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:
- Initialize a variable, say ans to 0 to store the resultant count of pairs.
- Now, generate all possible pairs of coordinates and if the slope of the 2 points (X[i], Y[i]) and (X[j], Y[j]) lies in the range [-K, K], then increment ans by 1.
- After completing the above steps, print the value of and as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>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 Codeint 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 approachimport 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 Codepublic 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 Codeif __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 approachusing 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 Codepublic 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
<script> // Javascript 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] function findPairs(x, y, K) { let n = x.length; // Store the result let ans = 0; // Traverse through all the // combination of points for (let i = 0; i < n; ++i) { for (let 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 document.write(ans); } // Driver code let X = [ 2, 1, 0 ], Y = [ 1, 2, 0 ]; let K = 1; // Function Call findPairs(X, Y, K); // This code is contributed by divyesh072019.</script> |
Output:
2
Time Complexity: O(N2)
Auxiliary Space: O(1)
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