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++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
#define PI 3.141592653589
// Return a random double between 0 & 1
double uniform()
{
return (double)rand() / RAND_MAX;
}
// Function to find the N random points on
// the given circle
vector<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 A
void 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 Code
int 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 program for the above approach
import 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 & 1
static double uniform(){return Math.random();}
// Function to find the N random points on
// the given circle
static 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 A
static 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 Code
public 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
# Python program for the above approach
import math
import random
PI = 3.141592653589;
class pair:
def __init__(self, first, second):
self.first = first;
self.second = second;
# Return a random between 0 & 1
def uniform():
return random.random();
# Function to find the N random points on
# the given circle
def 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 A
def 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 Code
if __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# program for the above approach
using 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 & 1
static double uniform()
{
return new Random().NextDouble();
}
// Function to find the N random points on
// the given circle
static 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 A
static 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 Code
public 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 program for the above approach
// Return a random double between 0 & 1
function uniform()
{
return Math.random();
}
// Function to find the N random points on
// the given circle
function 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 A
function 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 dimensions
let R = 12;
let X = 3;
let Y = 3;
let N = 5;
// Function Call
printVector(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)
