How to split a string into as few palindromes as possible?

Question

This is an interview question: \"You\'re given a string, and you want to split it into as few strings as possible such that each string is a palindrome\". (I guess a one char st

Answer 1

First find all the palindromes in the string such that L[i][j] represents the length of j-th longest palindrome that ends at S[i]. Lets say S is the input string. This could be done in O(N^2) time by first considering length1 palindromes then then length 2 palindromes and so on. Finding Length i palindromes after you know all length i-2 palindromes is the matter of a single character comparison.

This is a dynamic programming problem after that. Let A[i] represent the smallest number of palindrome that Substring(S,0,i-1) can be decomposed into.

A[i+1] = min_{0 <= j < length(L[i])} A[i - L[i][j]] + 1;

Edit based on Micron's request: Here is the idea behind comuting L[i][j]. I just wrote this up to convey the idea, the code may have problems.

// Every single char is palindrome so L[i][0] = 1;
vector > L(S.length(), vector(1,1));

for (i = 0; i < S.length(); i++) {
 for (j = 2; j < S.length; j++) {
   if (i - j + 1 >= 0 && S[i] == S[i-j + 1]) {
     // See if there was a palindrome of length j - 2 ending at S[i-1]
     bool inner_palindrome = false;
     if (j ==2) {
      inner_palindrome = true;
     } else {
       int k = L[i-1].length;
       if (L[i-1][k-1] == j-2 || (k >= 2 && L[i-1][k-2] == j-2)) {
         inner_palindrome = true;
       }
     }
     if (inner_palindrome) {
       L[i].push_back(j);
     }
   } 
 }
}