Pascal’s triangle is a triangular array of the binomial coefficients. Write a function that takes an integer value n as input and prints first n lines of the Pascal’s triangle. Following are the first 6 rows of Pascal’s Triangle.

pascal.cpp

/*
Pascal’s triangle is a triangular array of the binomial coefficients. 
Write a function that takes an integer value n as input and prints 
first n lines of the Pascal’s triangle. Following are the first 6 
rows of Pascal’s Triangle.

*/
#include <iostream>
using namespace std;
int binomialCoefficient(int, int);


void printPascal(int n){
    for(int line=0;line<n;line++)
    {
        for(int i=0;i<=line;i++)
            printf("%d ",binomialCoefficient(line,i));
        printf("\n");
    }
}

/*
	Time Complexity 	: O(n^3)
	Space Complexity 	: O(1) 
*/


int binomialCoefficient(int n,int k)
{
    int res = 1;
    if(k > n-k)
        k = n-k;
    for(int i=0;i<k;i++)
    {
        res*=(n-i);
        res/=(i+1);
    }
    
    return res;
}
/*
	Time Complexity 	: O(k)
	Space Complexity 	: O(1) 
*/
void printPascal2(int n)
{
	int arr[n][n];
	
	for(int line=0;line<n;line++)
    {
        for(int i=0;i<=line;i++)
        {
        	if(i==0||line==i)
        		arr[line][i]=1;
        	else
        		arr[line][i] = arr[line-1][i-1]+arr[line-1][i];
        	
        	printf("%d ",arr[line][i]);
        }
            
        printf("\n");
    }
	
}
/*
	Time Complexity 	: O(n^2)
	Space Complexity 	: O(n^2) 	
*/

// A O(n^2) time and O(1) extra space function for Pascal's Triangle
void printPascal3(int n)
{

for (int line = 1; line <= n; line++)
{
	int C = 1; // used to represent C(line, i)
	for (int i = 1; i <= line; i++) 
	{
	printf("%d ", C); // The first value in a line is always 1
	C = C * (line - i) / i; 
	}
	printf("\n");
}

}
/*
	Time Complexity 	: O(n^2)
	Space Complexity 	: O(1) 	
*/

int main() {
	// your code goes here
	printPascal3(5);
	
	return 0;
}