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RectangleArea.cpp
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// Source : https://leetcode.com/problems/rectangle-area/
// Author : Hao Chen
// Date : 2015-06-12
/**********************************************************************************
*
* Find the total area covered by two rectilinear rectangles in a 2D plane.
* Each rectangle is defined by its bottom left corner and top right corner as shown in the figure.
*
* Y
* ^
* |
* |
* |
* |
* | (C,D):(3,4)
* +------------------+
* | | |
* | | |
* | | | (G,H):(9,2)
* | +----------------------------+
* | | | |
* | | | |
* | | | |
* +---------|--------+-------------------|---------> X
* (A,B):(-3,0) | |
* +----------------------------+
* (E,F):(0,-1)
*
*
*
* Assume that the total area is never beyond the maximum possible value of int.
*
* Credits:Special thanks to @mithmatt for adding this problem, creating the above image and all test cases.
*
**********************************************************************************/
#include <iostream>
using namespace std;
namespace leetcode
{
class Point {
public:
Point(int _x, int _y):x(_x),y(_y) {}
int x, y;
};
class Rectangle {
public:
Rectangle(int a, int b, int c, int d):topLeft(a,d), bottomRight(c,b) { }
int Area(){
return (bottomRight.x - topLeft.x)*(topLeft.y - bottomRight.y);
}
int InclusiveArea (Rectangle &r){
// I include it
if (r.topLeft.x >= topLeft.x && r.bottomRight.x <= bottomRight.x &&
r.topLeft.y <= topLeft.y && r.bottomRight.y >= bottomRight.y ) {
return this->Area();
}
// it includes me
if (r.topLeft.x <= topLeft.x && r.bottomRight.x >= bottomRight.x &&
r.topLeft.y >= topLeft.y && r.bottomRight.y <= bottomRight.y ) {
return r.Area();
}
// 0 - no inclusive
return 0;
}
int OverlappedArea(Rectangle &r) {
int overlap_x = max(0, min(r.bottomRight.x, bottomRight.x) - max(r.topLeft.x, topLeft.x));
int overlap_y = max(0, min(r.topLeft.y, topLeft.y) - max(r.bottomRight.y, bottomRight.y));
return overlap_x * overlap_y;
}
Point topLeft;
Point bottomRight;
};
};
int computeArea(int A, int B, int C, int D, int E, int F, int G, int H) {
using namespace leetcode;
Rectangle r1(A,B,C,D);
Rectangle r2(E,F,G,H);
int area = r1.InclusiveArea(r2);
if (area > 0) return area;
return r1.Area() + r2.Area() - r1.OverlappedArea(r2);
}
int main()
{
//16
cout << "16 : " << computeArea(-1, -1, 1, 1, -2, -2, 2, 2) << endl;
//16
cout << "16 : " << computeArea(-2, -2, 2, 2, -1, -1, 1, 1) << endl;
//17
cout << "17 : " << computeArea(-2, -2, 2, 2, -4, 3, -3, 4) << endl;
//45
cout << "45 : " << computeArea(-3, -0, 3, 4, 0, -1, 9, 2) << endl;
//24
cout << "24 : " << computeArea(-2, -2, 2, 2, -3, -3, 3, -1) << endl;
return 0;
}