由前n个自然数组成的集合的所有子集的总和

给定数字n，我们需要从由前n个自然数组成的集合的所有可能子集中找到所有元素的总和。
例子 ：

Input :  n = 2
Output : 6
Possible subsets are {{1}, {2}, 
{1, 2}}. Sum of elements in subsets
is 1 + 2 + 1 + 2 = 6

Input :  n = 3
Output : 24
Possible subsets are {{1}, {2}, {3}, 
{1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Sum of subsets is : 
1 + 2 + 3 + (1 + 2) + (1 + 3) + 
(2 + 3) + (1 + 2 + 3)

一个简单的解决方案是生成所有子集。对于每个子集，计算其总和，最后返回总和。
一个有效的解决方案基于以下事实：从1到n的每个数字都恰好出现2 ^(n-1)次。因此，我们所需的总和为(1 + 2 + 3 + .. + n)* 2 ^(n-1) 。总和可以写成(n *(n + 1)/ 2)* 2 ^(n-1)

C++

// CPP program to find sum of all subsets
// of a set.
#include 
using namespace std;
 
unsigned long long findSumSubsets(int n)
{
    // sum of subsets is (n * (n + 1) / 2) *
    // pow(2, n-1)
    return (n * (n + 1) / 2) * (1 << (n - 1));
}
 
int main()
{
    int n = 3;
    cout << findSumSubsets(n);
    return 0;
}

Java

// Java program to find sum of all subsets
// of a set.
 
class GFG {
    static long findSumSubsets(int n)
    {
        // sum of subsets is (n * (n + 1) / 2) *
        // pow(2, n-1)
        return (n * (n + 1) / 2) * (1 << (n - 1));
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 3;
        System.out.print(findSumSubsets(n));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python program to find
# sum of all subsets
# of a set.
 
def findSumSubsets( n):
 
    # sum of subsets
    # is (n * (n + 1) / 2) *
    # pow(2, n-1)
    return (n * (n + 1) / 2) * (1 << (n - 1))
     
# Driver code    
n = 3
print(findSumSubsets(n))
 
# This code is contributed
# by sunnysingh.

C#

// C# program to find sum of all subsets
// of a set.
using System;
 
class GFG {
 
    static long findSumSubsets(int n)
    {
 
        // sum of subsets is (n * (n + 1) / 2) *
        // pow(2, n-1)
        return (n * (n + 1) / 2) * (1 << (n - 1));
    }
 
    // Driver code
    public static void Main()
    {
        int n = 3;
 
        Console.WriteLine(findSumSubsets(n));
    }
}
 
// This code is contributed by vt_m.

Javascript

 
// javascript program to find sum of all subsets
// of a set.
 
 
function findSumSubsets( n)
{
    // sum of subsets is (n * (n + 1) / 2) *
    // pow(2, n-1)
    return (n * (n + 1) / 2) * (1 << (n - 1));
}
 
 
// Driven Program
 
    let n = 3;
     document.write(findSumSubsets(n));
 
// This code contributed by aashish1995
 

输出 ：

24