Pascal's triangle is a way to represent integers in the form of triangles. One well-known representation is using the binomial equation. We can do this using combinations and factorials.
All values outside the triangle are treated as zero (0). The first line is 0 1 0, and while only 1 occupies a space in Pascal's triangle, 0 is invisible. The second row is obtained by adding (0 1) and (1 0). The output is sandwiched between two zeros. This process continues until the desired level is reached.
From a programming perspective, Pascal's triangle is defined as an array built by adding adjacent elements in previous rows.
In this program, we will print the integers in Pascal's triangle in the form of an array -
Online Demonstration
#include <stdio.h> int fact(int); int main(){ int i,rows,j; printf("enter no of rows :"); scanf("%d",&rows); for (i = 0; i < rows; i++){ for (j = 0; j <= (rows- i - 2); j++) printf(" "); for (j = 0 ; j <= i; j++) printf("%d ",fact(i)/(fact(j)*fact(i-j))); printf("</p><p>"); } return 0; } int fact(int n){ int a; int sum = 1; for (a = 1; a <= n; a++) sum = sum*a; return sum; }
Enter no of rows :5 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
Here we will see the printing of integers in the form of Pascal’s triangle without using arrays
Live Demonstration
#include<stdio.h> int main(){ int num,row,i; printf("Enter the number of rows: "); scanf("%d",&num); for(row=1; row<=num; row++){ int a=1; for(i=1; i<=row; i++){ printf("%d ",a); a = a * (row-i)/i; } printf("</p><p>"); } return 0; }
Enter the number of rows: 6 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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