Given coordinates of 4 points, bottom-left and top-right corners of two rectangles. The task is to find the coordinates of the intersecting rectangle formed by the given two rectangles.
Examples:
Input:
rec1: bottom-left(0, 0), top-right(10, 8),
rec2: bottom-left(2, 3), top-right(7, 9)
Output: (2, 3) (7, 8) (2, 8) (7, 3)
Input:
rec1: bottom-left(0, 0), top-right(3, 3),
rec2: bottom-left(1, 1), top-right(2, 2)
Output: (1, 1) (2, 2) (1, 2) (2, 1)
Approach :
As two given points are diagonals of a rectangle. so, x1 < x2, y1 < y2. similarly x3 < x4, y3 < y4.
so, bottom-left and top-right points of intersection rectangle can be found by using formula.
x5 = max(x1, x3); y5 = max(y1, y3); x6 = min(x2, x4); y6 = min(y2, y4);
In case of no intersection, x5 and y5 will always exceed x6 and y5 respectively. The other two points of the rectangle can be found by using simple geometry.
Below is the implementation of the above approach:
// CPP program to find intersection // rectangle of given two rectangles. #include <bits/stdc++.h> using namespace std;
// function to find intersection rectangle of given two rectangles. void FindPoints( int x1, int y1, int x2, int y2,
int x3, int y3, int x4, int y4)
{ // gives bottom-left point
// of intersection rectangle
int x5 = max(x1, x3);
int y5 = max(y1, y3);
// gives top-right point
// of intersection rectangle
int x6 = min(x2, x4);
int y6 = min(y2, y4);
// no intersection
if (x5 > x6 || y5 > y6) {
cout << "No intersection" ;
return ;
}
cout << "(" << x5 << ", " << y5 << ") " ;
cout << "(" << x6 << ", " << y6 << ") " ;
// gives top-left point
// of intersection rectangle
int x7 = x5;
int y7 = y6;
cout << "(" << x7 << ", " << y7 << ") " ;
// gives bottom-right point
// of intersection rectangle
int x8 = x6;
int y8 = y5;
cout << "(" << x8 << ", " << y8 << ") " ;
} // Driver code int main()
{ // bottom-left and top-right
// corners of first rectangle
int x1 = 0, y1 = 0, x2 = 10, y2 = 8;
// bottom-left and top-right
// corners of first rectangle
int x3 = 2, y3 = 3, x4 = 7, y4 = 9;
// function call
FindPoints(x1, y1, x2, y2, x3, y3, x4, y4);
return 0;
} |
// C program to find intersection // rectangle of given two rectangles. #include <stdio.h> int min( int a, int b)
{ int min = a;
if (min > b)
min = b;
return min;
} int max( int a, int b)
{ int max = a;
if (max < b)
max = b;
return max;
} // function to find intersection rectangle of given two rectangles. void FindPoints( int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4)
{ // gives bottom-left point
// of intersection rectangle
int x5 = max(x1, x3);
int y5 = max(y1, y3);
// gives top-right point
// of intersection rectangle
int x6 = min(x2, x4);
int y6 = min(y2, y4);
// no intersection
if (x5 > x6 || y5 > y6) {
printf ( "No intersection" );
return ;
}
printf ( "(%d, %d) " ,x5,y5);
printf ( "(%d, %d) " ,x6,y6);
// gives top-left point
// of intersection rectangle
int x7 = x5;
int y7 = y6;
printf ( "(%d, %d) " ,x7,y7);
// gives bottom-right point
// of intersection rectangle
int x8 = x6;
int y8 = y5;
printf ( "(%d, %d) " ,x8,y8);
} // Driver code int main()
{ // bottom-left and top-right
// corners of first rectangle
