Given a string s and an integer k, partition s into k substrings such that the letter changes needed to make each substring a semi-palindrome are minimized.
Return the minimum number of letter changes required.
A semi-palindrome is a special type of string that can be divided into palindromes based on a repeating pattern. To check if a string is a semi-palindrome:
d of the string's length. d can range from 1 up to, but not including, the string's length. For a string of length 1, it does not have a valid divisor as per this definition, since the only divisor is its length, which is not allowed.d, divide the string into groups where each group contains characters from the string that follow a repeating pattern of length d. Specifically, the first group consists of characters at positions 1, 1 + d, 1 + 2d, and so on; the second group includes characters at positions 2, 2 + d, 2 + 2d, etc.Consider the string "abcabc":
"abcabc" is 6. Valid divisors are 1, 2, and 3.d = 1: The entire string "abcabc" forms one group. Not a palindrome.d = 2:
1, 3, 5): "acb"2, 4, 6): "bac"d = 3:
1, 4): "aa"2, 5): "bb"3, 6): "cc""abcabc" is a semi-palindrome.
Example 1:
Input: s = "abcac", k = 2
Output: 1
Explanation: Divide s into "ab" and "cac". "cac" is already semi-palindrome. Change "ab" to "aa", it becomes semi-palindrome with d = 1.
Example 2:
Input: s = "abcdef", k = 2
Output: 2
Explanation: Divide s into substrings "abc" and "def". Each needs one change to become semi-palindrome.
Example 3:
Input: s = "aabbaa", k = 3
Output: 0
Explanation: Divide s into substrings "aa", "bb" and "aa". All are already semi-palindromes.
Constraints:
2 <= s.length <= 2001 <= k <= s.length / 2s contains only lowercase English letters.Use dynamic programming to solve this problem by calculating the minimum changes needed to convert each substring into a semi-palindrome. This involves breaking the problem into subproblems where each subproblem calculates the minimum changes required for a semi-palindrome for every substring division at different indices.
The C solution defines a helper function palindrome_changes to calculate the number of changes needed to make a substring a palindrome. The main function minChangesToMakeKPalindromes uses dynamic programming to fill out dp[i][j] which represents the minimum changes needed to create j semi-palindromes from the first i characters. It uses a double loop to ensure that every division is considered, and previous calculated results are reused to optimize the solution.
C++
Time Complexity: O(n^3) due to triple nested loop for each substring division
Space Complexity: O(n*k) for the dp array
This approach involves a preprocessing step to approximate the number of changes needed to convert each possible substring into a semi-palindrome. Using a greedy strategy, we then try to partition the string into k substrings while minimizing changes for each partition step.
The Java solution uses a greedy approach complemented by a preprocessing step that calculates changes required for each potential substring to become a semi-palindrome. The greedy part tries various partitions and adjusts for the minimum necessary changes using preprocessed values to decide the optimal split points.
Python
Time Complexity: O(n^2 * k) simplified by preprocessing
| Approach | Complexity |
|---|---|
| Dynamic Programming | Time Complexity: O(n^3) due to triple nested loop for each substring division |
| Greedy with Preprocessing | Time Complexity: O(n^2 * k) simplified by preprocessing |
Longest Palindromic Substring - Python - Leetcode 5 • NeetCode • 629,150 views views
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