Dados dos rectángulos superpuestos en un plano. Nos dan los puntos inferior izquierdo y superior derecho de los dos rectángulos. Necesitamos encontrar el área total (áreas verde y rosa en el siguiente diagrama).
Ejemplos:
Input : Point l1 = {2, 2}, r1 = {5, 7};
Point l2 = {3, 4}, r2 = {6, 9};
Output :Total Area = 24
Input : Point l1 = {2, 1}, r1 = {5, 5};
Point l2 = {3, 2}, r2 = {5, 7};
Output :Total Area = 16
Preguntado en Juniper
Básicamente sumamos áreas de dos rectángulos. Esto incluye la parte de intersección dos veces, por lo que restamos el área de la parte de intersección.
Total Area = (Area of 1st rectangle +
Area of 2nd rectangle) -
Area of Intersecting part
Área del Rectángulo = x_distancia * y_distancia
Donde,
distancia_x para el primer rectángulo = abs(l1.x – r1.x)
distancia_y para el primer rectángulo = abs(l1.y – r1.y)
De manera similar, podemos calcular el área del segundo rectángulo.
Para el área de la parte de intersección,
x_distance para el rectángulo de intersección = min(r1.x, r2.x) – max(l1.x, l2.x)
y_distance para el primer rectángulo = min(r1.y, r2.y) – max( l1.y, l2.y)
Si x_distance o y_distance es negativo, entonces los dos rectángulos no se intersecan. En ese caso, el área de superposición es 0.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ program to find total area of two
// overlapping Rectangles
#include <bits/stdc++.h>
using namespace std;
struct Point {
int x, y;
};
// Returns Total Area of two overlap
// rectangles
int overlappingArea(Point l1, Point r1,
Point l2, Point r2)
{
// Area of 1st Rectangle
int area1 = abs(l1.x - r1.x)
* abs(l1.y - r1.y);
// Area of 2nd Rectangle
int area2 = abs(l2.x - r2.x)
* abs(l2.y - r2.y);
// Length of intersecting part i.e
// start from max(l1.x, l2.x) of
// x-coordinate and end at min(r1.x,
// r2.x) x-coordinate by subtracting
// start from end we get required
// lengths
int x_dist = min(r1.x, r2.x)
- max(l1.x, l2.x);
int y_dist = (min(r1.y, r2.y)
- max(l1.y, l2.y));
int areaI = 0;
if( x_dist > 0 && y_dist > 0 )
{
areaI = x_dist * y_dist;
}
return (area1 + area2 - areaI);
}
// Driver Code
int main()
{
Point l1 = { 2, 2 }, r1 = { 5, 7 };
Point l2 = { 3, 4 }, r2 = { 6, 9 };
// Function Call
cout << overlappingArea(l1, r1, l2, r2);
return 0;
}
Java
// Java program to find total area of two
// overlapping Rectangles
class GFG {
static class Point {
int x, y;
public Point(int x, int y)
{
this.x = x;
this.y = y;
}
};
// Returns Total Area of two overlap
// rectangles
static int overlappingArea(Point l1, Point r1,
Point l2, Point r2)
{
// Area of 1st Rectangle
int area1
= Math.abs(l1.x - r1.x)
* Math.abs(l1.y - r1.y);
// Area of 2nd Rectangle
int area2
= Math.abs(l2.x - r2.x)
* Math.abs(l2.y - r2.y);
// Length of intersecting part i.e
// start from max(l1.x, l2.x) of
// x-coordinate and end at min(r1.x,
// r2.x) x-coordinate by subtracting
// start from end we get required
// lengths
int x_dist = (Math.min(r1.x, r2.x)
- Math.max(l1.x, l2.x);
int y_dist = (Math.min(r1.y, r2.y)
- Math.max(l1.y, l2.y);
int areaI = 0;
if( x_dist > 0 && y_dist > 0 )
{
areaI = x_dist * y_dist;
}
return (area1 + area2 - areaI);
}
// Driver Code
public static void main(String[] args)
{
Point l1 = new Point(2, 2), r1 = new Point(5, 7);