int x1 = 0, y1 = 0, x2 = 10, y2 = 8;
// bottom-left and top-right
// corners of first rectangle
int x3 = 2, y3 = 3, x4 = 7, y4 = 9;
// function call
FindPoints(x1, y1, x2, y2, x3, y3, x4, y4);
return 0;
} // This code is contributed by kothavvsaakash. |
// Java program to find intersection // rectangle of given two rectangles. class GFG
{ // function to find intersection // rectangle of given two rectangles. static void FindPoints( int x1, int y1,
int x2, int y2,
int x3, int y3,
int x4, int y4)
{ // gives bottom-left point
// of intersection rectangle
int x5 = Math.max(x1, x3);
int y5 = Math.max(y1, y3);
// gives top-right point
// of intersection rectangle
int x6 = Math.min(x2, x4);
int y6 = Math.min(y2, y4);
// no intersection
if (x5 > x6 || y5 > y6)
{
System.out.println( "No intersection" );
return ;
}
System.out.print( "(" + x5 + ", " +
y5 + ") " );
System.out.print( "(" + x6 + ", " +
y6 + ") " );
// gives top-left point
// of intersection rectangle
int x7 = x5;
int y7 = y6;
System.out.print( "(" + x7 + ", " +
y7 + ") " );
// gives bottom-right point
// of intersection rectangle
int x8 = x6;
int y8 = y5;
System.out.print( "(" + x8 + ", " +
y8 + ") " );
} // Driver code public static void main(String args[])
{ // bottom-left and top-right
// corners of first rectangle
int x1 = 0 , y1 = 0 ,
x2 = 10 , y2 = 8 ;
// bottom-left and top-right
// corners of first rectangle
int x3 = 2 , y3 = 3 ,
x4 = 7 , y4 = 9 ;
// function call
FindPoints(x1, y1, x2, y2,
x3, y3, x4, y4);
} } // This code is contributed // by Arnab Kundu |
# Python 3 program to find intersection # rectangle of given two rectangles. # function to find intersection # rectangle of given two rectangles. def FindPoints(x1, y1, x2, y2,
x3, y3, x4, y4):
# gives bottom-left point
# of intersection rectangle
x5 = max (x1, x3)
y5 = max (y1, y3)
# gives top-right point
# of intersection rectangle
x6 = min (x2, x4)
y6 = min (y2, y4)
# no intersection
if (x5 > x6 or y5 > y6) :
print ( "No intersection" )
return
print ( "(" , x5, ", " , y5, ") " , end = " " )
print ( "(" , x6, ", " , y6, ") " , end = " " )
# gives top-left point
# of intersection rectangle
x7 = x5
y7 = y6
print ( "(" , x7, ", " , y7, ") " , end = " " )
# gives bottom-right point
# of intersection rectangle
x8 = x6
y8 = y5
print ( "(" , x8, ", " , y8, ") " )
# Driver code if __name__ = = "__main__" :
# bottom-left and top-right
# corners of first rectangle
x1 = 0
y1 = 0
x2 = 10
y2 = 8
# bottom-left and top-right
# corners of first rectangle
x3 = 2
y3 = 3
x4 = 7
y4 = 9
# function call
FindPoints(x1, y1, x2, y2, x3, y3, x4, y4)
# This code is contributed # by ChitraNayal |
// C# program to find intersection // rectangle of given two rectangles. using System;
class GFG
{ // function to find intersection // rectangle of given two rectangles. static void FindPoints( int x1, int y1,
int x2, int y2,
int x3, int y3,
int x4, int y4)
{ // gives bottom-left point
// of intersection rectangle
int x5 = Math.Max(x1, x3);
int y5 = Math.Max(y1, y3);
// gives top-right point
// of intersection rectangle
int x6 = Math.Min(x2, x4);
int y6 = Math.Min(y2, y4);
// no intersection
if (x5 > x6 || y5 > y6)
{
