Sum of all subsequences of a number

Given a number as string s, find the sum of all the elements present in all possible subsequences of s.

Examples :

Input : s = "123" 
Output : 24 
Explanation : all possible sub-sequences are 
1, 2, 3, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3} 
which add up to 24 

Input : s = "453" 
Output : 48

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach : Using power set, we can find all the subsequences and sum up all the subsequences individually in a different function. The total number of subsequences possible are 2ⁿ-1. Add the sum of all subsequences to the combined sum which is the final output.

Below is the implementation of above approach.

C++

// CPP program to find the sum of 
// elements present in all subsequences 
#include <bits/stdc++.h> 
using namespace std; 
  
// Returns numeric value of a subsequence of 
// s. The subsequence to be picked is decided 
// using bit pattern of num (We pick all those 
// digits for which there is a set bit in num) 
int findSubSequence(string s, int num) 
{   
    // Initialize the result 
    int res = 0; 
  
    // till n!=0 
    int i = 0; 
    while (num) { 
          
        // if i-th bit is set  
        // then add this number 
        if (num & 1) 
            res += s[i] - '0'; 
        i++; 
          
        // right shift i 
        num = num >> 1; 
    } 
  
    return res; 
} 
  
// function to find combined sum 
// of all individual subsequence sum 
int combinedSum(string s) 
{ 
    // length of string 
    int n = s.length(); 
      
    // stores the combined 
    int c_sum = 0; 
  
    // 2^n-1 subsequences 
    int range = (1 << n) - 1; 
  
    // loop for all subsequences 
    for (int i = 0; i <= range; i++) 
        c_sum += findSubSequence(s, i); 
  
    // returns the combined sum 
    return c_sum; 
} 
  
// driver code 
int main() 
{ 
    string s = "123"; 
    cout << combinedSum(s);     
    return 0; 
} 

Java

// Java program to find the sum of elements 
// present in all subsequences 
import java.io.*; 
  
class GFG { 
      
    // Returns numeric value of a  
    // subsequence of s. The subsequence 
    // to be picked is decided using bit 
    // pattern of num (We pick all those 
    // digits for which there is a set  
    // bit in num) 
    static int findSubSequence(String s,  
                                int num) 
    {  
        // Initialize the result 
        int res = 0; 
      
        // till n!=0 
        int i = 0; 
        while (num > 0) { 
              
            // if i-th bit is set  
            // then add this number 
            if ((num & 1) == 1) 
                res += s.charAt(i) - '0'; 
            i++; 
              
            // right shift i 
            num = num >> 1; 
        } 
      
        return res; 
    } 
  
    // function to find combined sum 
    // of all individual subsequence 
    // sum 
    static int combinedSum(String s) 
    { 
          
        // length of String 
        int n = s.length(); 
          
        // stores the combined 
        int c_sum = 0; 
      
        // 2^n-1 subsequences 
        int range = (1 << n) - 1; 
      
        // loop for all subsequences 
        for (int i = 0; i <= range; i++) 
            c_sum += findSubSequence(s, i); 
      
        // returns the combined sum 
        return c_sum; 
    } 
  
    // Driver function 
    public static void main (String[] args) { 
      
        String s = "123"; 
        System.out.println(combinedSum(s)); 
    } 
  
} 
  
// This code is contributed by Anuj_ 67 

Python 3

# Python 3 program to find the sum of 
# elements present in all subsequences 
   
# Returns numeric value of a subsequence of 
# s. The subsequence to be picked is decided 
# using bit pattern of num (We pick all those 
# digits for which there is a set bit in num) 
def findSubSequence(s, num): 
  
    # Initialize the result 
    res = 0
   
    # till n!=0 
    i = 0
    while (num) : 
           
        # if i-th bit is set  
        # then add this number 
        if (num & 1): 
            res += ord(s[i]) - ord('0') 
        i+=1
           
        # right shift i 
        num = num >> 1
   
    return res 
   
# function to find combined sum 
# of all individual subsequence sum 
def combinedSum(s): 
  
    # length of string 
    n = len(s) 
       
    # stores the combined 
    c_sum = 0
   
    # 2^n-1 subsequences 
    ran = (1 << n) - 1
   
    # loop for all subsequences 
    for i in range( ran+1): 
        c_sum += findSubSequence(s, i) 
   
    # returns the combined sum 
    return c_sum 
   
# driver code 
if __name__ == "__main__": 
      
    s = "123"
    print(combinedSum(s)) 

C#

// C# program to find the sum of elements 
// present in all subsequences 
using System; 
  
class GFG { 
      
    // Returns numeric value of a  
    // subsequence of s. The subsequence 
    // to be picked is decided using bit 
    // pattern of num (We pick all those 
    // digits for which there is a set  
    // bit in num) 
    static int findSubSequence(string s,  
                                 int num) 
    {  
        // Initialize the result 
        int res = 0; 
      
        // till n!=0 
        int i = 0; 
        while (num > 0) { 
              
            // if i-th bit is set  
            // then add this number 
            if ((num & 1) == 1) 
                res += s[i] - '0'; 
            i++; 
              
            // right shift i 
            num = num >> 1; 
        } 
      
        return res; 
    } 
  
    // function to find combined sum 
    // of all individual subsequence 
    // sum 
    static int combinedSum(string s) 
    { 
          
        // length of string 
        int n = s.Length; 
          
        // stores the combined 
        int c_sum = 0; 
      
        // 2^n-1 subsequences 
        int range = (1 << n) - 1; 
      
        // loop for all subsequences 
        for (int i = 0; i <= range; i++) 
            c_sum += findSubSequence(s, i); 
      
        // returns the combined sum 
        return c_sum; 
    } 
  
    // Driver function 
    public static void Main() 
    { 
        string s = "123"; 
        Console.Write(combinedSum(s)); 
    } 
  
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to find the sum of 
// elements present in all subsequences 
  
// Returns numeric value of a subsequence of 
// s. The subsequence to be picked is decided 
// using bit pattern of num (We pick all those 
// digits for which there is a set bit in num) 
function findSubSequence($s, $num) 
{  
      
    // Initialize the result 
    $res = 0; 
  
    // till n!=0 
    $i = 0; 
    while ($num) { 
          
        // if i-th bit is set  
        // then add this number 
        if ($num & 1) 
            $res += $s[$i] - '0'; 
        $i++; 
          
        // right shintift i 
        $num = $num >> 1; 
    } 
  
    return $res; 
} 
  
// function to find combined sum 
// of all individual subsequence sum 
function combinedSum(string $s) 
{ 
      
    // length of string 
    $n = strlen($s); 
      
    // stores the combined 
    $c_sum = 0; 
  
    // 2^n-1 subsequences 
    $range = (1 << $n) - 1; 
  
    // loop for all subsequences 
    for ($i = 0; $i <= $range; $i++) 
        $c_sum += findSubSequence($s, $i); 
  
    // returns the combined sum 
    return $c_sum; 
} 
  
    // Driver Code 
    $s = "123"; 
    echo combinedSum($s);  
      
// This code is contributed by Anuj_67 
?> 

Output:

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

PHP

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