Point l2 = new Point(3, 4), r2 = new Point(6, 9);
// Function Call
System.out.println(overlappingArea(l1, r1, l2, r2));
}
}
// This code is contributed by PrinciRaj1992
Python3
# Python program to find total area of two # overlapping Rectangles # Returns Total Area of two overlap # rectangles def overlappingArea(l1, r1, l2, r2): x = 0 y = 1 # Area of 1st Rectangle area1 = abs(l1[x] - r1[x]) * abs(l1[y] - r1[y]) # Area of 2nd Rectangle area2 = abs(l2[x] - r2[x]) * abs(l2[y] - r2[y]) ''' Length of intersecting part i.e start from max(l1[x], l2[x]) of x-coordinate and end at min(r1[x], r2[x]) x-coordinate by subtracting start from end we get required lengths ''' x_dist = (min(r1[x], r2[x]) - max(l1[x], l2[x])) y_dist = (min(r1[y], r2[y]) - max(l1[y], l2[y])) areaI = 0 if x_dist > 0 and y_dist > 0: areaI = x_dist * y_dist return (area1 + area2 - areaI) # Driver's Code l1 = [2, 2] r1 = [5, 7] l2 = [3, 4] r2 = [6, 9] # Function call print(overlappingArea(l1, r1, l2, r2)) # This code is contributed by Manisha_Ediga
C#
// C# program to find total area of two
// overlapping Rectangles
using System;
class GFG {
public class Point {
public int x, y;
public Point(int x, int y)
{
this.x = x;
this.y = y;
}
};
// Returns Total Area of two overlap
// rectangles
static int overlappingArea(Point l1, Point r1, Point l2,
Point r2)
{
// Area of 1st Rectangle
int area1
= Math.Abs(l1.x - r1.x) * Math.Abs(l1.y - r1.y);
// Area of 2nd Rectangle
int area2
= Math.Abs(l2.x - r2.x) * Math.Abs(l2.y - r2.y);
// Length of intersecting part i.e
// start from max(l1.x, l2.x) of
// x-coordinate and end at min(r1.x,
// r2.x) x-coordinate by subtracting
// start from end we get required
// lengths
int x_dist
= (Math.Min(r1.x, r2.x) - Math.Max(l1.x, l2.x));
int y_dist
= (Math.Min(r1.y, r2.y) - Math.Max(l1.y, l2.y));
int areaI = 0;
if (x_dist > 0 && y_dist > 0) {
areaI = x_dist * y_dist;
}
return (area1 + area2 - areaI);
}
// Driver Code
public static void Main(String[] args)
{
Point l1 = new Point(2, 2), r1 = new Point(5, 7);
Point l2 = new Point(3, 4), r2 = new Point(6, 9);
// Function Call
Console.WriteLine(overlappingArea(l1, r1, l2, r2));
}
}
// This code is contributed by PrinciRaj1992
Javascript
<script>
// Javascript program to find total area of two
// overlapping Rectangles
// Returns Total Area of two overlap
// rectangles
function overlappingArea(l1, r1, l2, r2)
{
let x = 0
let y = 1
// Area of 1st Rectangle
let area1 = Math.abs(l1[x] - r1[x]) * Math.abs(l1[y] - r1[y])
// Area of 2nd Rectangle
let area2 = Math.abs(l2[x] - r2[x]) * Math.abs(l2[y] - r2[y])
// Length of intersecting part i.e
// start from max(l1[x], l2[x]) of
// x-coordinate and end at min(r1[x],
// r2[x]) x-coordinate by subtracting
// start from end we get required
// lengths
let x_dist = (Math.min(r1[x], r2[x]) -
Math.max(l1[x], l2[x]))
let y_dist = (Math.min(r1[y], r2[y]) -
Math.max(l1[y], l2[y]))
let areaI = 0
if (x_dist > 0 && y_dist > 0)
areaI = x_dist * y_dist
return (area1 + area2 - areaI)
}
// Driver Code
let l1 = [2, 2]
let r1 = [5, 7]
let l2 = [3, 4]
let r2 = [6, 9]
// Function call
document.write(overlappingArea(l1, r1, l2, r2))
// This code is contributed by jana_sayantan.
</script>
Producción
24
Complejidad del tiempo: O(1)
Espacio Auxiliar: O(1)