Console.WriteLine( "No intersection" );
return ;
}
Console.Write( "(" + x5 + ", " +
y5 + ") " );
Console.Write( "(" + x6 + ", " +
y6 + ") " );
// gives top-left point
// of intersection rectangle
int x7 = x5;
int y7 = y6;
Console.Write( "(" + x7 + ", " +
y7 + ") " );
// gives bottom-right point
// of intersection rectangle
int x8 = x6;
int y8 = y5;
Console.Write( "(" + x8 + ", " +
y8 + ") " );
} // Driver code public static void Main()
{ // bottom-left and top-right
// corners of first rectangle
int x1 = 0, y1 = 0,
x2 = 10, y2 = 8;
// bottom-left and top-right
// corners of first rectangle
int x3 = 2, y3 = 3,
x4 = 7, y4 = 9;
// function call
FindPoints(x1, y1, x2, y2,
x3, y3, x4, y4);
} } // This code is contributed // by Akanksha Rai |
<?php // PHP program to find intersection // rectangle of given two rectangles. // function to find intersection rectangle // of given two rectangles. function FindPoints( $x1 , $y1 , $x2 , $y2 ,
$x3 , $y3 , $x4 , $y4 )
{ // gives bottom-left point
// of intersection rectangle
$x5 = max( $x1 , $x3 );
$y5 = max( $y1 , $y3 );
// gives top-right point
// of intersection rectangle
$x6 = min( $x2 , $x4 );
$y6 = min( $y2 , $y4 );
// no intersection
if ( $x5 > $x6 || $y5 > $y6 )
{
echo "No intersection" ;
return ;
}
echo "(" . $x5 . ", " . $y5 . ") " ;
echo "(" . $x6 . ", " . $y6 . ") " ;
// gives top-left point
// of intersection rectangle
$x7 = $x5 ;
$y7 = $y6 ;
echo "(" . $x7 . ", " . $y7 . ") " ;
// gives bottom-right point
// of intersection rectangle
$x8 = $x6 ;
$y8 = $y5 ;
echo "(" . $x8 . ", " . $y8 . ") " ;
} // Driver code // bottom-left and top-right // corners of first rectangle $x1 = 0; $y1 = 0; $x2 = 10; $y2 = 8;
// bottom-left and top-right // corners of first rectangle $x3 = 2; $y3 = 3; $x4 = 7; $y4 = 9;
// function call FindPoints( $x1 , $y1 , $x2 , $y2 ,
$x3 , $y3 , $x4 , $y4 );
// This code is contributed // by Akanksha Rai ?> |
<script> // Javascript program to find intersection // rectangle of given two rectangles. // Function to find intersection // rectangle of given two rectangles. function FindPoints(x1, y1, x2, y2,
x3, y3, x4, y4)
{ // Gives bottom-left point
// of intersection rectangle
var x5 = Math.max(x1, x3);
var y5 = Math.max(y1, y3);
// Gives top-right point
// of intersection rectangle
var x6 = Math.min(x2, x4);
var y6 = Math.min(y2, y4);
// No intersection
if (x5 > x6 || y5 > y6)
{
document.write( "No intersection" );
return ;
}
document.write( "(" + x5 + ", " +
y5 + ") " );
document.write( "(" + x6 + ", " +
y6 + ") " );
// Gives top-left point
// of intersection rectangle
var x7 = x5;
var y7 = y6;
document.write( "(" + x7 + ", " +
y7 + ") " );
// Gives bottom-right point
// of intersection rectangle
var x8 = x6;
var y8 = y5;
document.write( "(" + x8 + ", " +
y8 + ") " );
} // Driver Code // bottom-left and top-right // corners of first rectangle var x1 = 0, y1 = 0,
x2 = 10, y2 = 8;
// bottom-left and top-right // corners of first rectangle var x3 = 2, y3 = 3,
x4 = 7, y4 = 9;
// Function call FindPoints(x1, y1, x2, y2, x3, y3, x4, y4);
// This code is contributed by kirti </script> |
(2, 3) (7, 8) (2, 8) (7, 3)
Time Complexity: O(1)
Auxiliary Space: O(1)