Program to check minimum number of characters needed to make string palindrome in Python

A palindrome is a string that reads the same forwards and backwards. To make any string a palindrome, we need to find the minimum number of characters to insert. This can be solved using dynamic programming by comparing characters from both ends.

Problem Statement

Given a string, find the minimum number of characters needed to be inserted to make it a palindrome ?

For example, if the input is s = "mad", we can insert "am" to get "madam", requiring 2 insertions.

Algorithm

The approach uses a recursive function dp(i, j) that compares characters at positions i and j ?

• If i >= j, return 0 (base case)

• If s[i] == s[j], move inward: dp(i + 1, j - 1)

• Otherwise, try both options and take minimum: min(dp(i + 1, j), dp(i, j - 1)) + 1

Implementation

class Solution:
    def solve(self, s):
        def dp(i, j):
            if i >= j:
                return 0
            if s[i] == s[j]:
                return dp(i + 1, j - 1)
            else:
                return min(dp(i + 1, j), dp(i, j - 1)) + 1
        return dp(0, len(s) - 1)

# Test the solution
ob = Solution()
s = "mad"
result = ob.solve(s)
print(f"Minimum insertions needed for '{s}': {result}")

Minimum insertions needed for 'mad': 2

How It Works

For the string "mad" ?

• Compare 'm' and 'd': they don't match

• Try both possibilities: skip 'm' or skip 'd'

• Recursively solve subproblems until base case

• Return minimum insertions needed

Additional Examples

ob = Solution()

# Test multiple strings
test_cases = ["abc", "aab", "abcd", "racecar"]

for s in test_cases:
    result = ob.solve(s)
    print(f"'{s}' needs {result} insertions")

'abc' needs 2 insertions
'aab' needs 1 insertions
'abcd' needs 3 insertions
'racecar' needs 0 insertions

Conclusion

This dynamic programming solution efficiently finds the minimum character insertions needed to create a palindrome. The recursive approach compares characters from both ends and explores all possibilities to find the optimal solution.