Minimum lines to cover all points

Given N points in 2-dimensional space, we need to print the count of the minimum number of lines which traverse through all these N points and which go through a specific (xO, yO) point also.


If given points are (-1, 3), (4, 3), (2, 1), (-1, -2), 
(3, -3) and (xO, yO) point is (1, 0) i.e. every line
must go through this point. 
Then we have to draw at least two lines to cover all
these points going through (xO, yO) as shown in below

We can solve this problem by considering the slope of all points with (xO, yO). If two distinct points have the same slope with (xO, yO) then they can be covered with same line only so we can track slope of each point and whenever we get a new slope we will increase our line count by one.
In below code slope is stored as a pair of integer to get rid of the precision problem and a set is used to keep track of occurred slopes.
Please see below code for better understanding.

// C++ program to get minimum lines to cover
// all the points
#include <bits/stdc++.h>
using namespace std;
//  Utility method to get gcd of a and b
int gcd(int a, int b)
    if (b == 0)
        return a;
    return gcd(b, a % b);
//  method returns reduced form of dy/dx as a pair
pair<int, int> getReducedForm(int dy, int dx)
    int g = gcd(abs(dy), abs(dx));
    //  get sign of result
    bool sign = (dy < 0) ^ (dx < 0);
    if (sign)
        return make_pair(-abs(dy) / g, abs(dx) / g);
        return make_pair(abs(dy) / g, abs(dx) / g);
/*  method returns minimum number of lines to
    cover all points where all lines goes
    through (xO, yO) */
int minLinesToCoverPoints(int points[][2], int N,
                                   int xO, int yO)
    //  set to store slope as a pair
    set< pair<int, int> > st;
    pair<int, int> temp;
    int minLines = 0;
    //  loop over all points once
    for (int i = 0; i < N; i++)
        //  get x and y co-ordinate of current point
        int curX = points[i][0];
        int curY = points[i][1];
        temp = getReducedForm(curY - yO, curX - xO);
        // if this slope is not there in set,
        // increase ans by 1 and insert in set
        if (st.find(temp) == st.end())
    return minLines;
// Driver code to test above methods
int main()
    int xO, yO;
    xO = 1;
    yO = 0;
    int points[][2] =
        {-1, 3},
        {4, 3},
        {2, 1},
        {-1, -2},
        {3, -3}
    int N = sizeof(points) / sizeof(points[0]);
    cout << minLinesToCoverPoints(points, N, xO, yO);
    return 0;



Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

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