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Equal Sum and XOR of three Numbers

  • Difficulty Level : Easy
  • Last Updated : 17 Aug, 2021

Given an integer N. The task is to count the numbers of pairs of integers A and B such that A + B + N = A ^ B ^ N and A and B are less than N.
Examples: 
 

Input: N = 2 
Output:
Explanation:- 
For N = 2 
2 XOR 0 XOR 0 = 2+0+0 
2 XOR 0 XOR 1 = 2+0+1 
2 XOR 0 XOR 2 != 2+0+2 
2 XOR 1 XOR 0 = 2+1+0 
2 XOR 1 XOR 1 != 2+1+1 
2 XOR 1 XOR 2 != 2+1+2 
2 XOR 2 XOR 0 != 2+2+0 
2 XOR 2 XOR 1 != 2+2+1 
2 XOR 2 XOR 2 != 2+2+2
So (0, 0), (0, 1) and (1, 0) are the required pairs. So the output is 3.
Input: N = 4 
Output:
 

 

Approach
To make the sum of three numbers equal to the xor of three number with one of the number given we can do following:- 
 

  1. Represent the fixed number in binary form.
  2. Traverse the binary expansion of the fixed number. 
    • If you find a 1 there is only one condition i.e. you take the other two number’s binary bits as 0 and 0.
    • If you find a 0 there will be three conditions i.e. either you can have binary bits as (0, 0), (1, 0) 
      or (0, 1).
  3. The following triplets of bits will never go for a carry so they are valid.
  4. So the answer will be 3^(number of zeros in binary representation).

Below is the implementation of the above approach: 
 



C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Defining ull to unsigned long long int
typedef unsigned long long int ull;
 
// Function to calculate power of 3
ull calculate(int bit_cnt)
{
    ull res = 1;
    while (bit_cnt--) {
        res = res * 3;
    }
 
    return res;
}
 
// Function to return the count of the
// unset bit ( zeros )
int unset_bit_count(ull n)
{
    int count = 0;
    while (n) {
 
        // Check the bit is 0 or not
        if ((n & 1) == 0)
            count++;
        // Right shifting ( dividing by 2 )
        n = n >> 1;
    }
    return count;
}
 
// Driver Code
int main()
{
    ull n;
    n = 2;
 
    int count = unset_bit_count(n);
 
    ull ans = calculate(count);
 
    cout << ans << endl;
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
// Function to calculate power of 3
static long calculate(int bit_cnt)
{
    long res = 1;
    while (bit_cnt-- > 0)
    {
        res = res * 3;
    }
 
    return res;
}
 
// Function to return the count of the
// unset bit ( zeros )
static int unset_bit_count(long n)
{
    int count = 0;
    while (n > 0)
    {
 
        // Check the bit is 0 or not
        if ((n & 1) == 0)
            count++;
             
        // Right shifting ( dividing by 2 )
        n = n >> 1;
    }
    return count;
}
 
// Driver Code
public static void main(String[] args)
{
    long n;
    n = 2;
 
    int count = unset_bit_count(n);
 
    long ans = calculate(count);
 
    System.out.println(ans);
}
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 implementation of the approach
 
# Function to calculate power of 3
def calculate(bit_cnt):
 
    res = 1;
    while (bit_cnt > 0):
        bit_cnt -= 1;
        res = res * 3;
    return res;
 
# Function to return the count of the
# unset bit ( zeros )
def unset_bit_count(n):
 
    count = 0;
    while (n > 0):
         
        # Check the bit is 0 or not
        if ((n & 1) == 0):
            count += 1;
             
        # Right shifting ( dividing by 2 )
        n = n >> 1;
     
    return count;
 
# Driver Code
if __name__ == '__main__':
 
    n = 2;
 
    count = unset_bit_count(n);
 
    ans = calculate(count);
 
    print(ans);
 
# This code contributed by Rajput-Ji

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
// Function to calculate power of 3
static long calculate(int bit_cnt)
{
    long res = 1;
    while (bit_cnt-- > 0)
    {
        res = res * 3;
    }
 
    return res;
}
 
// Function to return the count of the
// unset bit (zeros)
static int unset_bit_count(long n)
{
    int count = 0;
    while (n > 0)
    {
 
        // Check the bit is 0 or not
        if ((n & 1) == 0)
            count++;
             
        // Right shifting ( dividing by 2 )
        n = n >> 1;
    }
    return count;
}
 
// Driver Code
public static void Main(String[] args)
{
    long n;
    n = 2;
 
    int count = unset_bit_count(n);
 
    long ans = calculate(count);
 
    Console.WriteLine(ans);
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
// Javascript implementation of
// the above approach
 
// Function to calculate power of 3
function calculate(bit_cnt)
{
    let res = 1;
    while (bit_cnt--) {
        res = res * 3;
    }
 
    return res;
}
 
// Function to return the count of the
// unset bit ( zeros )
function unset_bit_count(n)
{
    let count = 0;
    while (n) {
 
        // Check the bit is 0 or not
        if ((n & 1) == 0)
            count++;
        // Right shifting ( dividing by 2 )
        n = n >> 1;
    }
    return count;
}
 
// Driver Code
    let n;
    n = 2;
 
    let count = unset_bit_count(n);
 
    let ans = calculate(count);
 
    document.write(ans);
 
</script>
Output: 
3

 

Time Complexity: O(Number of unset_bits). 
Auxiliary Space: O(1).  




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