Rectangle Area

描述

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.

Assume that the total area is never beyond the maximum possible value of int.

分析

简单平面几何。根据容斥原理：S(M ∪ N) = S(M) + S(N) - S(M ∩ N)，最关键的是求出相交部分的面积。

代码

// Rectangle Area
// Time Complexity: O(1), Space Complexity: O(1)
public class Solution {
    public int computeArea(int A, int B, int C, int D, int E, int F, int G, int H) {
        final int area = (C - A) * (D- B) + (G - E) * (H - F);
        // prevent overflow
        if (C < E || G < A || D < F || H < B) return area;
        final int intersection = Math.max(Math.min(C, G) - Math.max(A, E), 0) *
                Math.max(Math.min(D, H) - Math.max(B, F), 0);
        return area - intersection;
    }
}