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Sum of decimal equivalent of all possible pairs of Binary representation of a Number

  • Difficulty Level : Medium
  • Last Updated : 11 May, 2021

Given a number N. The task is to find the sum of the decimal equivalent of all the pairs formed from the binary representation of the given number.

Examples: 

Input: N = 4 
Output: 4 
Binary equivalent of 4 is 100. 
All possible pairs are 10, 10, 00 and their decimal equivalent are 2, 2, 0 respectively. 
So, 2 + 2+ 0 = 4

Input: N = 11 
Output: 13 
All possible pairs are: 10, 11, 11, 01, 01, 11 
Sum = 2 + 3 + 3 + 1 + 1 + 3 = 13

Approach:  



  1. Find the binary equivalent of N and store it in a vector.
  2. Run two loops to consider each and every pair formed from the bits of binary equivalent stored in the vector.
  3. Find the decimal equivalent of all the pairs and add them.
  4. Return the sum.

Below is the implementation of the above approach: 

C++




// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the sum
int sumOfPairs(int n)
{
 
    // Store the Binary equivalent of decimal
    // number in reverse order
    vector<int> v;
    int sum = 0;
 
    // Calculate binary equivalent of decimal number
    while (n > 0) {
        v.push_back(n % 2);
        n = n / 2;
    }
 
    // for correct binary representation
    reverse(v.begin(), v.end());
 
    // Consider every pair
    for (int i = 0; i < v.size() - 1; i++) {
        for (int j = i + 1; j < v.size(); j++)
 
        {
            // handles all combinations of 01
            if (v[i] == 0 && v[j] == 1)
                sum += 1;
 
            // handles all combinations of 11
            if (v[i] == 1 && v[j] == 1)
                sum += 3;
 
            // handles all combinations of 10
            if (v[i] == 1 && v[j] == 0)
                sum += 2;
        }
    }
 
    return sum;
}
 
// Driver code
int main()
{
    int N = 5;
 
    cout << sumOfPairs(N);
 
    return 0;
}

Java




// Java implementation of above approach
import java.util.*;
 
class GFG
{
public static int sumOfPairs(int n)
{
    // Store the Binary equivalent 
    // of decimal number in reverse order
    ArrayList<Integer> v = new ArrayList<Integer>();
    int sum = 0;
     
    // Calculate binary equivalent
    // of decimal number
    while (n > 0)
    {
        v.add(n % 2);
        n = n / 2;
}
 
Collections.reverse(v);
     
for (int i = 0; i < v.size() - 1; i++)
{
    for (int j = i + 1; j < v.size(); j++)
 
    {
        // handles all combinations of 01
        if (v.get(i) == 0 && v.get(j) == 1)
            sum += 1;
 
        // handles all combinations of 11
        if (v.get(i) == 1 && v.get(j) == 1)
            sum += 3;
 
        // handles all combinations of 10
        if (v.get(i) == 1 && v.get(j) == 0)
            sum += 2;
    }
}
 
return sum;
}
 
// Driver Code
public static void main (String[] args)
{
    int N = 5;
 
    System.out.print(sumOfPairs(N));
}
}
 
// This code is contributed by Kirti_Mangal

Python3




# Python3 program to find the sum
 
# Function to find the sum
def sumofPairs(n) :
 
    # Store the Binary equivalent of decimal
    # number in reverse order
    v = []
    sum = 0
 
    # Calculate binary equivalent of decimal number
    while n > 0 :
        v.append(n % 2)
        n = n // 2
 
    # for correct binary representation
    v.reverse()
 
    # Consider every pair
    for i in range(len(v) - 1) :
 
        for j in range(i + 1, len(v)) :
 
            # handles all combinations of 01
            if v[i] == 0 and v[j] == 1 :
                sum += 1
 
            #  handles all combinations of 11
            if v[i] == 1 and v[j] == 1 :
                sum += 3
 
            # handles all combinations of 10
            if v[i] == 1 and v[j] == 0 :
                sum += 2
 
    return sum
 
# Driver Code
if __name__ == "__main__" :
     
    N = 5
 
    # function calling
    print(sumofPairs(N))
 
# This code is contributed by ANKITRAI1

C#




// C# implementation of above approach
using System;
using System.Collections.Generic;
 
class GFG
{
    public static int sumOfPairs(int n)
    {
        // Store the Binary equivalent
        // of decimal number in reverse order
        List<int> v = new List<int>();
        int sum = 0;
 
        // Calculate binary equivalent
        // of decimal number
        while (n > 0)
        {
            v.Add(n % 2);
            n = n / 2;
        }
 
    v.Reverse();
 
    for (int i = 0; i < v.Count - 1; i++)
    {
        for (int j = i + 1; j < v.Count; j++)
 
        {
            // handles all combinations of 01
            if (v[i] == 0 && v[j] == 1)
                sum += 1;
 
            // handles all combinations of 11
            if (v[i] == 1 && v[j] == 1)
                sum += 3;
 
            // handles all combinations of 10
            if (v[i] == 1 && v[j] == 0)
                sum += 2;
        }
    }
 
    return sum;
    }
 
    // Driver Code
    public static void Main (String[] args)
    {
        int N = 5;
 
        Console.WriteLine(sumOfPairs(N));
    }
}
 
/* This code contributed by PrinciRaj1992 */

Javascript




<script>
 
// Javascript implementation of above approach
 
// Function to find the sum
function sumOfPairs(n)
{
     
    // Store the Binary equivalent of
    // decimal number in reverse order
    var v = [];
    var sum = 0;
 
    // Calculate binary equivalent
    // of decimal number
    while (n > 0)
    {
        v.push(n % 2);
        n = parseInt(n / 2);
    }
 
    // For correct binary representation
    v.reverse();
 
    // Consider every pair
    for(var i = 0; i < v.length - 1; i++)
    {
        for(var j = i + 1; j < v.length; j++)
        {
             
            // Handles all combinations of 01
            if (v[i] == 0 && v[j] == 1)
                sum += 1;
 
            // Handles all combinations of 11
            if (v[i] == 1 && v[j] == 1)
                sum += 3;
 
            // Handles all combinations of 10
            if (v[i] == 1 && v[j] == 0)
                sum += 2;
        }
    }
    return sum;
}
 
// Driver code
var N = 5;
document.write(sumOfPairs(N));
 
// This code is contributed by rrrtnx
 
</script>
Output: 
6

 




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