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Count ordered pairs of positive numbers such that their sum is S and XOR is K in C++
We are given two numbers S and K. The goal is to find ordered pairs of positive numbers such that their sum is S and XOR is K.
We will do this by starting from i=1 to i<S-1 and j=i+1 to j<S. If any pair (i,j) has sum==S and i^j==K (XOR). Then increment count by 2 as (i,j) and (j,i) both will be counted as different pairs.
Let’s understand with examples.
Input
S=10 K=4
Output
Ordered pairs such that sum is S and XOR is K: 2
Explanation
Pairs will be (3,7) and (7,3)
Input
S=12 K=6
Output
Ordered pairs such that sum is S and XOR is K: 0
Explanation
No such pairs possible.
Approach used in the below program is as follows
We take integers S and K.
Function sumXOR(int s, int k) takes s and k and returns the count of ordered pairs with sum=s and xor=k
Take the initial variable count as 0 for pairs.
Traverse using two for loops for making pairs.
Start from i=1 to i<s-1. And j=i+1 to j<s-1.
Now for each pair (i,j) check if (i+j==s) && (i^j==k). If true increment count by 2 as (i,j) and (j,i) both are different pairs.
At the end of all loops count will have a total number of such pairs.
Return the count as result.
Example
#include <bits/stdc++.h>
using namespace std;
int sumXOR(int s, int k){
int count = 0;
for (int i = 1; i < s; i++){
for(int j=i+1; j<s-1; j++){
if( (i+j)==s && (i^j)==k){
count+=2; //(i,j) and (j,i) are two pairs
}
}
}
return count;
}
int main(){
int S = 9, K = 5;
cout <<"Ordered pairs such that sum is S and XOR is K: "<< sumXOR(S,K);
return 0;
}Output
If we run the above code it will generate the following output −
Ordered pairs such that sum is S and XOR is K: 4
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