# Count elements in first Array with absolute difference greater than K with an element in second Array

Given two **arrays arr1[] and arr2[]** and an **integer K**, our task is to find the number elements in the first array, for an element **x, in arr1[]**, there exists at least one element **y, in arr2[]** such that **absolute difference** of x and y is greater than the integer **K**.

**Examples:**

Input:arr1 = {3, 1, 4}, arr2 = {5, 1, 2}, K = 2

Output:2

Explanation:

Such elements are 1 and 4.

For 1, arr2[] has 5 and abs(1 – 5) = 4 which is greater than 2.

For 4, arr2[] has 1 and abs(4 – 1) = 3 which again is greater than 2.

Input:arr1 = {1, 2}, arr2 = {4, 6}, K = 3

Output:2

Explanation:

Such elements are 1 and 2.

For 1, arr2[] has 6 and abs(1 – 6) = 5 which is greater than 3.

For 2, arr2[] has 6 and abs(2 – 6) = 4 which is greater than 3.

**Naive Approach:** Iterate for each element in arr1[] and check whether or not there exists an element in arr2 such that their absolute difference is greater than the value K.

* Time complexity: O(N * M)* where N and M are the sizes of the arrays 1 and 2 respectively.

**Efficient Approach:** To optimize the above method we have to observe that for each element in arr1[], we need only the **smallest and largest element of arr2[]** to check if it is distant or not. For each element x, in arr1, if the absolute difference of smallest or the largest value and x is greater than K then that element is distant.

Below is the implementation of the above approach:

## C++

`// C++ program to count elements in first Array ` `// with absolute difference greater than K ` `// with an element in second Array ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to count the such elements ` `void` `countDist(` `int` `arr1[], ` `int` `n, ` `int` `arr2[], ` ` ` `int` `m, ` `int` `k) ` `{ ` ` ` `// Store count of required elements in arr1 ` ` ` `int` `count = 0; ` ` ` ` ` `// Initialise the smallest and the largest ` ` ` `// value from the second array arr2[] ` ` ` `int` `smallest = arr2[0]; ` ` ` `int` `largest = arr2[0]; ` ` ` ` ` `// Find the smallest and ` ` ` `// the largest element in arr2 ` ` ` `for` `(` `int` `i = 0; i < m; i++) { ` ` ` `smallest = max(smallest, arr2[i]); ` ` ` `largest = min(largest, arr1[i]); ` ` ` `} ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` ` ` `// Check if absolute difference of smallest ` ` ` `// and arr1[i] or largest and arr1[i] is > K ` ` ` `// then arr[i] is a required element ` ` ` `if` `(` `abs` `(arr1[i] - smallest) > k ` ` ` `|| ` `abs` `(arr1[i] - largest) > k) ` ` ` `count++; ` ` ` `} ` ` ` ` ` `// Print the final result ` ` ` `cout << count; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `arr1[] = { 3, 1, 4 }; ` ` ` `int` `n = ` `sizeof` `(arr1) / ` `sizeof` `(arr1[0]); ` ` ` `int` `arr2[] = { 5, 1, 2 }; ` ` ` `int` `m = ` `sizeof` `(arr2) / ` `sizeof` `(arr2[0]); ` ` ` `int` `k = 2; ` ` ` ` ` `countDist(arr1, n, arr2, m, k); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count elements in first Array ` `// with absolute difference greater than K ` `// with an element in second Array ` `class` `GFG{ ` ` ` `// Function to count the such elements ` `static` `void` `countDist(` `int` `arr1[], ` `int` `n, ` ` ` `int` `arr2[], ` `int` `m, ` ` ` `int` `k) ` `{ ` ` ` `// Store count of required elements in arr1 ` ` ` `int` `count = ` `0` `; ` ` ` ` ` `// Initialise the smallest and the largest ` ` ` `// value from the second array arr2[] ` ` ` `int` `smallest = arr2[` `0` `]; ` ` ` `int` `largest = arr2[` `0` `]; ` ` ` ` ` `// Find the smallest and ` ` ` `// the largest element in arr2 ` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++) ` ` ` `{ ` ` ` `smallest = Math.max(smallest, arr2[i]); ` ` ` `largest = Math.min(largest, arr1[i]); ` ` ` `} ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) ` ` ` `{ ` ` ` ` ` `// Check if absolute difference ` ` ` `// of smallest and arr1[i] or ` ` ` `// largest and arr1[i] is > K ` ` ` `// then arr[i] is a required element ` ` ` `if` `(Math.abs(arr1[i] - smallest) > k || ` ` ` `Math.abs(arr1[i] - largest) > k) ` ` ` `count++; ` ` ` `} ` ` ` ` ` `// Print the final result ` ` ` `System.out.print(count); ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `arr1[] = { ` `3` `, ` `1` `, ` `4` `}; ` ` ` `int` `n = arr1.length; ` ` ` `int` `arr2[] = { ` `5` `, ` `1` `, ` `2` `}; ` ` ` `int` `m = arr2.length; ` ` ` `int` `k = ` `2` `; ` ` ` ` ` `countDist(arr1, n, arr2, m, k); ` `} ` `} ` ` ` `// This code is contributed by 29AjayKumar ` |

