In this post, you will learn to write a C++ program to print pascal triangle. A Pascal triangle is a very important mathematical concept. It is named after French mathematician Blaise Pascal. A Pascal triangle is used to find the coefficients of a **binomial expansion**.

Read: C++ program to print number triangles

This program is intended for intermediate learner of C++ programming language. We used Dev C++ compiler version 4.9.9.2 installed on Windows 7 64-bit system to compile and test the program.

## Problem Definition

A typical binomial look like the following, because it has only two variables – **a** and **b.**

=

The right-hand equation is called the binomial expansion. Each of the binomial expansion terms have a coefficient.

= coefficient is 1.

= coefficient is 2.

= coefficient is 1.

**Pascal Triangle**

The Pascal triangle display all coefficients of all powers from 0 for a binomial expansion.

Where n is the power of binomial whose coefficient we want to know.

The top (n = 0) is one has a coefficient of 1. The coefficient of 4^{th} row (n = 4) 2^{nd} element is 6.

You can find coefficient of any term by adding previous two terms just above the term you are looking for.

Get coefficient of 3^{rd} row and 1^{st} term = 3

Get coefficient of 3^{rd} row and 3^{rd} term = 3

Add them together and you get

Coefficient of 4^{th} row and 2^{nd} term = 6

### Formula

There is a formula for finding the coefficient of any term – given the row (n) and the term (r);`nCr = n! / r! (n – r)!`

To understand the formula and C++ program, you must learn these two mathematical concepts.

- Factorial
- Combination

We have used the formula of a coefficient to find coefficients of all the rows in this program.

## Program Code – Program to Print Pascal Triangle

[cc lang=”cpp” tab_size=”4″]

#include

#include

#include

#include

using namespace std;

int main()

{

int p, j;

int row, lines, element, term;

cout << "Enter Number of Rows in Pascal Triangle:"; cin >> lines;

int fact (int);

for (row = 0; row < lines; row++) { for (j = 0; j <= (lines - row - 2); j++) cout << " "; for (element = 0; element <= row; element++) { p = row - element; term = fact (row)/ (fact (element)* fact (p)); cout << " " << term; } cout << "\n"; }getch ();return 0;}/* Factorial Function */ int fact (int x) { if (x == 1 || x == 0) { return 1; } else { return (x * fact(x-1)); } }[/cc]

## Output – Program to Print Pascal Triangle

The output of the program is given below. The program requires that you input the number of row. A row is equal to power of a binomial. The program prints all the coefficients of all the previous rows.