Given four integers N, R, X, and Y such that it represents a circle of radius R with [X, Y] as coordinates of the center. The task is to find N random points inside or on the circle.
Examples:
Input: R = 12, X = 3, Y = 3, N = 5
Output: (7.05, -3.36) (5.21, -7.49) (7.53, 0.19) (-2.37, 12.05) (1.45, 11.80)
Input: R = 5, X = 1, Y = 1, N = 3
Output: (4.75, 1.03) (2.57, 5.21) (-1.98, -0.76)
Approach: To find a random point in or on a circle we need two components, an angle(theta) and distance(D) from the center. After that Now, the point (xi, yi) can be expressed as:
xi = X + D * cos(theta) yi = Y + D * sin(theta)
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;#define PI 3.141592653589// Return a random double between 0 & 1double uniform(){ return (double)rand() / RAND_MAX;}// Function to find the N random points on// the given circlevector<pair<double, double> > randPoint( int r, int x, int y, int n){ // Result vector vector<pair<double, double> > res; for (int i = 0; i < n; i++) { // Get Angle in radians double theta = 2 * PI * uniform(); // Get length from center double len = sqrt(uniform()) * r; // Add point to results. res.push_back({ x + len * cos(theta), y + len * sin(theta) }); } // Return the N points return res;}// Function to display the content of// the vector Avoid printVector( vector<pair<double, double> > A){ // Iterate over A for (pair<double, double> P : A) { // Print the N random points stored printf("(%.2lf, %.2lf)\n", P.first, P.second); }}// Driver Codeint main(){ // Given dimensions int R = 12; int X = 3; int Y = 3; int N = 5; // Function Call printVector(randPoint(R, X, Y, N)); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{ static final double PI = 3.141592653589;static class pair { double first, second; public pair(double first, double second) { super(); this.first = first; this.second = second; }}// Return a random double between 0 & 1static double uniform(){return Math.random();}// Function to find the N random points on// the given circlestatic Vector<pair> randPoint(int r, int x, int y, int n){ // Result vector Vector<pair> res = new Vector<pair>(); for(int i = 0; i < n; i++) { // Get Angle in radians double theta = 2 * PI * uniform(); // Get length from center double len = Math.sqrt(uniform()) * r; // Add point to results. res.add(new pair(x + len * Math.cos(theta), y + len * Math.sin(theta))); } // Return the N points return res;}// Function to display the content of// the vector Astatic void printVector(Vector<pair> A){ // Iterate over A for(pair P : A) { // Print the N random points stored System.out.printf("(%.2f, %.2f)\n", P.first, P.second); }}// Driver Codepublic static void main(String[] args){ // Given dimensions int R = 12; int X = 3; int Y = 3; int N = 5; // Function call printVector(randPoint(R, X, Y, N));}}// This code is contributed by Rajput-Ji |
Python3
# Python program for the above approachimport mathimport randomPI = 3.141592653589;class pair: def __init__(self, first, second): self.first = first; self.second = second;# Return a random between 0 & 1def uniform(): return random.random();# Function to find the N random points on# the given circledef randPoint(r, x, y, n): # Result vector res = list(); for i in range(n): # Get Angle in radians theta = 2 * PI * uniform(); # Get length from center len = math.sqrt(uniform()) * r; # Add point to results. res.append(pair((x + len * math.cos(theta)), (y + len * math.sin(theta)))); # Return the N points return res;# Function to display the content of# the vector Adef printVector(A): # Iterate over A for P in A: # Print the N random points stored print("({0:.2f}".format(P.first),", ","{0:.2f})".format(P.second));# Driver Codeif __name__ == '__main__': # Given dimensions R = 12; X = 3; Y = 3; N = 5; # Function call printVector(randPoint(R, X, Y, N));# This code is contributed by 29AjayKumar |
C#
// C# program for the above approachusing System;using System.Collections.Generic;class GFG{ static readonly double PI = 3.141592653589;class pair { public double first, second; public pair(double first, double second) { this.first = first; this.second = second; }}// Return a random double between 0 & 1static double uniform(){ return new Random().NextDouble();}// Function to find the N random points on// the given circlestatic List<pair> randPoint(int r, int x, int y, int n){ // Result vector List<pair> res = new List<pair>(); for(int i = 0; i < n; i++) { // Get Angle in radians double theta = 2 * PI * uniform(); // Get length from center double len = Math.Sqrt(uniform()) * r; // Add point to results. res.Add(new pair(x + len * Math.Cos(theta), y + len * Math.Sin(theta))); } // Return the N points return res;}// Function to display the content of// the vector Astatic void printList(List<pair> A){ // Iterate over A foreach(pair P in A) { // Print the N random points stored Console.Write("({0:F2}, {1:F2})\n", P.first, P.second); }}// Driver Codepublic static void Main(String[] args){ // Given dimensions int R = 12; int X = 3; int Y = 3; int N = 5; // Function call printList(randPoint(R, X, Y, N));}}// This code is contributed by 29AjayKumar |
Javascript
// JavaScript program for the above approach// Return a random double between 0 & 1function uniform(){ return Math.random();}// Function to find the N random points on// the given circlefunction randPoint(r, x, y, n){ // Result vector let res = new Array(); for (let i = 0; i < n; i++) { // Get Angle in radians let theta = 2 * Math.PI * uniform(); // Get length from center let len = Math.sqrt(uniform()) * r; // Add point to results. res.push([x + len * Math.cos(theta), y + len * Math.sin(theta)]); } // Return the N points return res;}// Function to display the content of// the vector Afunction printVector(A){ // Iterate over A for (let i = 0; i < A.length; i++) { // Print the N random points stored console.log("(" + A[i][0].toFixed(2) + ", " + A[i][1].toFixed(2) + ")"); }}// Driver Code// Given dimensionslet R = 12;let X = 3;let Y = 3;let N = 5;// Function CallprintVector(randPoint(R, X, Y, N));// The code is contributed by gautam goel (gautamgoel962) |
Output:
(7.05, -3.36) (5.21, -7.49) (7.53, 0.19) (-2.37, 12.05) (1.45, 11.80)
Time Complexity: O(N)
Space Complexity: O(N)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
