223. Rectangle Area

Description

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.

Example:

Input: A = -3, B = 0, C = 3, D = 4, E = 0, F = -1, G = 9, H = 2
Output: 45

Note:

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

分析和方案

求的是两个长方形的面积的合，所以需要判断是否有重叠部分。

思路就是判断一个长方形的四个点，是否落在另一个长方形内，如果有则说明重叠了，需要在面积合中减去重叠面积。

/**
 * @param {number} A
 * @param {number} B
 * @param {number} C
 * @param {number} D
 * @param {number} E
 * @param {number} F
 * @param {number} G
 * @param {number} H
 * @return {number}
 */
var computeArea = function(A, B, C, D, E, F, G, H) {
    var r1 =  Math.abs(A-C)*Math.abs(B-D);
    var r2 =  Math.abs(E-G)*Math.abs(F-H);

    // 如果ABCD與EGFH沒重疊，直接將r1,r2加總
    if( A >= G || B >= H || C <= E || D <= F){
        return r1+r2;
    }

    // 計算重疊的部分
    var rD = Math.abs( (Math.max(A,E) - Math.min(C,G)) * (Math.max(B,F) - Math.min(D,H)) )

    return r1+r2 - rD;
};

最快

var computeArea = function(A, B, C, D, E, F, G, H) {
    var left = Math.max(A, E);
    var right = Math.min(C, G);
    var down = Math.max(B, F);
    var up = Math.min(D, H);

    if(right > left && up > down)
        return (C-A)*(D-B)+(G-E)*(H-F)-(right-left)*(up-down);
    return (C-A)*(D-B)+(G-E)*(H-F)
};

第二

var computeArea = function(A, B, C, D, E, F, G, H) {
    var xa = C-A;
    var ya = D-B;
    var xb = G-E;
    var yb = H-F;

    var left = Math.max(A,E);
    var right = Math.min(C,G);
    var bottom = Math.max(B,F);
    var top = Math.min(D,H);

    var overlap = 0;
    if( right>left && top>bottom ){
       overlap = (right-left)*(top-bottom);
    }

    return xa*ya + xb*yb - overlap;
};

第三

var computeArea = function(A, B, C, D, E, F, G, H) {
    var left = Math.max(A, E);
    var right = Math.min(C, G);
    var down = Math.max(B, F);
    var up = Math.min(D, H);

    if (right > left && up > down)
        return (C - A) * (D - B) + (G - E) * (H - F) - (right - left) * (up - down);
    return (C - A) * (D - B) + (G - E) * (H - F)
};