求所有子序列之和

给定一个包含n 个整数的数组。任务是找到数组的每个子序列的总和。
例子：

Input : arr[] = { 6, 8, 5 }
Output : 76
All subsequence sum are:
{ 6 }, sum = 6
{ 8 }, sum = 8
{ 5 }, sum = 5
{ 6, 8 }, sum = 14
{ 6, 5 }, sum = 11
{ 8, 5 }, sum = 13
{ 6, 8, 5 }, sum = 19
Total sum = 76.

Input  : arr[] = {1, 2}
Output : 6

方法1（蛮力）：
生成所有子序列，求每个子序列之和。
方法2（高效方法）：
对于大小为 n 的数组，我们总共有 2^n 个子序列（包括空的）。观察，总共 2 ⁿ个子序列，每个元素出现 2 ^n-1次。
例如，arr[] = { 5, 6, 7 }

因此，所有子序列的总和将是 (所有元素的总和) * 2 ^n-1 。
下面是这种方法的实现：

C++

// C++ program to find sum of all sub-sequences
// of an array.
#include
using namespace std;
 
// Return sum of sum of all sub-sequence.
int sum(int arr[], int n)
{
  int ans = 0;
 
  // Finding sum of the array.
  for (int i = 0; i < n; i++)
    ans += arr[i];
 
  return ans * pow(2, n - 1);
}
 
// Driver Code
int main()
{
  int arr[] = { 6, 7, 8 };
  int n = sizeof(arr)/sizeof(arr[0]);
 
  cout << sum(arr, n) << endl;
 
  return 0;
}

Java

// Java program to find sum of
// all sub-sequences of an array.
import java.io.*;
import java.math.*;
 
class GFG {
     
    // Return sum of sum of all sub-sequence.
    static int sum(int arr[], int n)
    {
    int ans = 0;
     
    // Finding sum of the array.
    for (int i = 0; i < n; i++)
        ans += arr[i];
     
    return ans * (int)(Math.pow(2, n - 1));
    }
     
    // Driver Code
    public static void main(String args[])
    {
    int arr[]= { 6, 7, 8 };
    int n = arr.length;
     
    System.out.println(sum(arr, n));
    }
}
     
// This code is contributed by Nikita Tiwari.

Python3

# Python 3 program to find sum of
# all sub-sequences of an array.
 
 
# Return sum of sum of all sub-sequence.
def sm(arr , n) :
    ans = 0
 
    # Finding sum of the array.
    for i in range(0, n) :
        ans = ans + arr[i]
     
    return ans * pow(2, n - 1)
     
     
# Driver Code
arr = [ 6, 7, 8 ]
n=len(arr)
 
print(sm(arr, n))
 
 
# This code is contributed by Nikita Tiwari.

C#

// C# program to find sum of
// all sub-sequences of an array.
using System;
 
class GFG
{
     
    // Return sum of sum of all sub-sequence.
    static int sum(int []arr, int n)
    {
    int ans = 0;
     
    // Finding sum of the array.
    for (int i = 0; i < n; i++)
        ans += arr[i];
     
    return ans * (int)(Math.Pow(2, n - 1));
    }
     
    // Driver Code
    public static void Main()
    {
    int []arr= { 6, 7, 8 };
    int n = arr.Length;
     
    Console.Write(sum(arr, n));
    }
}
     
// This code is contributed by nitin mittal

PHP

Javascript

输出：