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Coordinates of rectangle with given points lie inside
  • Difficulty Level : Medium
  • Last Updated : 03 May, 2021

Given two arrays X[] and Y[] with n-elements, where (Xi, Yi) represent a point on coordinate system, find the smallest rectangle such that all points from given input lie inside that rectangle and sides of rectangle must be parallel to Coordinate axis. Print all four coordinates of an obtained rectangle. 
Note: n >= 4 (we have at least 4 points as input).
Examples : 
 

Input : X[] = {1, 3, 0, 4},  y[] = {2, 1, 0, 2}
Output : {0, 0}, {0, 2}, {4, 2}, {4, 0}

Input : X[] = {3, 6, 1, 9, 13, 0, 4}, Y[] = {4, 2, 6, 5, 2, 3, 1}
Output : {0, 1}, {0, 6}, {13, 6}, {13, 1} 

For finding the smallest rectangle you may take two of basic approach : 
 

  1. Consider origin of coordinate plane as the smallest rectangle and then step by step keep expanding it as per the value of coordinates of points if they don’t lie inside the current rectangle. This concept requires a little of complex logic to find the exact smallest rectangle.
  2. A very simple and efficient logic behind this is to find the smallest, as well as largest x & y coordinates among all given points and then the all possible four combinations of these values, result in the four points of the required rectangle as {Xmin, Ymin}, {Xmin, Ymax}, {Xmax, Ymax}, {Xmax, Ymin}.

 

 

C++




// Program to find smallest rectangle
// to conquer all points
#include <bits/stdc++.h>
using namespace std;
 
// function to print coordinate of smallest rectangle
void printRect(int X[], int Y[], int n)
{
    // find Xmax and Xmin
    int Xmax = *max_element(X, X + n);
    int Xmin = *min_element(X, X + n);
 
    // find Ymax and Ymin
    int Ymax = *max_element(Y, Y + n);
    int Ymin = *min_element(Y, Y + n);
 
    // print all four coordinates
    cout << "{" << Xmin << ", " << Ymin << "}" << endl;
    cout << "{" << Xmin << ", " << Ymax << "}" << endl;
    cout << "{" << Xmax << ", " << Ymax << "}" << endl;
    cout << "{" << Xmax << ", " << Ymin << "}" << endl;
}
 
// driver program
int main()
{
    int X[] = { 4, 3, 6, 1, -1, 12 };
    int Y[] = { 4, 1, 10, 3, 7, -1 };
    int n = sizeof(X) / sizeof(X[0]);
     
    printRect(X, Y, n);
     
    return 0;
}

Java




// Program to find smallest rectangle
// to conquer all points
import java.util.Arrays;
import java.util.Collections;
 
class GFG {
         
    // function to print coordinate of smallest rectangle
    static void printRect(Integer X[], Integer Y[], int n)
    {
         
        // find Xmax and Xmin
        int Xmax = Collections.max(Arrays.asList(X));
        int Xmin = Collections.min(Arrays.asList(X));
     
        // find Ymax and Ymin
        int Ymax = Collections.max(Arrays.asList(Y));
        int Ymin = Collections.min(Arrays.asList(Y));
     
        // print all four coordinates
        System.out.println("{" + Xmin + ", " + Ymin + "}");
        System.out.println("{" + Xmin + ", " + Ymax + "}");
        System.out.println("{" + Xmax + ", " + Ymax + "}");
        System.out.println("{" + Xmax + ", " + Ymin + "}");
    }
     
    //Driver code
    public static void main (String[] args)
    {
         
        Integer X[] = { 4, 3, 6, 1, -1, 12 };
        Integer Y[] = { 4, 1, 10, 3, 7, -1 };
        int n = X.length;
         
        printRect(X, Y, n);
    }
}
 
// This code is contributed by Anant Agarwal.

