We are given a list of (axis-aligned) rectangles. Each rectangle[i] = [x1, y1, x2, y2] , where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the ith rectangle.

Find the total area covered by all rectanglesin the plane. Since the answer may be too large, return it modulo 10^9 + 7.

Example 1:

Input: [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
Output: 6
Explanation: As illustrated in the picture.

Example 2:

Input: [[0,0,1000000000,1000000000]]
Output: 49
Explanation: The answer is 10^18 modulo (10^9 + 7), which is (10^9)^2 = (-7)^2 = 49.

Note:

• 1 <= rectangles.length <= 200
• rectanges[i].length = 4
• 0 <= rectangles[i][j] <= 10^9
• The total area covered by all rectangles will never exceed 2^63 - 1 and thus will fit in a 64-bit signed integer.

我們給出了一個（軸對齊的）矩形列表 rectangles 。 對於 rectangle[i] = [x1, y1, x2, y2]，其中（x1，y1）是矩形 i 左下角的坐標，（x2，y2）是該矩形右上角的坐標。

找出平面中所有矩形疊加覆蓋後的總面積。 由於答案可能太大，請返回它對 10 ^ 9 + 7 取模的結果。

示例 1：

輸入：[[0,0,2,2],[1,0,2,3],[1,0,3,1]]
輸出：6
解釋：如圖所示。

示例 2：

輸入：[[0,0,1000000000,1000000000]]
輸出：49
解釋：答案是 10^18 對 (10^9 + 7) 取模的結果， 即 (10^9)^2 → (-7)^2 = 49 。

提示：

• 1 <= rectangles.length <= 200
• rectanges[i].length = 4
• 0 <= rectangles[i][j] <= 10^9
• 矩形疊加覆蓋後的總面積不會超越 2^63 - 1 ，這意味著可以用一個 64 位有符號整數來保存面積結果。

 1 class Solution {
 2     func rectangleArea(_ rectangles: [[Int]]) -> Int {
 3         var M:Int = 1000000007
 4         var data:[Point] = [Point]()
 5         for r in rectangles
 6         {
 7             data.append(Point(r[0], r[1], 1))
 8             data.append(Point(r[0], r[3], -1))
 9             data.append(Point(r[2], r[1], -1))
10             data.append(Point(r[2], r[3], 1))
11         }
12         data.sort(by:{(a:Point,b:Point) -> Bool in
13                   if a.x == b.x {return b.y <= a.y}
14                   return a.x < b.x})
15         var map:[Int:Int] = [Int:Int]()
16         var preX:Int = -1
17         var preY:Int = -1
18         var result:Int = 0
19         for i in 0..<data.count
20         {
21             var p:Point = data[i]
22             map[p.y,default:0] += p.val
23             if i == data.count - 1 || data[i + 1].x > p.x
24             {
25                 if preX > -1
26                 {
27                     result += (preY * (p.x - preX)) % M
28                     result %= M
29                 }
30                 preY = calcY(map)
31                 preX = p.x
32 
33             }
34         }
35         return result
36     }
37 
38     func calcY(_ p:[Int:Int]) -> Int
39     {
40         var result:Int = 0
41         var pre:Int = -1
42         var count:Int = 0
43         var nums = Set(p.keys).sorted(by:<)
44         for key in nums
45         {
46             if pre >= 0 && count > 0
47             {
48                 result += key - pre
49             }
50             count += p[key,default:0]
51             pre = key
52         }
53         return result
54     }
55 }
56 
57 class Point
58 {
59     var x:Int 
60     var y:Int 
61     var val:Int
62     init(_ x:Int,_ y:Int,_ val:Int)
63     {
64         self.x = x
65         self.y = y
66         self.val = val
67     }
68 }

[Swift]LeetCode850. 矩形面積 II | Rectangle Area II