Q. Write An Algorithm And Program to Print Pascal's Triangle.

Here you will find an Algorithm And Program to print Pascal's Triangle. Given an integer value n and our task is to print first n lines of the Pascal's triangle
Pascal's Triangle : Pascal's triangle is a triangular array of binomial coefficients. Pascal's triangle is a type of number pattern. The numbers are so arranged that they are reflected as triangles. For Example :-

Input : Enter the number of rows: 6
Output :

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

Explanation : As we can see that input integer number : Num = 6. Output will be the Pascal's Triangle.
Now let us understand what logic we need to use in this - In the program three loop are used. :
1. Outer loop will run throughout the program. The loop will start from i = 0 to rows.
2. Inner loop 1 is used to give space between the number. The loop will start from space = 1 to rows-i
3. Inner loop 2 is used to calculate the coef and print the coef. The inner loop 2 start from j= 0 to i.

Algorithm To Print Pascal's Triangle

\\Algorithm To Print Pascal's Triangle
START
Step 1: [ Take Input ] Read: Number of rows
Step 2 : [Define] coef = 1, space, i, j.
Step 3: Loop start from i = 0 to rows:
Loop start from space = 1 to rows-i[for space between number]:
print space " "
Loop end
Loop start from j= 0 to i:
[Check If Condition] if i or j equals 0
print 1
[Check Else Condition] 
print coef * (i - j + 1) / j;
Loop end
Give one line space
Loop end
Stop

Program To Print Pascal's Triangle

C++

Java

Python

PHP

//C Program To Print Pascal's Triangle
#include <stdio.h> 
int main() {
int rows, coef = 1, space, i, j;
//Enter the number of rows
printf("Enter the number of rows: ");
scanf("%d", &rows);
//Outer loop
for (i = 0; i < rows; i++) {
//Inner Loop 1 to give space
for (space = 1; space <= rows - i; space++)
printf("  ");
//Inner Loop 2 to calculate coef
for (j = 0; j <= i; j++) {
if (j == 0 || i == 0)
coef = 1;
else
coef = coef * (i - j + 1) / j;
printf("%4d", coef);
}
printf("\n");
}
return 0;
}

//C++ Program To Print Pascal's Triangle
#include <iostream>
using namespace std;
int main()
{
int rows, coef = 1, space, i, j;
//Enter the number of rows
cout<<"Enter the number of rows: ";
cin>>rows;
//Outer loop
for (i = 0; i < rows; i++) {
//Inner Loop 1 to give space
for (space = 1; space <= rows - i; space++)
cout<<"  ";
//Inner Loop 2 to calculate coef
for (j = 0; j <= i; j++) {
if (j == 0 || i == 0)
coef = 1;
else
coef = coef * (i - j + 1) / j;
cout<<" "<<coef<<" ";
}
cout<<"\n";
}
return 0;
}

//Java Program To Print Pascal's Triangle
public class LFC
{
public static void main(String[] args) {
int coef = 1, space, i, j;
//Enter the number of rows
int rows = 6;
//Outer loop
for (i = 0; i < rows; i++) {
//Inner Loop 1 to give space
for (space = 1; space <= rows - i; space++)
System.out.print(" "); 
//Inner Loop 2 to calculate coef
for (j = 0; j <= i; j++) {
if (j == 0 || i == 0)
coef = 1;
else
coef = coef * (i - j + 1) / j;
System.out.print(" "+coef+" "); 
}
System.out.println(); 
}
}
}

#Python Program To Print Pascal's Triangle
from math import factorial 
# Enter the number of rows 
rows = 6
for i in range(rows): 
# Inner Loop 1 to give space
for space in range(rows-i+1): 
print(end=" ") 
# Inner Loop 2 for calculation
for j in range(i+1): 
# nCr = n!/((n-r)!*r!) 
print(factorial(i)//(factorial(j)*factorial(i-j)), end=" ") 
# for new line 
print()

//C# Program To Print Pascal's Triangle
using System;
class LFC {
static void Main() {
int coef = 1, space, i, j;
//Enter the number of rows
int rows = 6;
//Outer loop
for (i = 0; i < rows; i++) {
//Inner Loop 1 to give space
for (space = 1; space <= rows - i; space++)
Console.Write(" ");
//Inner Loop 2 to calculate coef
for (j = 0; j <= i; j++) {
if (j == 0 || i == 0)
coef = 1;
else
coef = coef * (i - j + 1) / j;
Console.Write(" "+coef+" "); 
}
Console.WriteLine();
}
}
}

<?php
//PHP Program To Print Pascal's Triangle
//Enter the number of rows
$rows = 6;
$coef = 1;
//Outer loop
for ($i = 0; $i < $rows; $i++) {
echo "\t";
//Inner Loop 1 to give space
for ($space = 1; $space <= $rows - $i; $space++) {
echo "  ";
}
//Inner Loop 2 to calculate coef
for ($j = 0; $j <= $i; $j++) {
if ($j == 0 || $i == 0)
$coef = 1;
else
$coef = $coef * ($i - $j + 1) / $j;
echo $coef . "   ";
}
echo "\n";
}

//C Program To Print Pascal's Triangle
#include <stdio.h> 
int main() {
int rows, coef = 1, space, i, j;
//Enter the number of rows
printf("Enter the number of rows: ");
scanf("%d", &rows);
//Outer loop
for (i = 0; i < rows; i++) {
//Inner Loop 1 to give space
for (space = 1; space <= rows - i; space++)
printf("  ");
//Inner Loop 2 to calculate coef
for (j = 0; j <= i; j++) {
if (j == 0 || i == 0)
coef = 1;
else
coef = coef * (i - j + 1) / j;
printf("%4d", coef);
}
printf("\n");
}
return 0;
}

Output

Number of rows: 6
Output : 
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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