# Intersecting rectangle when bottom-left and top-right corners of two rectangles are given

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:

## C++

 `// CPP program to find intersection ` `// rectangle of given two rectangles. ` `#include ` `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; ` `} `

## Java

 `// 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

 `# 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#

 `// 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

 ` ``\$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 ` `?> `

Output:

```(2, 3) (7, 8) (2, 8) (7, 3)
```

Time Complexity: O(1)

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