Program to generate Pascal's Triangle

Approach 1 : In this case, we are given the row number r and the column number c, and we need to find out the element at position (r,c). 


#include <bits/stdc++.h>
using namespace std;

int nCr(int n, int r) {
    long long res = 1;

    // calculating nCr:
    for (int i = 0; i < r; i++) {
        res = res * (n - i);
        res = res / (i + 1);
    }
    return res;
}

int pascalTriangle(int r, int c) {
    int element = nCr(r - 1, c - 1);
    return element;
}

int main()
{
    int r = 5; // row number
    int c = 3; // col number
    int element = pascalTriangle(r, c);
    cout << "The element at position (r,c) is: "
            << element << "n";
    return 0;
}


Aproach 2 : Given the row number n. Print the n-th row of Pascal’s triangle.

#include <bits/stdc++.h>
using namespace std;

int nCr(int n, int r) {
    long long res = 1;

    // calculating nCr:
    for (int i = 0; i < r; i++) {
        res = res * (n - i);
        res = res / (i + 1);
    }
    return res;
}

void pascalTriangle(int n) {
    // printing the entire row n:
    for (int c = 1; c <= n; c++) {
        cout << nCr(n - 1, c - 1) << " ";
    }
    cout << "n";
}

int main()
{
    int n = 5;
    pascalTriangle(n);
    return 0;
}

Approch 3 :  We will try to generate all the row elements by simply using the naive approach of variation 2.


#include <bits/stdc++.h>
using namespace std;

int nCr(int n, int r) {
    long long res = 1;

    // calculating nCr:
    for (int i = 0; i < r; i++) {
        res = res * (n - i);
        res = res / (i + 1);
    }
    return (int)(res);
}

vector<vector<int>> pascalTriangle(int n) {
    vector<vector<int>> ans;

    //Store the entire pascal's triangle:
    for (int row = 1; row <= n; row++) {
        vector<int> tempLst; // temporary list
        for (int col = 1; col <= row; col++) {
            tempLst.push_back(nCr(row - 1, col - 1));
        }
        ans.push_back(tempLst);
    }
    return ans;
}

int main()
{
    int n = 5;
    vector<vector<int>> ans = pascalTriangle(n);
    for (auto it : ans) {
        for (auto ele : it) {
            cout << ele << " ";
        }
        cout << "n";
    }
    return 0;
}