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Palindrome Partitioning II

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to find the minimum number of cuts needed to partition a string such that every substring of the partition is a palindrome. A palindrome is a string that reads the same backward as forward.

Example 1
    
  
  • Input: s = "aab"
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  • Output: 1
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  • Explanation: We need to partition the string "aab" into palindromic substrings. One possible partition is ["aa", "b"], which requires 1 cut. Both "aa" and "b" are palindromes.
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Example 2
    
  
  • Input: s = "abccbc"
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  • Output: 2
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  • Explanation: We need to partition the string "abccbc" into palindromic substrings. One possible partition is ["a", "b", "ccbc"], which requires 2 cuts. All substrings "a", "b", and "ccbc" are palindromes.
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Constraints
    
  
  • 1 ≤ s.length ≤ 2000
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  • s consists of lowercase English letters only
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  • Time Complexity: O(n²) where n is the length of the string
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  • Space Complexity: O(n²)
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming approach to solve this problem
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  • Create a 2D boolean array to keep track of whether substring s[i...j] is a palindrome
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  • Create a 1D array to store the minimum cuts needed for substring s[0...i]
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  • For each position i, check all possible substrings ending at i
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  • If a substring s[j...i] is a palindrome, update the minimum cuts
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  • Be careful of the base case where the entire string is already a palindrome
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Steps to solve by this approach:

 Step 1: Create a 2D boolean array isPalindrome[n][n] to identify if substring s[start...end] is a palindrome.

 Step 2: Create a 1D array minCuts[n] to store the minimum cuts needed for substring s[0...i]. Initialize each minCuts[i] with i.

 Step 3: Fill the isPalindrome table by checking all possible substrings.

 Step 4: For each end position, check all possible start positions to see if s[start...end] is a palindrome.

 Step 5: If s[start...end] is a palindrome and starts from index 0, no cuts needed up to end index.

 Step 6: If s[start...end] is a palindrome but doesn't start from index 0, calculate minimum cuts as minCuts[start-1] + 1.

 Step 7: The final answer is minCuts[n-1], representing the minimum cuts for the whole string.

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