数组所有子集的子集总和| O(3 ^ N)

给定长度为N的数组arr [] ，任务是找到该数组所有子集的子集的总和。

例子：

Input: arr[] = {1, 1}
Output: 6
All possible subsets:
a) {} : 0
All the possible subsets of this subset
will be {}, Sum = 0
b) {1} : 1
All the possible subsets of this subset
will be {} and {1}, Sum = 0 + 1 = 1
c) {1} : 1
All the possible subsets of this subset
will be {} and {1}, Sum = 0 + 1 = 1
d) {1, 1} : 4
All the possible subsets of this subset
will be {}, {1}, {1} and {1, 1}, Sum = 0 + 1 + 1 + 2 = 4
Thus, ans = 0 + 1 + 1 + 4 = 6

Input: arr[] = {1, 4, 2, 12}
Output: 513

方法：在本文中，将讨论O(3 ^N )时间复杂度来解决给定问题的方法。
首先，生成数组的所有可能子集。总共将有2 ^N个子集。然后，对于每个子集，找到其所有子集的总和。
现在，让我们了解此解决方案的时间复杂性。
存在长度为K的^N C _k个子集，找到长度为K的数组的时间为2 ^K。
总时间=( ^N C ₁ * 2 ¹ )+( ^N C ₂ * 2 ² )+…+( ^N C _k * ^K )= 3 ^K

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
  
// Function to sum of all subsets of a
// given array
void subsetSum(vector& c, int i,
               int& ans, int curr)
{
    // Base case
    if (i == c.size()) {
        ans += curr;
        return;
    }
  
    // Recursively calling subsetSum
    subsetSum(c, i + 1, ans, curr + c[i]);
    subsetSum(c, i + 1, ans, curr);
}
  
// Function to generate the subsets
void subsetGen(int* arr, int i, int n,
               int& ans, vector& c)
{
    // Base-case
    if (i == n) {
  
        // Finding the sum of all the subsets
        // of the generated subset
        subsetSum(c, 0, ans, 0);
        return;
    }
  
    // Recursively accepting and rejecting
    // the current number
    subsetGen(arr, i + 1, n, ans, c);
    c.push_back(arr[i]);
    subsetGen(arr, i + 1, n, ans, c);
    c.pop_back();
}
  
// Driver code
int main()
{
    int arr[] = { 1, 1 };
    int n = sizeof(arr) / sizeof(int);
  
    // To store the final ans
    int ans = 0;
    vector c;
  
    subsetGen(arr, 0, n, ans, c);
    cout << ans;
  
    return 0;
}

Java

// Java implementation of the approach
import java.util.*;
  
class GFG
{
    static Vector c = new Vector<>();
  
    // To store the final ans
    static int ans = 0;
  
    // Function to sum of all subsets of a
    // given array
    static void subsetSum(int i, int curr) 
    {
  
        // Base case
        if (i == c.size()) 
        {
            ans += curr;
            return;
        }
  
        // Recursively calling subsetSum
        subsetSum(i + 1, curr + c.elementAt(i));
        subsetSum(i + 1, curr);
    }
  
    // Function to generate the subsets
    static void subsetGen(int[] arr, int i, int n)
    {
  
        // Base-case
        if (i == n) 
        {
  
            // Finding the sum of all the subsets
            // of the generated subset
            subsetSum(0, 0);
            return;
        }
  
        // Recursively accepting and rejecting
        // the current number
        subsetGen(arr, i + 1, n);
        c.add(arr[i]);
        subsetGen(arr, i + 1, n);
        c.remove(c.size() - 1);
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 1, 1 };
        int n = arr.length;
  
        subsetGen(arr, 0, n);
        System.out.println(ans);
    }
}
  
// This code is contributed by
// sanjeev2552

Python3

# Python3 implementation of the approach
  
# Function to sum of all subsets 
# of a given array
c = []
ans = 0
  
def subsetSum(i, curr):
    global ans, c
      
    # Base case
    if (i == len(c)):
        ans += curr
        return
  
    # Recursively calling subsetSum
    subsetSum(i + 1, curr + c[i])
    subsetSum(i + 1, curr)
  
# Function to generate the subsets
def subsetGen(arr, i, n):
    global ans, c
      
    # Base-case
    if (i == n):
  
        # Finding the sum of all the subsets
        # of the generated subset
        subsetSum(0, 0)
        return
  
    # Recursively accepting and rejecting
    # the current number
    subsetGen(arr, i + 1, n)
    c.append(arr[i])
    subsetGen(arr, i + 1, n)
    del c[-1]
  
# Driver code
arr = [1, 1]
n = len(arr)
  
subsetGen(arr, 0, n)
  
print(ans)
  
# This code is contributed by Mohit Kumar

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;
  
class GFG
{
    static List c = new List();
  
    // To store the readonly ans
    static int ans = 0;
  
    // Function to sum of all subsets of a
    // given array
    static void subsetSum(int i, int curr) 
    {
  
        // Base case
        if (i == c.Count) 
        {
            ans += curr;
            return;
        }
  
        // Recursively calling subsetSum
        subsetSum(i + 1, curr + c[i]);
        subsetSum(i + 1, curr);
    }
  
    // Function to generate the subsets
    static void subsetGen(int[] arr, int i, int n)
    {
  
        // Base-case
        if (i == n) 
        {
  
            // Finding the sum of all the subsets
            // of the generated subset
            subsetSum(0, 0);
            return;
        }
  
        // Recursively accepting and rejecting
        // the current number
        subsetGen(arr, i + 1, n);
        c.Add(arr[i]);
        subsetGen(arr, i + 1, n);
        c.RemoveAt(c.Count - 1);
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
        int[] arr = { 1, 1 };
        int n = arr.Length;
  
        subsetGen(arr, 0, n);
        Console.WriteLine(ans);
    }
}
  
// This code is contributed by Rajput-Ji

输出：

6