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# 2857. Count Pairs of Points With Distance k

## Problem Statement

<br>

You are given a **2D** integer array `coordinates` and an integer `k`, where `coordinates[i] = [xi, yi]` are the coordinates of the `ith` point in a 2D plane.

We define the **distance** between two points `(x1, y1)` and `(x2, y2)` as `(x1 XOR x2) + (y1 XOR y2)` where `XOR` is the bitwise `XOR` operation.

Return *the number of pairs* `(i, j)` *such that* `i < j` *and the distance between points* `i` *and* `j` *is equal to* `k`.

&#x20;

**Example 1:**

<pre><code><strong>Input: coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5
</strong><strong>Output: 2
</strong><strong>Explanation: We can choose the following pairs:
</strong>- (0,1): Because we have (1 XOR 4) + (2 XOR 2) = 5.
- (2,3): Because we have (1 XOR 5) + (3 XOR 2) = 5.
</code></pre>

**Example 2:**

<pre><code><strong>Input: coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0
</strong><strong>Output: 10
</strong><strong>Explanation: Any two chosen pairs will have a distance of 0. There are 10 ways to choose two pairs.
</strong></code></pre>

&#x20;

**Constraints:**

* `2 <= coordinates.length <= 50000`
* `0 <= xi, yi <= 106`
* `0 <= k <= 100`

## Intuition

```
Approach:

Since K constraint is less,
We can iterate throught the k

x1^x2 = i , y1^y2 = k-i
a^b = c -> b = c^a

Go through all k's


```

### Links

<https://leetcode.com/problems/count-pairs-of-points-with-distance-k/description/>

### Video Links

<https://www.youtube.com/watch?v=1Hp6Hsghtno&ab_channel=AryanMittal>

### Approach 1:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    int countPairs(vector<vector<int>>& arr, int k) {
        map<pair<int,int> , int> mp;
        int ans = 0;
        for(auto &it: arr){
            int x1 = it[0], y1 = it[1];
            for(int i=0; i<=k; i++){
                int x2 = x1^i;
                int y2 = y1^(k-i);

                ans += mp[{x2,y2}];
            }

            mp[{x1,y1}]++;
        }

        return ans;
    }
};
```

{% endcode %}

### Approach 2:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###