Problem 40: Palindrome Partitioning Minimum Cuts

Problem Statement: Given a string, partition it into substrings such that every substring is a palindrome. Determine the minimum number of cuts needed for such a partition. If the string is already a palindrome, no cuts are needed.

Input

A single line containing the string.

Output

Print the minimum number of cuts needed.

Examples


Input:
aab

Output:
1

Solution Explanation

Method 1: Use dynamic programming to precompute a 2D table of palindromic substrings and then use another DP to calculate the minimum cuts required. Method 2: Use recursion with memoization to try all possible palindrome partitions and choose the minimum cut count.

Solution in C++


#include 
#include 
#include 
using namespace std;

bool isPalindrome(const string &s, int i, int j) {
    while(i < j){
        if(s[i] != s[j]) return false;
        i++; j--;
    }
    return true;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    string s; cin >> s;
    int n = s.size();
    vector cuts(n, 0);
    vector> pal(n, vector(n, false));

    for (int i = 0; i < n; i++) {
        pal[i][i] = true;
    }

    for (int len = 2; len <= n; len++){
        for (int i = 0; i <= n - len; i++){
            int j = i + len - 1;
            if(s[i] == s[j]) {
                pal[i][j] = (len == 2) ? true : pal[i+1][j-1];
            }
        }
    }

    for (int i = 0; i < n; i++){
        if(pal[0][i]) {
            cuts[i] = 0;
        } else {
            int minCut = i;
            for (int j = 0; j < i; j++){
                if(pal[j+1][i] && 1 + cuts[j] < minCut)
                    minCut = 1 + cuts[j];
            }
            cuts[i] = minCut;
        }
    }
    cout << cuts[n-1] << "
";
    return 0;
}