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134 lines
3.9 KiB
Markdown
Executable File
134 lines
3.9 KiB
Markdown
Executable File
# [497. Random Point in Non-overlapping Rectangles](https://leetcode.com/problems/random-point-in-non-overlapping-rectangles)
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## 题目
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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.
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**Note**:
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1. An **integer point** is a point that has integer coordinates.
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2. A point on the perimeter of a rectangle is **included** in the space covered by the rectangles.
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3. `i`th 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.
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4. length and width of each rectangle does not exceed `2000`.
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5. `1 <= rects.length <= 100`
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6. `pick` return a point as an array of integer coordinates `[p_x, p_y]`
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7. `pick` is called at most `10000` times.
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**Example 1**:
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Input:
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["Solution","pick","pick","pick"]
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[[[[1,1,5,5]]],[],[],[]]
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Output:
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[null,[4,1],[4,1],[3,3]]
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**Example 2**:
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Input:
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["Solution","pick","pick","pick","pick","pick"]
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[[[[-2,-2,-1,-1],[1,0,3,0]]],[],[],[],[],[]]
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Output:
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[null,[-1,-2],[2,0],[-2,-1],[3,0],[-2,-2]]
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**Explanation of Input Syntax:**
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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.
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## 题目大意
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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。
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提示：
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1. 整数点是具有整数坐标的点。
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2. 矩形周边上的点包含在矩形覆盖的空间中。
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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。
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4. 每个矩形的长度和宽度不超过 2000。
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5. 1 <= rects.length <= 100
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6. pick 以整数坐标数组 [p_x, p_y] 的形式返回一个点。
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7. pick 最多被调用10000次。
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输入语法的说明：
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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。
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## 解题思路
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- 给出一个非重叠轴对齐矩形列表，每个矩形用左下角和右上角的两个坐标表示。要求 `pick()` 随机均匀地选取矩形覆盖的空间中的整数点。
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- 这一题是第 528 题的变种题，这一题权重是面积，按权重（面积）选择一个矩形，然后再从矩形中随机选择一个点即可。思路和代码和第 528 题一样。
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## 代码
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```go
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package leetcode
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import "math/rand"
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// Solution497 define
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type Solution497 struct {
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rects [][]int
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arr []int
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}
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// Constructor497 define
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func Constructor497(rects [][]int) Solution497 {
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s := Solution497{
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rects: rects,
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arr: make([]int, len(rects)),
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}
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for i := 0; i < len(rects); i++ {
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area := (rects[i][2] - rects[i][0] + 1) * (rects[i][3] - rects[i][1] + 1)
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if area < 0 {
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area = -area
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}
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if i == 0 {
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s.arr[0] = area
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} else {
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s.arr[i] = s.arr[i-1] + area
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}
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}
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return s
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}
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// Pick define
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func (so *Solution497) Pick() []int {
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r := rand.Int() % so.arr[len(so.arr)-1]
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//get rectangle first
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low, high, index := 0, len(so.arr)-1, -1
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for low <= high {
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mid := low + (high-low)>>1
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if so.arr[mid] > r {
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if mid == 0 || so.arr[mid-1] <= r {
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index = mid
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break
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}
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high = mid - 1
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} else {
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low = mid + 1
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}
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}
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if index == -1 {
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index = low
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}
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if index > 0 {
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r = r - so.arr[index-1]
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}
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length := so.rects[index][2] - so.rects[index][0]
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return []int{so.rects[index][0] + r%(length+1), so.rects[index][1] + r/(length+1)}
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}
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/**
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* Your Solution object will be instantiated and called as such:
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* obj := Constructor(rects);
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* param_1 := obj.Pick();
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*/
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``` |