Given a level L. The task is to find the sum of all the integers present at the given level in Pascal’s triangle .
A Pascal triangle with 6 levels is shown below:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Examples:
Input: L = 3
Output: 4
1 + 2 + 1 = 4Input: L = 2
Output:2
Approach: If we observe carefully the series of the sum of levels will go on like 1, 2, 4, 8, 16…., which is a GP series with a = 1 and r = 2.
Therefore, sum of Lth level is L’th term in the above series.
Lth term = 2L-1
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach#include <bits/stdc++.h>using namespace std;// Function to find sum of numbers at // Lth level in Pascals Triangleint sum(int h){ return pow(2, h - 1);}// Driver Codeint main(){ int L = 3; cout << sum(L); return 0;} |
Java
// Java implementation of the approach class GFG{ // Function to find sum of numbers at // Lth level in Pascals Triangle static int sum(int h) { return (int)Math.pow(2, h - 1); } // Driver Code public static void main (String[] args) { int L = 3; System.out.println(sum(L)); } }// This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the above approach# Function to find sum of numbers at# Lth level in Pascals Triangledef summ(h): return pow(2, h - 1)# Driver CodeL = 3print(summ(L))# This code is contributed by mohit kumar |
C#
// C# implementation of the approach using System;class GFG{ // Function to find sum of numbers at // Lth level in Pascals Triangle static int sum(int h) { return (int)Math.Pow(2, h - 1); } // Driver Code public static void Main () { int L = 3; Console.WriteLine(sum(L)); } }// This code is contributed by anuj_67.. |
Javascript
<script>// Javascript implementation of the above approach// Function to find sum of numbers at // Lth level in Pascals Trianglefunction sum(h){ return Math.pow(2, h - 1);}// Driver Codevar L = 3;document.write(sum(L));</script> |
Output:
4
Time Complexity: O(log2L) because it is using pow function
Auxiliary Space: O(1)
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