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
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; } |
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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 |
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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)) |
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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 |
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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 ?> |
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Output:
24
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