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Count pairs in an array such that the absolute difference between them is ≥ K

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  • Difficulty Level : Easy
  • Last Updated : 07 Jun, 2022

Given an array arr[] and an integer K, the task is to find the count of pairs (arr[i], arr[j]) from the array such that |arr[i] – arr[j]| ≥ K. Note that (arr[i], arr[j]) and arr[j], arr[i] will be counted only once.
Examples: 
 

Input: arr[] = {1, 2, 3, 4}, K = 2 
Output:
All valid pairs are (1, 3), (1, 4) and (2, 4)
Input: arr[] = {7, 4, 12, 56, 123}, K = 50 
Output:
 

Approach: Sort the given array. Now for every element arr[i], find the first element on the right arr[j] such that (arr[j] – arr[i]) ≥ K. This is because after this element, every element will satisfy the same condition with arr[i] as the array is sorted and the count of elements that will make a valid pair with arr[i] will be (N – j) where N is the size of the given array.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the count of required pairs
int count(int arr[], int n, int k)
{
 
    // Sort the given array
    sort(arr, arr + n);
 
    // To store the required count
    int cnt = 0;
    int i = 0, j = 1;
 
    while (i < n && j < n) {
 
        // Update j such that it is always > i
        j = (j <= i) ? (i + 1) : j;
 
        // Find the first element arr[j] such that
        // (arr[j] - arr[i]) >= K
        // This is because after this element, all
        // the elements will have absolute difference
        // with arr[i] >= k and the count of
        // valid pairs will be (n - j)
        while (j < n && (arr[j] - arr[i]) < k)
            j++;
 
        // Update the count of valid pairs
        cnt += (n - j);
 
        // Get to the next element to repeat the steps
        i++;
    }
 
    // Return the count
    return cnt;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 3, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int k = 2;
 
    cout << count(arr, n, k);
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class solution
{
 
// Function to return the count of required pairs
static int count(int arr[], int n, int k)
{
 
    // Sort the given array
    Arrays.sort(arr);
 
    // To store the required count
    int cnt = 0;
    int i = 0, j = 1;
 
    while (i < n && j < n) {
 
        // Update j such that it is always > i
        j = (j <= i) ? (i + 1) : j;
 
        // Find the first element arr[j] such that
        // (arr[j] - arr[i]) >= K
        // This is because after this element, all
        // the elements will have absolute difference
        // with arr[i] >= k and the count of
        // valid pairs will be (n - j)
        while (j < n && (arr[j] - arr[i]) < k)
            j++;
 
        // Update the count of valid pairs
        cnt += (n - j);
 
        // Get to the next element to repeat the steps
        i++;
    }
 
    // Return the count
    return cnt;
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 1, 2, 3, 4 };
    int n = arr.length;
    int k = 2;
 
    System.out.println(count(arr, n, k));
 
}
}

Python3




# Python3 implementation of the approach
 
# Function to return the count of required pairs
def count(arr, n, k) :
 
    # Sort the given array
    arr.sort();
 
    # To store the required count
    cnt = 0;
    i = 0; j = 1;
 
    while (i < n and j < n) :
 
        # Update j such that it is always > i
        if j <= i :
            j = i + 1
        else :
            j = j
 
        # Find the first element arr[j] such that
        # (arr[j] - arr[i]) >= K
        # This is because after this element, all
        # the elements will have absolute difference
        # with arr[i] >= k and the count of
        # valid pairs will be (n - j)
        while (j < n and (arr[j] - arr[i]) < k) :
            j += 1;
 
        # Update the count of valid pairs
        cnt += (n - j);
 
        # Get to the next element to repeat the steps
        i += 1;
 
    # Return the count
    return cnt;
 
 
# Driver code
if __name__ == "__main__" :
 
    arr = [ 1, 2, 3, 4 ];
    n = len(arr);
    k = 2;
 
    print(count(arr, n, k));
     
# This code is contributed by AnkitRai01

C#




// C# implementation of the approach
using System;
 
class GFG
{
     
// Function to return the count of required pairs
static int count(int []arr, int n, int k)
{
 
    // Sort the given array
    Array.Sort(arr);
 
    // To store the required count
    int cnt = 0;
    int i = 0, j = 1;
 
    while (i < n && j < n)
    {
 
        // Update j such that it is always > i
        j = (j <= i) ? (i + 1) : j;
 
        // Find the first element arr[j] such that
        // (arr[j] - arr[i]) >= K
        // This is because after this element, all
        // the elements will have absolute difference
        // with arr[i] >= k and the count of
        // valid pairs will be (n - j)
        while (j < n && (arr[j] - arr[i]) < k)
            j++;
 
        // Update the count of valid pairs
        cnt += (n - j);
 
        // Get to the next element to repeat the steps
        i++;
    }
 
    // Return the count
    return cnt;
}
 
// Driver code
static public void Main ()
{
     
    int []arr = { 1, 2, 3, 4 };
    int n = arr.Length;
    int k = 2;
 
    Console.Write(count(arr, n, k));
 
}
}
 
// This code is contributed by jit_t.

Javascript




<script>
 
// JavaScript implementation of the approach
 
// Function to return the count of required pairs
function count(arr, n, k) {
 
    // Sort the given array
    arr.sort();
 
    // To store the required count
    var cnt = 0;
    var i = 0;
    var j = 1;
 
    while (i < n && j < n) {
 
        // Update j such that it is always > i
        if (j <= i)
            j = i + 1
        else
            j = j
 
        // Find the first element arr[j] such that
        // (arr[j] - arr[i]) >= K
        // This is because after this element, all
        // the elements will have absolute difference
        // with arr[i] >= k and the count of
        // valid pairs will be (n - j)
        while (j < n && (arr[j] - arr[i]) < k)
            j += 1;
 
        // Update the count of valid pairs
        cnt += (n - j);
 
        // Get to the next element to repeat the steps
        i += 1;
    }
 
    // Return the count
    return cnt;
 
}
 
// Driver code 
var arr = [ 1, 2, 3, 4 ];
var n = arr.length;
var k = 2;
 
document.write(count(arr, n, k));
     
// This code is contributed by AnkThon
 
 
</script>

Output: 

3

 

Time Complexity: O(n * log n)

Auxiliary Space: O(1)


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