Given a list of non-overlapping axis-aligned rectangles rects, write a function pick which randomly and uniformily picks an integer point in the space covered by the rectangles.

Note:

1. An integer point is a point that has integer coordinates.
2. A point on the perimeter of a rectangle is included in the space covered by the rectangles.
3. ith rectangle = rects[i]= [x1,y1,x2,y2], where [x1, y1] are the integer coordinates of the bottom-left corner, and [x2, y2] are the integer coordinates of the top-right corner.
4. length and width of each rectangle does not exceed 2000.
5. 1 <= rects.length <= 100
6. pick return a point as an array of integer coordinates [p_x, p_y]
7. pick is called at most 10000 times.

Example 1:

Input: 
["Solution","pick","pick","pick"]
[[[[1,1,5,5]]],[],[],[]]
Output: 
[null,[4,1],[4,1],[3,3]]

Example 2:

Input: 
["Solution","pick","pick","pick","pick","pick"]
[[[[-2,-2,-1,-1],[1,0,3,0]]],[],[],[],[],[]]
Output: 
[null,[-1,-2],[2,0],[-2,-1],[3,0],[-2,-2]]
 

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution‘s constructor has one argument, the array of rectangles rects. pick has no arguments. Arguments are always wrapped with a list, even if there aren‘t any.

給定一個非重疊軸對齊矩形的列表 rects，寫一個函數 pick 隨機均勻地選取矩形覆蓋的空間中的整數點。

提示：

1. 整數點是具有整數坐標的點。
2. 矩形周邊上的點包含在矩形覆蓋的空間中。
3. 第 i 個矩形 rects [i] = [x1，y1，x2，y2]，其中 [x1，y1] 是左下角的整數坐標，[x2，y2] 是右上角的整數坐標。
4. 每個矩形的長度和寬度不超過 2000。
5. 1 <= rects.length <= 100
6. pick 以整數坐標數組 [p_x, p_y] 的形式返回一個點。
7. pick 最多被調用10000次。

示例 1：

輸入: 
["Solution","pick","pick","pick"]
[[[[1,1,5,5]]],[],[],[]]
輸出: 
[null,[4,1],[4,1],[3,3]]

示例 2：

輸入: 
["Solution","pick","pick","pick","pick","pick"]
[[[[-2,-2,-1,-1],[1,0,3,0]]],[],[],[],[],[]]
輸出: 
[null,[-1,-2],[2,0],[-2,-1],[3,0],[-2,-2]] 

輸入語法的說明：

輸入是兩個列表：調用的子例程及其參數。Solution的構造函數有一個參數，即矩形數組 rects。pick沒有參數。參數總是用列表包裝的，即使沒有也是如此。

 1 class Solution {
 2 
 3     let rects : [[Int]]
 4     let w: [Int]
 5     let sum: Int
 6     
 7     init(_ rects: [[Int]]) {
 8         func area(_ a: [Int]) -> Int {
 9             return abs(a[2]-a[0]+1)*abs(a[3]-a[1]+1)
10         }
11         self.rects = rects
12         w = rects.reduce(into: [Int]()) { $0.append(area($1)+($0.last ?? 0))}
13         sum = rects.reduce(0) { $0+area($1) }
14     }
15         
16     func pick() -> [Int] {
17       let random = Int.random(in: 0...sum-1)
18         let i = searchInsert(w, random)
19       let r = rects[searchInsert(w, random)]
20       return [Int.random(in: r[0]...r[2]), Int.random(in: r[1]...r[3])]
21     }
22     
23     func searchInsert(_ nums: [Int], _ target: Int) -> Int {
24         var low = 0
25         var high = nums.count-1
26         while low <= high {
27             let middle = (low + high) / 2
28             if nums[middle] == target {
29                 return middle+1
30             } else if nums[middle] > target {
31                 high = middle - 1
32             } else {
33                 low = middle + 1
34             }
35         }
36         return low
37     }
38 }
39 
40 /**
41  * Your Solution object will be instantiated and called as such:
42  * let obj = Solution(rects)
43  * let ret_1: [Int] = obj.pick()
44  */
45  
46 /**
47  * Your Solution object will be instantiated and called as such:
48  * let obj = Solution(rects)
49  * let ret_1: [Int] = obj.pick()
50  */

 1 class Solution {
 2     var _rects:[[Int]]
 3 
 4     init(_ rects: [[Int]]) {
 5         _rects = rects        
 6     }
 7     
 8     func pick() -> [Int] {
 9         var sumArea:Int = 0
10         var selected:[Int] = [Int]()
11         for rect in _rects
12         {
13             var area:Int = (rect[2] - rect[0] + 1) * (rect[3] - rect[1] + 1)
14             sumArea += area
15             if Int.random(in: 0..<sumArea) < area
16             {
17                 selected = rect
18             }
19         }
20         var x:Int = Int.random(in: 0..<(selected[2] - selected[0] + 1)) + selected[0]
21         var y:Int = Int.random(in: 0..<(selected[3] - selected[1] + 1)) + selected[1]
22         return [x,y]      
23     }
24 }
25 
26 /**
27  * Your Solution object will be instantiated and called as such:
28  * let obj = Solution(rects)
29  * let ret_1: [Int] = obj.pick()
30  */
31  

[Swift]LeetCode497. 非重疊矩形中的隨機點 | Random Point in Non-overlapping Rectangles