What is Pascal's Triangle?

Pascal's Triangle is a triangular array of binomial coefficients. Each number is the sum of the two numbers directly above it:

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C(n, k) = n! / (k! × (n - k)!)

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Complete C Implementation

c (ISO Standard)
Run in Compiler.cCopy
#include <stdio.h>

void printPascalsTriangle(int rows) {
    for (int i = 0; i < rows; i++) {
        /* Print leading spaces for triangular alignment */
        for (int space = 0; space < rows - i - 1; space++) {
            printf("  ");
        }

        int val = 1;
        for (int j = 0; j <= i; j++) {
            printf("%4d", val);
            /* Compute next coefficient in O(1) time: val * (i - j) / (j + 1) */
            val = val * (i - j) / (j + 1);
        }
        printf("\n");
    }
}

int main() {
    int rows = 6;
    printf("Pascal's Triangle with %d rows:\n\n", rows);
    printPascalsTriangle(rows);
    return 0;
}

Sample Output

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Pascal's Triangle with 6 rows:

             1
           1   1
         1   2   1
       1   3   3   1
     1   4   6   4   1
   1   5  10  10   5   1

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Complexity Analysis

• Time Complexity: O(rows²) — Iterates through nested loop of row elements.
• Space Complexity: O(1) — Computes terms on the fly using binomial ratios without extra memory.

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Related Guides

• Calculate factorials in Factorial Program in C.
• Master 2D nested loops in Arrays in C Programming.