Palindrome Partitioning DP Minimum Cuts in DSA C - Build from Scratch

Palindrome Partitioning DP Minimum Cuts

📖 Scenario: Imagine you have a string of letters and you want to cut it into pieces so that each piece is a palindrome. A palindrome is a word or phrase that reads the same forwards and backwards, like "madam" or "racecar". Your goal is to find the smallest number of cuts needed to split the string into palindromic pieces.

🎯 Goal: You will build a program in C that uses dynamic programming to find the minimum number of cuts needed to partition a given string into palindromes.

📋 What You'll Learn

Create a string variable with the exact value "aab"

Create an integer variable to store the length of the string

Create a 2D boolean array to store palindrome checks

Create an integer array to store minimum cuts for each substring

Use nested loops to fill the palindrome table

Use dynamic programming to find minimum cuts

Print the minimum cuts for the entire string

💡 Why This Matters

🌍 Real World

This technique helps in text processing tasks like DNA sequence analysis, data compression, and natural language processing where palindrome detection is important.

💼 Career

Understanding dynamic programming and string manipulation is essential for software engineering roles, especially those involving algorithms and optimization.

1

Create the input string and its length

Create a character array called s with the exact value "aab" and an integer variable called n that stores the length of s.

DSA C

char s[] = "aab";
int n = 0;  // Your code here

Hint

Use sizeof(s) / sizeof(s[0]) - 1 to get the length of the string excluding the null character.

2

Create the palindrome table and cuts array

Create a 2D boolean array called pal of size n by n to store palindrome checks, and an integer array called cuts of size n to store minimum cuts for substrings.

DSA C

char s[] = "aab";
int n = sizeof(s) / sizeof(s[0]) - 1;

int pal[n][n];
int cuts[n];  // Your code here

Hint

Use int pal[n][n]; and int cuts[n]; to declare the arrays.

3

Fill palindrome table and compute minimum cuts

Use nested for loops with variables j and i to fill the pal table for palindromes and compute minimum cuts in the cuts array using dynamic programming.

DSA C

char s[] = "aab";
int n = sizeof(s) / sizeof(s[0]) - 1;

int pal[n][n];
int cuts[n];

// Your code here

Hint

Use the condition s[i] == s[j] && (i - j < 2 || pal[j + 1][i - 1]) to check palindromes.

4

Print the minimum cuts for the entire string

Print the minimum cuts needed for the entire string by printing cuts[n - 1].

DSA C

char s[] = "aab";
int n = sizeof(s) / sizeof(s[0]) - 1;

int pal[n][n];
int cuts[n];

for (int i = 0; i < n; i++) {
    cuts[i] = i;  
    for (int j = 0; j <= i; j++) {
        if (s[i] == s[j] && (i - j < 2 || pal[j + 1][i - 1])) {
            pal[j][i] = 1;
            if (j == 0) {
                cuts[i] = 0;
            } else if (cuts[j - 1] + 1 < cuts[i]) {
                cuts[i] = cuts[j - 1] + 1;
            }
        } else {
            pal[j][i] = 0;
        }
    }
}

// Your code here

Hint

Use printf("%d\n", cuts[n - 1]); to print the minimum cuts.