
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if i >= j:
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return 0
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return palindromeChange(i + 1, j - 1) + (s[i] != s[j])
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@cache
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def subPartition(i: int, k: int) -> int:
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if k == 1:
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return palindromeChange(i, len(s) - 1)
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return min(palindromeChange(i, j) + subPartition(j + 1, k - 1) for j in range(i, len(s) - k + 1))
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return subPartition(0, k)

‎README.md

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[1275][1275l]|[Find Winner on a Tic Tac Toe Game][1275] |![rs]
840840
[1276][1276l]|[Number of Burgers with No Waste of Ingredients][1276] |![py]&nbsp;&nbsp;![rs]
841841
[1277][1277l]|[Count Square Submatrices with All Ones][1277] |![rs]
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[1278][1278l]|[Palindrome Partitioning III][1278] |![py]
842843
[1281][1281l]|[Subtract the Product and Sum of Digits of an Integer][1281] |![rs]
843844
[1282][1282l]|[Group the People Given the Group Size They Belong To][1282] |![rs]
844845
[1283][1283l]|[Find the Smallest Divisor Given a Threshold][1283] |![py]
@@ -2501,6 +2502,7 @@
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[1275]:Problemset/1275-Find%20Winner%20on%20a%20Tic%20Tac%20Toe%20Game/README.md#1275-find-winner-on-a-tic-tac-toe-game
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[1276]:Problemset/1276-Number%20of%20Burgers%20with%20No%20Waste%20of%20Ingredients/README.md#1276-number-of-burgers-with-no-waste-of-ingredients
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[1277]:Problemset/1277-Count%20Square%20Submatrices%20with%20All%20Ones/README.md#1277-count-square-submatrices-with-all-ones
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[1278]:Problemset/1278-Palindrome%20Partitioning%20III/README.md#1278-palindrome-partitioning-iii
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[1281]:Problemset/1281-Subtract%20the%20Product%20and%20Sum%20of%20Digits%20of%20an%20Integer/README.md#1281-subtract-the-product-and-sum-of-digits-of-an-integer
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[1282]:Problemset/1282-Group%20the%20People%20Given%20the%20Group%20Size%20They%20Belong%20To/README.md#1282-group-the-people-given-the-group-size-they-belong-to
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[1283]:Problemset/1283-Find%20the%20Smallest%20Divisor%20Given%20a%20Threshold/README.md#1283-find-the-smallest-divisor-given-a-threshold
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[1275l]:https://leetcode.com/problems/find-winner-on-a-tic-tac-toe-game/
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[1276l]:https://leetcode.com/problems/number-of-burgers-with-no-waste-of-ingredients/
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[1277l]:https://leetcode.com/problems/count-square-submatrices-with-all-ones/
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[1278l]:https://leetcode.com/problems/palindrome-partitioning-iii/
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[1281l]:https://leetcode.com/problems/subtract-the-product-and-sum-of-digits-of-an-integer/
41614164
[1282l]:https://leetcode.com/problems/group-the-people-given-the-group-size-they-belong-to/
41624165
[1283l]:https://leetcode.com/problems/find-the-smallest-divisor-given-a-threshold/

‎README_CN.md

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[1275][1275l]|[找出井字棋的获胜者][1275] |![rs]
840840
[1276][1276l]|[不浪费原料的汉堡制作方案][1276] |![py]&nbsp;&nbsp;![rs]
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[1277][1277l]|[统计全为 1 的正方形子矩阵][1277] |![rs]
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[1278][1278l]|[分割回文串 III][1278] |![py]
842843
[1281][1281l]|[整数的各位积和之差][1281] |![rs]
843844
[1282][1282l]|[用户分组][1282] |![rs]
844845
[1283][1283l]|[使结果不超过阈值的最小除数][1283] |![py]
@@ -2501,6 +2502,7 @@
25012502
[1275]:Problemset/1275-Find%20Winner%20on%20a%20Tic%20Tac%20Toe%20Game/README_CN.md#1275-找出井字棋的获胜者
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[1276]:Problemset/1276-Number%20of%20Burgers%20with%20No%20Waste%20of%20Ingredients/README_CN.md#1276-不浪费原料的汉堡制作方案
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[1277]:Problemset/1277-Count%20Square%20Submatrices%20with%20All%20Ones/README_CN.md#1277-统计全为-1-的正方形子矩阵
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[1278]:Problemset/1278-Palindrome%20Partitioning%20III/README_CN.md#1278-分割回文串-iii
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[1281]:Problemset/1281-Subtract%20the%20Product%20and%20Sum%20of%20Digits%20of%20an%20Integer/README_CN.md#1281-整数的各位积和之差
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[1282]:Problemset/1282-Group%20the%20People%20Given%20the%20Group%20Size%20They%20Belong%20To/README_CN.md#1282-用户分组
25062508
[1283]:Problemset/1283-Find%20the%20Smallest%20Divisor%20Given%20a%20Threshold/README_CN.md#1283-使结果不超过阈值的最小除数
@@ -4157,6 +4159,7 @@
41574159
[1275l]:https://leetcode.cn/problems/find-winner-on-a-tic-tac-toe-game/
41584160
[1276l]:https://leetcode.cn/problems/number-of-burgers-with-no-waste-of-ingredients/
41594161
[1277l]:https://leetcode.cn/problems/count-square-submatrices-with-all-ones/
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[1278l]:https://leetcode.cn/problems/palindrome-partitioning-iii/
41604163
[1281l]:https://leetcode.cn/problems/subtract-the-product-and-sum-of-digits-of-an-integer/
41614164
[1282l]:https://leetcode.cn/problems/group-the-people-given-the-group-size-they-belong-to/
41624165
[1283l]:https://leetcode.cn/problems/find-the-smallest-divisor-given-a-threshold/

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