Java Program to Find Count of Different Straight Lines with Total n Points With m collinear

In the previous article, we have seen Java Program to Check if Line Passes Through the Origin

In this article we will discuss about how to find count of different straight lines we can draw with total n points with m collinear using Java programming language.

Java Program to Find Count of Different Straight Lines with Total n Points With m collinear

Before jumping into the program directly, let’s first know how can we count the number of lines we can draw with m collinear points out of n points.

Explanation:

Formula to Find Total Number Of Lines That Can Be Drawn: ⁿC₂ – ^mC₂ + 1

Example:

When n=5 and Nm=3

Number of lines : ⁿC₂ – ^mC₂ + 1

=> ⁵C₂ – ³C₂ + 1

=> 5!/(2!(5-2)!) – 3!/(2!(3-2)!) + 1

=> 120/12 – 6/2 + 1

=> 10-3 + 1

=> 8

Let’s see different ways to find number of lines.

By Using Static Input Values
By Using User Input Values

Method-1: Java Program to Find Count of Different Straight Lines with Total n Points With m collinear By Using Static Input Values

Approach:

Declare the value for ‘m’ and ‘n’.
Then call the straightLinesCount() method by passing m and n value as parameter.
This method then calls the combination() method to find out ⁵C₂ – ³C₂ + 1 i.e. the number of straight lines.
Then print the result.

Program:

// JAVA Code to count number of  
// straight lines passing through 

public class Main
{
    public static void main(String[] args)
    {
        int n =5, m=3;
        // Prints the total number of lines
        System.out.println("The number of straight lines with total of "+n+" points and "
        +m+" collinear points is "+straightLinesCount(m,n));
    }

    // Returns number of straight lines
    public static int straightLinesCount(int m, int n)
    {
        int lines = 0;
        // Calculates the number of lines 
        lines = combination(n,2) - combination(m,2) + 1;
        return lines;
    }

    // Function that returns the number of combinations
    public static int combination(int n, int r)
    {
        return factorial(n) / (factorial(r) * factorial(n - r));
    }

    // Function that returns the factorial of the number
    public static int factorial(int number) {
        int res = 1;
        for (int factor = 2; factor <= number; factor++) 
        {
            res *= factor;
        }
        return res;
    }
}

Output:

The number of straight lines with total of 5 points and 3 collinear points is 8

Method-2: Java Program to Find Count of Different Straight Lines with Total n Points With m collinear By Using User Input Values

Approach:

Take user input the value for ‘m’ and ‘n’.
Then call the straightLinesCount() method by passing m and n value as parameter.
This method then calls the combination() method to find out ⁵C₂ – ³C₂ + 1 i.e. the number of straight lines.
Then print the result.

Program:

// JAVA Code to count number of  
// straight lines passing through 

import java.util.Scanner;

public class Main
{
    public static void main(String[] args)
    {
        // Scanner class to take input from user
        Scanner scan = new Scanner(System.in);
        System.out.print("Enter total points and number of collinear points : ");
        int n = scan.nextInt(), m=scan.nextInt();
        // Prints the total number of lines
        System.out.println("The number of straight lines with total of "+n+" points and "
        +m+" collinear points is "+straightLinesCount(m,n));
    }

    // Returns number of straight lines
    public static int straightLinesCount(int m, int n)
    {
        int lines = 0;
        // Calculates the number of lines 
        lines = combination(n,2) - combination(m,2) + 1;
        return lines;
    }

    // Function that returns the number of combinations
    public static int combination(int n, int r)
    {
        return factorial(n) / (factorial(r) * factorial(n - r));
    }

    // Function that returns the factorial of the number
    public static int factorial(int number) 
    {
        int res = 1;
        for (int factor = 2; factor <= number; factor++) 
        {
            res *= factor;
        }
        return res;
    }
}

Output:

Enter total points and number of collinear points : 9 5
The number of straight lines with total of 9 points and 5 collinear points is 27

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