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Prashant Mishra
Prashant Mishra

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Minimum Insertion steps needed to make a string palindrome (Same as LCS)

Given a string s. In one step you can insert any character at any index of the string.

Return the minimum number of steps to make s palindrome.

A Palindrome String is one that reads the same backward as well as forward.

Example 1:

Input: s = "zzazz"
Output: 0
Explanation: The string "zzazz" is already palindrome we don't need any insertions. 
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Tabulation approach
Time complexity : O(n*m), space complexity : o(n*m) for dp array

class Solution {
    public int minInsertions(String s) {
        //going with the hint given 
        //i.e. finding length of the longest palindromic subsequence x
        //now , s.length()-x = n ,so n insertion are needed to make the entire string as palindromic string
        String r = new StringBuilder(s).reverse().toString();
        int dp[][] = new int[s.length()+1][r.length()+1];// 1 based indexing
        for(int i =0;i<=s.length();i++){
            dp[i][0] =0;
            dp[0][i] =0;
        for(int  i =1;i<=s.length();i++){
            for(int j=1;j<=r.length();j++){
                    dp[i][j] = 1 + dp[i-1][j-1];
                else dp[i][j] = Integer.max(dp[i][j-1],dp[i-1][j]);
        return s.length() - dp[s.length()][r.length()];
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