Skip to content
Related Articles

Related Articles

Check if four segments form a rectangle

View Discussion
Improve Article
Save Article
Like Article
  • Difficulty Level : Medium
  • Last Updated : 23 Jun, 2022

We are given four segments as a pair of coordinates of their end points. We need to tell whether those four line segments make a rectangle or not. 
Examples: 
 

Input : segments[] =  [(4, 2), (7, 5),
                       (2, 4), (4, 2),
                       (2, 4), (5, 7),
                       (5, 7), (7, 5)]
Output : Yes
Given these segment make a rectangle of length 3X2.

Input : segment[] = [(7, 0), (10, 0),
                     (7, 0), (7, 3),
                     (7, 3), (10, 2),
                     (10, 2), (10, 0)]
Output : Not
These segments do not make a rectangle.

Above examples are shown in below diagram.

This problem is mainly an extension of How to check if given four points form a square
 

We can solve this problem by using properties of a rectangle. First, we check total unique end points of segments, if count of these points is not equal to 4 then the line segment can’t make a rectangle. Then we check distances between all pair of points, there should be at most 3 different distances, one for diagonal and two for sides and at the end we will check the relation among these three distances, for line segments to make a rectangle these distance should satisfy Pythagorean relation because sides and diagonal of rectangle makes a right angle triangle. If they satisfy mentioned conditions then we will flag polygon made by line segment as rectangle otherwise not.
 

CPP




// C++ program to check whether it is possible
// to make a rectangle from 4 segments
#include <bits/stdc++.h>
using namespace std;
#define N 4
 
// structure to represent a segment
struct Segment
{
    int ax, ay;
    int bx, by;
};
 
// Utility method to return square of distance
// between two points
int getDis(pair<int, int> a, pair<int, int> b)
{
    return (a.first - b.first)*(a.first - b.first) +
        (a.second - b.second)*(a.second - b.second);
}
 
// method returns true if line Segments make
// a rectangle
bool isPossibleRectangle(Segment segments[])
{
    set< pair<int, int> > st;
 
    // putting all end points in a set to
    // count total unique points
    for (int i = 0; i < N; i++)
    {
        st.insert(make_pair(segments[i].ax, segments[i].ay));
        st.insert(make_pair(segments[i].bx, segments[i].by));
    }
 
    // If total unique points are not 4, then
    // they can't make a rectangle
    if (st.size() != 4)
        return false;
 
    // dist will store unique 'square of distances'
    set<int> dist;
 
    // calculating distance between all pair of
    // end points of line segments
    for (auto it1=st.begin(); it1!=st.end(); it1++)
        for (auto it2=st.begin(); it2!=st.end(); it2++)
            if (*it1 != *it2)
                dist.insert(getDis(*it1, *it2));
 
    // if total unique distance are more than 3,
    // then line segment can't make a rectangle
    if (dist.size() > 3)
        return false;
 
    // copying distance into array. Note that set maintains
    // sorted order.
    int distance[3];
    int i = 0;
    for (auto it = dist.begin(); it != dist.end(); it++)
        distance[i++] = *it;
 
    // If line seqments form a square
    if (dist.size() == 2)
    return (2*distance[0] == distance[1]);
 
    // distance of sides should satisfy pythagorean
    // theorem
    return (distance[0] + distance[1] == distance[2]);
}
 
// Driver code to test above methods
int main()
{
    Segment segments[] =
    {
        {4, 2, 7, 5},
        {2, 4, 4, 2},
        {2, 4, 5, 7},
        {5, 7, 7, 5}
    };
 
    (isPossibleRectangle(segments))?cout << "Yes\n":cout << "No\n";
}

Javascript




// JavaScript program to check whether it is possible
// to make a rectangle from 4 segments
 
const N = 4;
 
// Utility method to return square of distance
// between two points
function getDis(a, b)
{
    return (parseInt(a[0]) - parseInt(b[0]))*(parseInt(a[0]) - parseInt(b[0])) + (parseInt(a[1]) - parseInt(b[1]))*(parseInt(a[1]) - parseInt(b[1]));
}
 
// method returns true if line Segments make
// a rectangle
function isPossibleRectangle(segments)
{  
    let st = new Set();
 
    // putting all end points in a set to
    // count total unique points
    for (let i = 0; i < N; i++)
    {
        let tmp1 = [segments[i][0], segments[i][1]];
        let tmp2 = [segments[i][2], segments[i][3]];
        st.add(tmp1.join(''));
        st.add(tmp2.join(''));
    }
 
    // If total unique points are not 4, then
    // they can't make a rectangle
    if (st.size != 4)
    {
        return false;
    }
         
    // dist will store unique 'square of distances'
    let dist = new Set();
 
    // calculating distance between all pair of
    // end points of line segments
    for(let it1 of st)
    {
        for(let it2 of st)
        {
            if(it1 !== it2)
            {
                dist.add(getDis(it1.split(''), it2.split('')));
            }
        }
    }
 
    // if total unique distance are more than 3,
    // then line segment can't make a rectangle
    if (dist.size > 3)
    {
        return false;
    }
         
    // copying distance into array. Note that set maintains
    // sorted order.
    let distance = new Array();
    for (let x of dist)
    {
        distance.push(x);
    }
         
    // If line seqments form a square
    if (dist.size === 2)
    {
        return (2*distance[0] == distance[1]);
    }
 
    // distance of sides should satisfy pythagorean
    // theorem
    return (distance[0] + distance[1] == distance[2]);
}
 
// Driver code to test above methods
{
    let segments = [
        [4, 2, 7, 5],
        [2, 4, 4, 2],
        [2, 4, 5, 7],
        [5, 7, 7, 5] ]
 
    if(isPossibleRectangle(segments)){
        console.log("Yes");
    }
    else{
        console.log("No");
    }
}
 
// The code is contributed by  Nidhi Goel

Output: 
 

Yes

Time Complexity: O(n2logn) 
Auxiliary Space: O(n)

This article is contributed by Aarti_Rathi and Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!