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Count pairs of coordinates connected by a line with slope in the range [-K, K]
• Last Updated : 24 Mar, 2021

Given an integer K, and two arrays X[] and Y[] both consisting of N integers, where (X[i], Y[i]) is a coordinate in a plane, the task is to find the total number of pairs of points such that the line passing through them has a slope in the range [-K, K].

Examples:

Input: X[] = {2, 1, 0}, Y[] = {1, 2, 0}, K = 1
Output: 2
Explanation:
The set of pairs satisfying the given condition are [(0, 0), (2, 1)] and [(1, 2), (2, 1)].

Input: X[] = {2, 4}, Y[][] = {5, 6}, K = 1
Output: 1

Approach: The idea is to traverse through all pairs of points and check whether their slope lies in the range [-K, K] or not. Follow the steps below to solve the problem:

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the number of pairs``// of points such that the line passing``// through them has a slope in the range[-k, k]``void` `findPairs(vector<``int``> x, vector<``int``> y,``               ``int` `K)``{``    ``int` `n = x.size();` `    ``// Store the result``    ``int` `ans = 0;` `    ``// Traverse through all the``    ``// combination of points``    ``for` `(``int` `i = 0; i < n; ++i) {` `        ``for` `(``int` `j = i + 1; j < n; ++j) {` `            ``// If pair satisfies``            ``// the given condition``            ``if` `(K * ``abs``(x[i] - x[j])``                ``>= ``abs``(y[i] - y[j])) {` `                ``// Increment ans by 1``                ``++ans;``            ``}``        ``}``    ``}` `    ``// Print the result``    ``cout << ans;``}` `// Driver Code``int` `main()``{``    ``vector<``int``> X = { 2, 1, 0 },``                ``Y = { 1, 2, 0 };``    ``int` `K = 1;` `    ``// Function Call``    ``findPairs(X, Y, K);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG``{` `// Function to find the number of pairs``// of points such that the line passing``// through them has a slope in the range[-k, k]``static` `void` `findPairs(``int``[] x, ``int``[] y,``               ``int` `K)``{``    ``int` `n = x.length;` `    ``// Store the result``    ``int` `ans = ``0``;` `    ``// Traverse through all the``    ``// combination of points``    ``for` `(``int` `i = ``0``; i < n; ++i) {` `        ``for` `(``int` `j = i + ``1``; j < n; ++j) {` `            ``// If pair satisfies``            ``// the given condition``            ``if` `(K * Math.abs(x[i] - x[j])``                ``>= Math.abs(y[i] - y[j])) {` `                ``// Increment ans by 1``                ``++ans;``            ``}``        ``}``    ``}` `    ``// Print the result``    ``System.out.print(ans);``}`  `// Driven Code``public` `static` `void` `main(String[] args)``{``    ``int``[] X = { ``2``, ``1``, ``0` `};``    ``int``[] Y = { ``1``, ``2``, ``0` `};``    ``int` `K = ``1``;` `    ``// Function Call``    ``findPairs(X, Y, K);``}``}` `// This code is contributed by sanjoy_62.`

## Python3

 `# Python3 program for the above approach` `# Function to find the number of pairs``# of points such that the line passing``# through them has a slope in the range[-k, k]``def` `findPairs(x, y, K):``    ``n ``=` `len``(x)` `    ``# Store the result``    ``ans ``=` `0` `    ``# Traverse through all the``    ``# combination of points``    ``for` `i ``in` `range``(n):``        ``for` `j ``in` `range``(i ``+` `1``, n):``          ` `            ``# If pair satisfies``            ``# the given condition``            ``if` `(K ``*` `abs``(x[i] ``-` `x[j]) >``=` `abs``(y[i] ``-` `y[j])):``              ` `                ``# Increment ans by 1``                ``ans ``+``=` `1` `    ``# Print the result``    ``print` `(ans)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``X ``=` `[``2``, ``1``, ``0``]``    ``Y ``=` `[``1``, ``2``, ``0``]``    ``K ``=` `1` `    ``# Function Call``    ``findPairs(X, Y, K)` ` ``# This code is contributed by mohit kumar 29.`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find the number of pairs``// of points such that the line passing``// through them has a slope in the range[-k, k]``static` `void` `findPairs(``int``[] x, ``int``[] y,``                      ``int` `K)``{``    ``int` `n = x.Length;` `    ``// Store the result``    ``int` `ans = 0;` `    ``// Traverse through all the``    ``// combination of points``    ``for``(``int` `i = 0; i < n; ++i)``    ``{``        ``for``(``int` `j = i + 1; j < n; ++j)``        ``{``            ` `            ``// If pair satisfies``            ``// the given condition``            ``if` `(K * Math.Abs(x[i] - x[j]) >=``                    ``Math.Abs(y[i] - y[j]))``            ``{``                ` `                ``// Increment ans by 1``                ``++ans;``            ``}``        ``}``    ``}` `    ``// Print the result``    ``Console.WriteLine(ans);``}` `// Driver Code``public` `static` `void` `Main(String []args)``{``    ``int``[] X = { 2, 1, 0 };``    ``int``[] Y = { 1, 2, 0 };``    ``int` `K = 1;` `    ``// Function Call``    ``findPairs(X, Y, K);``}``}` `// This code is contributed by souravghosh0416`

## Javascript

 ``
Output:
`2`

Time Complexity: O(N2)
Auxiliary Space: O(1)

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