Minimum Insertions for Palindrome in C, C++, Java & Python – Code with Explanation & Examples in Short and Simple

   

C Program

#include <stdio.h>
#include <string.h>

int min(int a, int b) { return (a < b) ? a : b; }

int minInsertions(char str[], int n) {
    int dp[n][n];
    for(int i=0;i<n;i++) dp[i][i]=0;

    for(int len=2; len<=n; len++) {
        for(int i=0; i<n-len+1; i++) {
            int j = i+len-1;
            if(str[i]==str[j])
                dp[i][j] = dp[i+1][j-1];
            else
                dp[i][j] = 1 + min(dp[i+1][j], dp[i][j-1]);
        }
    }
    return dp[0][n-1];
}

int main() {
    char str[] = "abcda";
    int n = strlen(str);
    printf("Minimum insertions needed: %d\n", minInsertions(str,n));
    return 0;
}

C Output

Input: abcda
Output: Minimum insertions needed: 2

C++ Program

#include <iostream>
#include <vector>
using namespace std;

int minInsertions(string s) {
    int n = s.size();
    vector<vector<int>> dp(n, vector<int>(n, 0));
    for(int len=2; len<=n; len++) {
        for(int i=0; i<n-len+1; i++) {
            int j=i+len-1;
            if(s[i]==s[j])
                dp[i][j]=dp[i+1][j-1];
            else
                dp[i][j]=1+min(dp[i+1][j],dp[i][j-1]);
        }
    }
    return dp[0][n-1];
}

int main() {
    string s="race";
    cout<<"Minimum insertions needed: "<<minInsertions(s)<<endl;
    return 0;
}

C++ Output

Input: race
Output: Minimum insertions needed: 3

JAVA Program

class Main {
    static int minInsertions(String s) {
        int n = s.length();
        int[][] dp = new int[n][n];
        for(int len=2; len<=n; len++) {
            for(int i=0; i<n-len+1; i++) {
                int j=i+len-1;
                if(s.charAt(i)==s.charAt(j))
                    dp[i][j]=dp[i+1][j-1];
                else
                    dp[i][j]=1+Math.min(dp[i+1][j],dp[i][j-1]);
            }
        }
        return dp[0][n-1];
    }
    public static void main(String[] args) {
        String s="google";
        System.out.println("Minimum insertions needed: "+minInsertions(s));
    }
}

JAVA Output

Input: google
Output: Minimum insertions needed: 2

Python Program

def minInsertions(s: str) -> int:
    n=len(s)
    dp=[[0]*n for _ in range(n)]
    for length in range(2,n+1):
        for i in range(n-length+1):
            j=i+length-1
            if s[i]==s[j]:
                dp[i][j]=dp[i+1][j-1]
            else:
                dp[i][j]=1+min(dp[i+1][j],dp[i][j-1])
    return dp[0][n-1]

s="abcda"
print("Minimum insertions needed:",minInsertions(s))

Python Output

Input: abcda
Output: Minimum insertions needed: 2

In-Depth Explanation

Example

Consider the string "abcda". If we attempt to convert it into a palindrome, one way to do this is by inserting "d" at the beginning and "b" at the end, resulting in "adbcda". The other way is "abcdcba". In either scenario, we require 2 insertions, which is the least we can do.

Real-Life Analogy

Consider putting books on a shelf in such a way that they are symmetric. If you have a perfectly symmetrical set already, no additional books are required. But if there are gaps on one side where the matches are absent, you will need to add additional books to make it even. The "minimum insertions for palindrome" is similar to calculating the least additional books you need to purchase so the shelf appears symmetrical.

Why It Matters

Palindromes have applications in data compression, analysis of DNA sequences, and even natural language processing. The minimum insertions idea also educates dynamic programming (DP), which is one of the most critical fields of computer science. This specific problem illustrates how overlapping subproblems and optimal substructure characteristics reduce intricate problems into easier ones. 

Learning Insights

This problem shows how to do string problems when insertions are permissible. Rather than brute force trying all insertions (which would be exponential), we employ DP to construct a table of solutions for substrings and then gradually extend them. It promotes the concept of bottom-up computation, and is frequently associated with the Longest Palindromic Subsequence (LPS) problem since the solution is n - LPS length.

Interview Relevance

This is a common interview favorite problem since it not only tests code skill but problem breaking skill. Employers would like to know if you know dynamic programming, recursion, and optimization. It also demonstrates that you are capable of dealing with edge cases such as an empty string or already-palindromic strings.

Practical Applications

In text correction software systems or DNA sequence mutation analysis systems, at times you might be interested in understanding the minimum change to achieve a symmetric or stable state. The minimum insertion algorithm is part of such systems.

SEO-Optimized Closing

The minimum insertions needed to get a string palindrome is a timeless dynamic programming problem that every coding student needs to know. It improves your skills in solving string-based coding interview problems and serves as a stepping stone to solving advanced concepts such as longest palindromic subsequence, edit distance, and text correction algorithms. Solving problems such as minimum insertions for palindrome assists you in establishing good programming fundamentals, and you will be able to crack technical interviews easily while being able to implement the concept in real-world scenarios such as DNA analysis, text processing, and software optimization.