Minimum Insertions to Make Palindrome 🎯

Welcome to the exciting world of Data Structures and Algorithms! Today, we'll dive into a fascinating problem called "Minimum Insertions to Make Palindrome".

What's a Palindrome? 📝

A palindrome is a word, phrase, number, or any sequence of characters that reads the same backward as forward. For example, "racecar", "level", "121", and "A man, a plan, a canal: Panama" are all palindromes.

Minimum Insertions to Make Palindrome 💡

Given a string s, the problem is to find the minimum number of insertions required to make it a palindrome.

Let's break this down:

Identify the Character Imbalance 📝
- Count the occurrences of each character in the string.
- If the count of a character is odd, it means we have an odd number of that character, and it causes the string to not be a palindrome.
- Remember, for a string to be a palindrome, the number of occurrences of all characters must be even (or zero).
Find the Characters to be Inserted 💡
- Identify the characters with odd counts.
- To balance the string, we need to insert these characters at appropriate places so that their count becomes even.
Insert and Check 🎯
- Start inserting characters one by one at the beginning of the string, checking after each insertion if the string is now a palindrome.
- The first insertion that makes the string a palindrome is the minimum number of insertions required.

Example 💡

Let's consider the string abccba. Here's how we'd find the minimum number of insertions to make it a palindrome:

Identify the Character Imbalance
- 'a' - 1 occurrence
- 'b' - 1 occurrence
- 'c' - 3 occurrences
Find the Characters to be Inserted
- Since 'a' and 'b' occur only once, we need to insert one of them at the beginning of the string.
Insert and Check
- Insert 'a' at the beginning: aabccba -> Not a palindrome.
- Insert 'b' at the beginning: babccba -> Not a palindrome.
- Insert 'a' again at the beginning: aaabccba -> Not a palindrome.
- Insert 'b' again at the beginning: bbabccba -> Not a palindrome.
- Now, insert 'c' at the beginning: ccbabccba -> cbcbabccba (reversed) -> ccbabccbac -> Palindrome!

Python Solution 💡

Here's a Python solution for the problem:

python

def min_insertions(s):
    char_count = {}
    for char in s:
        if char in char_count:
            char_count[char] += 1
        else:
            char_count[char] = 1

    min_insertions = 0
    for char in char_count:
        if char_count[char] % 2 != 0:
            min_insertions += 1

    for i in range(len(s)):
        temp_s = s[:i] + s[::-1][i:]
        if temp_s == s or (min_insertions > 0 and temp_s == s[::-1]):
            return min_insertions
        min_insertions += 1
        temp_s = s[:i] + char + s[i:] + s[::-1][i:]
    return min_insertions

# Test the function
print(min_insertions("abccba"))  # Output: 1

Quiz Time 🎯

Happy coding! Let's turn more strings into palindromes together! 🎯