[Swift]LeetCode497. 非重叠矩形中的随机点 | Random Point in Non-overlapping Rectangles

★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤微信公众号：山青咏芝（shanqingyongzhi）
➤博客园地址：山青咏芝（https://www.cnblogs.com/strengthen/）
➤GitHub地址：https://github.com/strengthen/LeetCode
➤原文地址：https://www.cnblogs.com/strengthen/p/10391824.html 
➤如果链接不是山青咏芝的博客园地址，则可能是爬取作者的文章。
➤原文已修改更新！强烈建议点击原文地址阅读！支持作者！支持原创！
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★

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.

---

给定一个非重叠轴对齐矩形的列表 rects，写一个函数 pick 随机均匀地选取矩形覆盖的空间中的整数点。

提示：

1. 整数点是具有整数坐标的点。
2. 矩形周边上的点包含在矩形覆盖的空间中。
3. 第 i 个矩形 rects [i] = [x1，y1，x2，y2]，其中 [x1，y1] 是左下角的整数坐标，[x2，y2] 是右上角的整数坐标。
4. 每个矩形的长度和宽度不超过 2000。
5. 1 <= rects.length <= 100
6. pick 以整数坐标数组 [p_x, p_y] 的形式返回一个点。
7. pick 最多被调用10000次。 

示例 1：

输入: 
["Solution","pick","pick","pick"]
[[[[1,1,5,5]]],[],[],[]]
输出: 
[null,[4,1],[4,1],[3,3]]

示例 2：

输入: 
["Solution","pick","pick","pick","pick","pick"]
[[[[-2,-2,-1,-1],[1,0,3,0]]],[],[],[],[],[]]
输出: 
[null,[-1,-2],[2,0],[-2,-1],[3,0],[-2,-2]] 

输入语法的说明：

输入是两个列表：调用的子例程及其参数。Solution的构造函数有一个参数，即矩形数组 rects。pick没有参数。参数总是用列表包装的，即使没有也是如此。

---

520ms

class Solution {

    let rects : [[Int]]
    let w: [Int]
    let sum: Int
    
    init(_ rects: [[Int]]) {
        func area(_ a: [Int]) -> Int {
            return abs(a[2]-a[0]+1)*abs(a[3]-a[1]+1)
        }
        self.rects = rects
        w = rects.reduce(into: [Int]()) { $0.append(area($1)+($0.last ?? 0))}
        sum = rects.reduce(0) { $0+area($1) }
    }
        
    func pick() -> [Int] {
      let random = Int.random(in: 0...sum-1)
        let i = searchInsert(w, random)
      let r = rects[searchInsert(w, random)]
      return [Int.random(in: r[0]...r[2]), Int.random(in: r[1]...r[3])]
    }
    
    func searchInsert(_ nums: [Int], _ target: Int) -> Int {
        var low = 0
        var high = nums.count-1
        while low <= high {
            let middle = (low + high) / 2
            if nums[middle] == target {
                return middle+1
            } else if nums[middle] > target {
                high = middle - 1
            } else {
                low = middle + 1
            }
        }
        return low
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * let obj = Solution(rects)
 * let ret_1: [Int] = obj.pick()
 */
 
/**
 * Your Solution object will be instantiated and called as such:
 * let obj = Solution(rects)
 * let ret_1: [Int] = obj.pick()
 */

---

Runtime: 844 ms

Memory Usage: 22.3 MB

class Solution {
    var _rects:[[Int]]

    init(_ rects: [[Int]]) {
        _rects = rects        
    }
    
    func pick() -> [Int] {
        var sumArea:Int = 0
        var selected:[Int] = [Int]()
        for rect in _rects
        {
            var area:Int = (rect[2] - rect[0] + 1) * (rect[3] - rect[1] + 1)
            sumArea += area
            if Int.random(in: 0..<sumArea) < area
            {
                selected = rect
            }
        }
        var x:Int = Int.random(in: 0..<(selected[2] - selected[0] + 1)) + selected[0]
        var y:Int = Int.random(in: 0..<(selected[3] - selected[1] + 1)) + selected[1]
        return [x,y]      
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * let obj = Solution(rects)
 * let ret_1: [Int] = obj.pick()
 */