Minimum Insertion Steps to Make a String Palindrome — LeetCode 1312 Python Solution

The problem

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

Example

Input

s = "zzazz"

Output

0

Explanation

The string "zzazz" is already palindrome we do not need any insertions.

Python solution

class Solution:
    def minInsertions(self, s: str) -> int:
        @cache
        def dfs(i: int, j: int) -> int:
            if i >= j:
                return 0
            if s[i] == s[j]:
                return dfs(i + 1, j - 1)
            return 1 + min(dfs(i + 1, j), dfs(i, j - 1))

        return dfs(0, len(s) - 1)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1312. Minimum Insertion Steps to Make a String Palindrome is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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