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 Triangle int sum( int h) { return pow (2, h - 1); } // Driver Code int 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 Triangle def summ(h): return pow ( 2 , h - 1 ) # Driver Code L = 3 print (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 Triangle function sum(h) { return Math.pow(2, h - 1); } // Driver Code var L = 3; document.write(sum(L)); </script> |
4
Time Complexity: O(log2L) because it is using pow function
Auxiliary Space: O(1)
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