Python 3




# Program to find smallest rectangle
# to conquer all points
 
# function to print coordinate of smallest rectangle
def printRect(X, Y, n):
 
    # find Xmax and Xmin
    Xmax = max(X)
    Xmin = min(X)
 
    # find Ymax and Ymin
    Ymax = max(Y)
    Ymin = min(Y)
 
    # print all four coordinates
    print("{",Xmin,", ",Ymin,"}",sep="" )
    print("{",Xmin,", ",Ymax,"}",sep="" )
    print("{",Xmax,", ",Ymax,"}",sep="" )
    print("{",Xmax,", ",Ymin,"}",sep="" )
 
# driver program
X = [4, 3, 6, 1, -1, 12]
Y =  [4, 1, 10, 3, 7, -1]
n = len(X)
printRect(X, Y, n)
# This code is contributed by
# Smitha Dinesh Semwal

C#




// Program to find smallest rectangle
// to conquer all points
using System.Linq;
using System;
 
public class GFG{
     
    // function to print coordinate
    // of smallest rectangle
    static void printRect(int[] X,
                        int[] Y, int n)
    {
         
        // find Xmax and Xmin
        int Xmax = X.Max();
        int Xmin = X.Min();
     
        // find Ymax and Ymin
        int Ymax = Y.Max();
        int Ymin = Y.Min();
     
        // print all four coordinates
        Console.WriteLine("{" + Xmin + ", "
                             + Ymin + "}");
                              
        Console.WriteLine("{" + Xmin + ", "
                             + Ymax + "}");
                              
        Console.WriteLine("{" + Xmax + ", "
                             + Ymax + "}");
                              
        Console.WriteLine("{" + Xmax + ", "
                             + Ymin + "}");
    }
     
    // Driver code
    static public void Main ()
    {
        int[] X = { 4, 3, 6, 1, -1, 12 };
        int[] Y = { 4, 1, 10, 3, 7, -1 };
        int n = X.Length;
         
        printRect(X, Y, n);
    }
}
 
// This code is contributed by Ajit.

PHP




<?php
// PHP Program to find smallest
// rectangle to conquer all points
 
// function to print coordinate
// of smallest rectangle
function printRect($X, $Y, $n)
{
     
    // find Xmax and Xmin
    $Xmax = max($X);
    $Xmin = min($X);
 
    // find Ymax and Ymin
    $Ymax = max($Y);
    $Ymin = min($Y);
 
    // print all four coordinates
    echo "{" , $Xmin , ", " , $Ymin , "}","\n";
    echo "{" , $Xmin , ", " , $Ymax , "}" ,"\n";
    echo "{" , $Xmax , ", " , $Ymax , "}","\n";
    echo "{" , $Xmax , ", " , $Ymin , "}" ;
}
 
    // Driver Code
    $X = array(4, 3, 6, 1, -1, 12);
    $Y = array(4, 1, 10, 3, 7, -1);
    $n =count($X);
    printRect($X, $Y, $n);
     
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
 
// Program to find smallest rectangle
// to conquer all points
 
// function to print coordinate of smallest rectangle
function printRect(X, Y, n)
{
    // find Xmax and Xmin
    var Xmax = X.reduce((a,b) => Math.max(a,b));
    var Xmin = X.reduce((a,b) => Math.min(a,b));
 
    // find Ymax and Ymin
    var Ymax =  Y.reduce((a,b) => Math.max(a,b));
    var Ymin = Y.reduce((a,b) => Math.min(a,b));
 
    // print all four coordinates
    document.write( "{" + Xmin + ", " + Ymin + "}" + "<br>");
    document.write( "{" + Xmin + ", " + Ymax + "}" + "<br>");
    document.write( "{" + Xmax + ", " + Ymax + "}" + "<br>");
    document.write( "{" + Xmax + ", " + Ymin + "}" + "<br>");
}
 
// driver program
var X = [ 4, 3, 6, 1, -1, 12 ];
var Y = [ 4, 1, 10, 3, 7, -1 ];
var n = X.length;
  
printRect(X, Y, n);
  
</script>
Output: 
{-1, -1}
{-1, 10}
{12, 10}
{12, -1}

 




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