# Palindrome Partitioning in C++

C++Server Side ProgrammingProgramming

Suppose we have one input string, a partitioning of that string is palindrome partitioning, when every substring of the partition is a palindrome. In this section, we have to find the minimum cuts are needed to palindrome partitioning the given string. So if the string is like “ababbbabbababa” Minimum cut to partition as palindrome. Here 3 cuts are needed. The palindromes are: a | babbbab | b | ababa

To solve this, we will follow these steps −

• n := length of str
• define cut matrix and pal matrix each of order n x n
• for i := 0 to n, do
• pal[i, i] := true and cut[i, i] := 0
• for len in range 2 to n, do
• for i in range 0 to n – len, do
• j := i + len – 1
• if len = 2, then
• if str[i] = str[j], then pal[i, j] := true
• else when str[i] = str[j] and pal[i+1, j-1] ≠ 0 pal[i, j] := true
• if pal[i, j] is true, then cut[i, j] := 0
• else
• cut[i, j] := ∞
• for k in range i to j-1, do
• cut[i, j] := minimum of cut[i, j] and (cut[i, k]+ cut[k+1, j+1]+1)
• return cut[0, n-1]

## Example

Let us see the following implementation to get better understanding −

#include <iostream>
#include <climits>
using namespace std;
int min (int a, int b){
return (a < b)? a : b;
}
int minPalPartion(string str){
int n = str.size();
int cut[n][n];
bool pal[n][n]; //true when palindrome present for i to j th element
for (int i=0; i<n; i++){
pal[i][i] = true; //substring of length 1 is plaindrome
cut[i][i] = 0;
}
for (int len=2; len<=n; len++){
for (int i=0; i<n-len+1; i++){//find all substrings of length len
int j = i+len-1; // Set ending index
if (len == 2) //for two character string
pal[i][j] = (str[i] == str[j]);
else //for string of more than two characters
pal[i][j] = (str[i] == str[j]) && pal[i+1][j-1];
if (pal[i][j] == true)
cut[i][j] = 0;
else{
cut[i][j] = INT_MAX; //initially set as infinity
for (int k=i; k<=j-1; k++)
cut[i][j] = min(cut[i][j], cut[i][k] + cut[k+1][j]+1);
}
}
}
return cut[n-1];
}
int main(){
string str= "ababbbabbababa";
cout << "Min cuts for Palindrome Partitioning is: "<<minPalPartion(str);
}

## Input

ababbbabbababa

## Output

Min cuts for Palindrome Partitioning is: 3