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Palindrome Partitioning II

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the minimum number of cuts needed to partition a string such that every substring of the partition is a palindrome. Given a string s, partition s such that every substring of the partition is a palindrome. Return the minimum cuts needed for a palindrome partitioning of s.

Example 1
    
      
  • Input: s = "aab"
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  • Output: 1
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  • Explanation: 
    • The string "aab" can be partitioned as ["aa", "b"]. 
    • "aa" is a palindrome and "b" is a palindrome. 
    • Only 1 cut is needed between "aa" and "b".
    • Therefore, minimum cuts needed = 1.
    •
Example 2
    
      
  • Input: s = "abcde"
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  • Output: 4
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  • Explanation: 
    • The string "abcde" has no palindromic substrings of length > 1. 
    • Each character must be separated: ["a", "b", "c", "d", "e"]. 
    • This requires 4 cuts to separate all characters. 
    • Therefore, minimum cuts needed = 4.
    •
Constraints
    
      
  • 1 ≤ s.length ≤ 2000
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  • s consists of lowercase English letters only
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  • Time Complexity: O(n^2)
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  • Space Complexity: O(n^2)
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StringsDynamic Programming KPMGPhillips
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Hint
Solution

Solution Hints

    
      
  • Use dynamic programming to precompute palindrome information
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  • Create a 2D boolean array to store if substring s[i..j] is palindrome
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  • Use another DP array to store minimum cuts needed for substring s[0..i]
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  • For each position, try all possible cuts and find minimum
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  • If s[0..i] is already palindrome, no cuts needed
    •

Steps to solve by this approach:

 Step 1: Create a 2D boolean array to precompute palindrome information for all substrings.
 Step 2: Fill the palindrome table using dynamic programming - single characters are palindromes.
 Step 3: For substrings of length 2 or more, check if first and last characters match and inner substring is palindrome.
 Step 4: Create a DP array to store minimum cuts needed for each prefix of the string.
 Step 5: For each position, if the entire prefix is palindrome, no cuts needed.
 Step 6: Otherwise, try all possible cut positions and find the minimum cuts required.
 Step 7: Return the minimum cuts needed for the entire string.

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