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) |
(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)