Example: Pascal's Triangle using Dynamic Programming in C

// Pascal's Triangle using Dynamic Programming
#include <stdio.h>

int main() {
    int rows = 5; // Number of rows to generate
    int triangle[rows][rows]; // 2D array to store triangle values

    printf("Pascal's Triangle (Dynamic Programming approach):\n");
    // Step 1: Iterate through each row
    for (int i = 0; i < rows; i++) {
        // Step 2: Print leading spaces
        for (int space = 0; space < rows - i - 1; space++) {
            printf(" ");
        }
        // Step 3: Iterate through each element in the current row
        for (int j = 0; j <= i; j++) {
            // Step 4: Calculate element value
            if (j == 0 || j == i) {
                triangle[i][j] = 1; // Edges are always 1
            } else {
                // Sum of two elements from the previous row
                triangle[i][j] = triangle[i-1][j-1] + triangle[i-1][j];
            }
            printf("%d ", triangle[i][j]); // Print the calculated value
        }
        printf("\n"); // Move to the next line
    }
    return 0;
}