# Maximum distinct lines passing through a single point

• Difficulty Level : Easy
• Last Updated : 11 May, 2021

Given lines represented by two points and . The task is to find maximum number of lines which can pass through a single point, without superimposing (or covering) any other line. We can move any line but not rotate it.
Examples:

Input : Line 1 : x1 = 1, y1 = 1, x2 = 2, y2 = 2
Line 2 : x2 = 2, y1 = 2, x2 = 4, y2 = 10
Output : 2
There are two lines. These two lines are not
parallel, so both of them will pass through
a single point.

Input : Line 1 : x1 = 1, y1 = 5, x2 = 1, y2 = 10
Line 2 : x2 = 5, y1 = 1, x2 = 10, y2 = 1
Output : 2

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• Represent lines as pair where line can be given as , called line slope form. We can now see that we can change the c for any line, but cannot modify m.
• Lines having same value of m parallel, given that (c1 ≠ c2). Also no two parallel lines can pass through same point without superimposing to each other.
• So, our problem reduces to finding different values of slopes from given set of lines.

We can calculate slope of a line as , add them to a set and count the number of distinct values of slope in set. But we have to handle vertical lines separately.
So, if then, slope = INT_MAX
Otherwise, slope = .
Below is the implementation of the approach.

## C++

 // C++ program to find maximum number of lines// which can pass through a single point#include using namespace std; // function to find maximum lines which passes// through a single pointint maxLines(int n, int x1[], int y1[],                int x2[], int y2[]){    unordered_set<double> s;     double slope;    for (int i = 0; i < n; ++i) {        if (x1[i] == x2[i])            slope = INT_MAX;        else            slope = (y2[i] - y1[i]) * 1.0                    / (x2[i] - x1[i]) * 1.0;         s.insert(slope);    }     return s.size();} // Driver programint main(){    int n = 2, x1[] = { 1, 2 }, y1[] = { 1, 2 },            x2[] = { 2, 4 }, y2[] = { 2, 10 };    cout << maxLines(n, x1, y1, x2, y2);    return 0;}// This code is written by// Sanjit_Prasad

## Java

 // Java program to find maximum number of lines// which can pass through a single point import java.util.*;import java.lang.*;import java.io.*; class GFG{ // function to find maximum lines which passes// through a single pointstatic int maxLines(int n, int x1[], int y1[],                    int x2[], int y2[]){    Set s=new HashSet();     double slope;    for (int i = 0; i < n; ++i) {        if (x1[i] == x2[i])            slope = Integer.MAX_VALUE;        else            slope = (y2[i] - y1[i]) * 1.0                    / (x2[i] - x1[i]) * 1.0;         s.add(slope);    }     return s.size();} // Driver programpublic static void main(String args[]){    int n = 2, x1[] = { 1, 2 }, y1[] = { 1, 2 },            x2[] = { 2, 4 }, y2[] = { 2, 10 };    System.out.print(maxLines(n, x1, y1, x2, y2));}}// This code is written by// Subhadeep

## Python3

 # Python3 program to find maximum number# of lines which can pass through a# single pointimport sys# function to find maximum lines# which passes through a single pointdef maxLines(n, x1, y1, x2, y2):     s = [];     slope=sys.maxsize;    for i in range(n):        if (x1[i] == x2[i]):            slope = sys.maxsize;        else:            slope = (y2[i] - y1[i]) * 1.0 /(x2[i] - x1[i]) * 1.0;         s.append(slope);     return len(s); # Driver Coden = 2;x1 = [ 1, 2 ];y1 = [1, 2];x2 = [2, 4];y2 = [2, 10];print(maxLines(n, x1, y1, x2, y2)); # This code is contributed by mits

## C#

 // C# program to find maximum number of lines// which can pass through a single pointusing System;using System.Collections.Generic; class GFG{ // function to find maximum lines which passes// through a single pointstatic int maxLines(int n, int []x1, int []y1,                    int []x2, int []y2){    HashSet s = new HashSet();     double slope;    for (int i = 0; i < n; ++i)    {        if (x1[i] == x2[i])            slope = int.MaxValue;        else            slope = (y2[i] - y1[i]) * 1.0                    / (x2[i] - x1[i]) * 1.0;         s.Add(slope);    }     return s.Count;} // Driver codepublic static void Main(){    int n = 2;    int []x1 = { 1, 2 }; int []y1 = { 1, 2 };    int []x2 = { 2, 4 }; int []y2 = { 2, 10 };    Console.Write(maxLines(n, x1, y1, x2, y2));}} /* This code contributed by PrinciRaj1992 */

## PHP

 

## Javascript

 
Output:
2

Time Complexity: My Personal Notes arrow_drop_up