## DEV Community

Prashant Mishra

Posted on • Originally published at leetcode.com

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

Problem:
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.
``````

Solution:
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++){
if(s.charAt(i-1)==r.charAt(j-1)){
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()];
}
}
``````

DEV Community

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