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Count Triplets That Can Form Two Arrays of Equal XOR in C++
Suppose we have an array of integers arr. We want to select three indices like i, j and k where (0 <= i < j <= k < N), N is the size of array. The values of a and b are as follows: a = arr[i] XOR arr[i + 1] XOR ... XOR arr[j - 1] b = arr[j] XOR arr[j + 1] XOR ... XOR arr[k] We have to find the number of triplets (i, j, k) Where a is same as b.
So, if the input is like [2,3,1,6,7], then the output will be 4, as the triplets are (0,1,2), (0,2,2), (2,3,4) and (2,4,4)
To solve this, we will follow these steps −
ret := 0
n := size of arr
for initialize i := 1, when i < n, update (increase i by 1), do −
Define one map m
x1 := 0, x2 := 0
for initialize j := i - 1, when j >= 0, update (decrease j by 1), do −
x1 := x1 XOR arr[j]
(increase m[x1] by 1)
for initialize j := i, when j < n, update (increase j by 1), do −
x2 := x2 XOR arr[j]
ret := ret + m[x2]
return ret
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int countTriplets(vector<int>& arr) {
int ret = 0;
int n = arr.size();
for (int i = 1; i < n; i++) {
map<int, int> m;
int x1 = 0;
int x2 = 0;
for (int j = i - 1; j >= 0; j--) {
x1 = x1 ^ arr[j];
m[x1]++;
}
for (int j = i; j < n; j++) {
x2 = x2 ^ arr[j];
ret += m[x2];
}
}
return ret;
}
};
main(){
Solution ob;
vector<int> v = {2,3,1,6,7};
cout << (ob.countTriplets(v));
}Input
{2,3,1,6,7}Output
4
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