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## Python3

`# Python3 program to count elements in the first Array ` `# with an absolute difference greater than K ` `# with an element in the second Array ` ` ` `# Function to count the such elements ` `def` `countDist(arr1, n, arr2, m, k): ` ` ` ` ` `# Store count of required elements in arr1 ` ` ` `count ` `=` `0` ` ` ` ` `# Initialise the smallest and the largest ` ` ` `# value from the second array arr2[] ` ` ` `smallest ` `=` `arr2[` `0` `] ` ` ` `largest ` `=` `arr2[` `0` `] ` ` ` ` ` `# Find the smallest and ` ` ` `# the largest element in arr2 ` ` ` `for` `i ` `in` `range` `(m): ` ` ` `smallest ` `=` `max` `(smallest, arr2[i]) ` ` ` `largest ` `=` `min` `(largest, arr1[i]) ` ` ` ` ` `for` `i ` `in` `range` `(n): ` ` ` ` ` `# Check if absolute difference of smallest ` ` ` `# and arr1[i] or largest and arr1[i] is > K ` ` ` `# then arr[i] is a required element ` ` ` `if` `(` `abs` `(arr1[i] ` `-` `smallest) > k ` ` ` `or` `abs` `(arr1[i] ` `-` `largest) > k): ` ` ` `count ` `+` `=` `1` ` ` ` ` `# Print final result ` ` ` `print` `(count) ` ` ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `arr1` `=` `[ ` `3` `, ` `1` `, ` `4` `] ` ` ` `n ` `=` `len` `(arr1) ` ` ` `arr2` `=` `[ ` `5` `, ` `1` `, ` `2` `] ` ` ` `m ` `=` `len` `(arr2) ` ` ` `k ` `=` `2` ` ` ` ` `countDist(arr1, n, arr2, m, k) ` ` ` `# This code is contributed by mohit kumar 29 ` |

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## C#

`// C# program to count elements in first array ` `// with absolute difference greater than K ` `// with an element in second Array ` `using` `System; ` ` ` `class` `GFG{ ` ` ` `// Function to count the such elements ` `static` `void` `countDist(` `int` `[]arr1, ` `int` `n, ` ` ` `int` `[]arr2, ` `int` `m, ` ` ` `int` `k) ` `{ ` ` ` `// Store count of required elements in arr1 ` ` ` `int` `count = 0; ` ` ` ` ` `// Initialise the smallest and the largest ` ` ` `// value from the second array arr2[] ` ` ` `int` `smallest = arr2[0]; ` ` ` `int` `largest = arr2[0]; ` ` ` ` ` `// Find the smallest and ` ` ` `// the largest element in arr2 ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `{ ` ` ` `smallest = Math.Max(smallest, arr2[i]); ` ` ` `largest = Math.Min(largest, arr1[i]); ` ` ` `} ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` ` ` `// Check if absolute difference ` ` ` `// of smallest and arr1[i] or ` ` ` `// largest and arr1[i] is > K ` ` ` `// then arr[i] is a required element ` ` ` `if` `(Math.Abs(arr1[i] - smallest) > k || ` ` ` `Math.Abs(arr1[i] - largest) > k) ` ` ` `count++; ` ` ` `} ` ` ` ` ` `// Print the readonly result ` ` ` `Console.Write(count); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `[]arr1 = { 3, 1, 4 }; ` ` ` `int` `n = arr1.Length; ` ` ` `int` `[]arr2 = { 5, 1, 2 }; ` ` ` `int` `m = arr2.Length; ` ` ` `int` `k = 2; ` ` ` ` ` `countDist(arr1, n, arr2, m, k); ` `} ` `} ` ` ` `// This code is contributed by gauravrajput1 ` |

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**Output:**

2

* Time Complexity: O(N + M)*, where N and M are the sizes of the given arrays.

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