Given a string, print all possible palindromic partitions

Given a string, find all possible palindromic partitions of given string.

Example:
AllPalindromPArtition



Note that this problem is different from Palindrome Partitioning Problem, there the task was to find the partitioning with minimum cuts in input string. Here we need to print all possible partitions.

The idea is to go through every substring starting from first character, check if it is palindrome. If yes, then add the substring to solution and recur for remaining part. Below is complete algorithm.

Below is C++ implementation of above idea

C++

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// C++ program to print all palindromic partitions of a given string
#include<bits/stdc++.h>
using namespace std;
  
// A utility function to check if str is palindroem
bool isPalindrome(string str, int low, int high)
{
    while (low < high)
    {
        if (str[low] != str[high])
            return false;
        low++;
        high--;
    }
    return true;
}
  
// Recursive function to find all palindromic partitions of str[start..n-1]
// allPart --> A vector of vector of strings. Every vector inside it stores
//             a partition
// currPart --> A vector of strings to store current partition 
void allPalPartUtil(vector<vector<string> >&allPart, vector<string> &currPart, 
                   int start, int n, string str)
{
    // If 'start' has reached len
    if (start >= n)
    {
        allPart.push_back(currPart);
        return;
    }
  
    // Pick all possible ending points for substrings
    for (int i=start; i<n; i++)
    {
        // If substring str[start..i] is palindrome
        if (isPalindrome(str, start, i))
        {
            // Add the substring to result
            currPart.push_back(str.substr(start, i-start+1));
  
            // Recur for remaining remaining substring
            allPalPartUtil(allPart, currPart, i+1, n, str);
              
            // Remove substring str[start..i] from current 
            // partition
            currPart.pop_back();
        }
    }
}
  
// Function to print all possible palindromic partitions of
// str. It mainly creates vectors and calls allPalPartUtil()
void allPalPartitions(string str)
{
    int n = str.length();
  
    // To Store all palindromic partitions
    vector<vector<string> > allPart;
  
    // To store current palindromic partition
    vector<string> currPart; 
  
    // Call recursive function to generate all partiions
    // and store in allPart
    allPalPartUtil(allPart, currPart, 0, n, str);
  
    // Print all partitions generated by above call
    for (int i=0; i< allPart.size(); i++ )
    {
        for (int j=0; j<allPart[i].size(); j++)
            cout << allPart[i][j] << " ";
        cout << "\n";
    }
}
  
// Driver program
int main()
{
    string str = "nitin";
    allPalPartitions(str);
    return 0;
}

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Output:

n i t i n
n iti n
nitin

This article is contributed by Ekta Goel. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



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