Is Minimum Insertion Steps to Make a String Palindrome easy or hard?

The problem is generally classified as Hard because it requires recognizing the transformation to the Longest Palindromic Subsequence problem or implementing substring dynamic programming. Candidates unfamiliar with LCS-based reductions often struggle to reach the optimal O(n^2) solution.

Minimum Insertion Steps to Make a String Palindrome Python/Java solution

Python and Java implementations typically build a DP table for the Longest Common Subsequence between the string and its reversed version. After computing the LCS length, subtract it from the string length to get the minimum insertions. Both implementations run in O(n^2) time.

How to solve Minimum Insertion Steps to Make a String Palindrome in O(n)?

An O(n) solution is not known for the general case. The problem requires evaluating relationships between many substring pairs, which leads to O(n^2) dynamic programming states. The best practical solution currently runs in O(n^2) time using DP.

What is the best approach for Minimum Insertion Steps to Make a String Palindrome?

The most common approach uses Dynamic Programming with the Longest Palindromic Subsequence (LPS). Compute LPS by finding the Longest Common Subsequence between the string and its reverse. The minimum insertions required equals n minus the LPS length. This runs in O(n^2) time and O(n^2) space.

Is Minimum Insertion Steps to Make a String Palindrome asked at Google/Amazon/Meta?

Palindrome dynamic programming problems frequently appear in interviews at companies like Google, Amazon, and Meta. Variants involving palindromic subsequences, substring DP, or minimum insertions/deletions are common in mid to senior algorithm rounds.

What data structure is used in Minimum Insertion Steps to Make a String Palindrome?

The solution mainly relies on a 2D dynamic programming table that stores results for substring ranges or prefix pairs. The algorithm also uses string manipulation and sometimes two-pointer recursion with memoization stored in arrays or hash maps.

What is the time complexity of Minimum Insertion Steps to Make a String Palindrome?

The optimal solution runs in O(n^2) time because it fills a dynamic programming table for all substring pairs. Both the LPS-based solution and the memoized recursion approach evaluate O(n^2) states. Each state is computed in constant time.

Description Hints 2 Solution Video 16:36

1312. Minimum Insertion Steps to Make a String Palindrome

Hard74.3% acceptance7 companies

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 do not need any insertions.

Example 2:

Input: s = "mbadm"
Output: 2
Explanation: String can be "mbdadbm" or "mdbabdm".

Example 3:

Input: s = "leetcode"
Output: 5
Explanation: Inserting 5 characters the string becomes "leetcodocteel".

Constraints:

1 <= s.length <= 500
s consists of lowercase English letters.

Asked at 7 companies

IBM Accenture Oracle Goldman Sachs

Google Amazon Microsoft

Topics

Dynamic Programming String

Hints open one at a time

Hint 1

Is dynamic programming suitable for this problem ?

Hint 2

If we know the longest palindromic sub-sequence is x and the length of the string is n then, what is the answer to this problem? It is n - x as we need n - x insertions to make the remaining characters also palindrome.

16:36

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