497. Random Point in Non-overlapping Rectangles

题目

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.

题目大意

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。

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。

解题思路

• 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。
• 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。

代码

package leetcode

import "math/rand"

// Solution497 define
type Solution497 struct {
	rects [][]int
	arr   []int
}

// Constructor497 define
func Constructor497(rects [][]int) Solution497 {
	s := Solution497{
		rects: rects,
		arr:   make([]int, len(rects)),
	}

	for i := 0; i < len(rects); i++ {
		area := (rects[i][2] - rects[i][0] + 1) * (rects[i][3] - rects[i][1] + 1)
		if area < 0 {
			area = -area
		}
		if i == 0 {
			s.arr[0] = area
		} else {
			s.arr[i] = s.arr[i-1] + area
		}
	}
	return s
}

// Pick define
func (so *Solution497) Pick() []int {
	r := rand.Int() % so.arr[len(so.arr)-1]
	//get rectangle first
	low, high, index := 0, len(so.arr)-1, -1
	for low <= high {
		mid := low + (high-low)>>1
		if so.arr[mid] > r {
			if mid == 0 || so.arr[mid-1] <= r {
				index = mid
				break
			}
			high = mid - 1
		} else {
			low = mid + 1
		}
	}
	if index == -1 {
		index = low
	}
	if index > 0 {
		r = r - so.arr[index-1]
	}
	length := so.rects[index][2] - so.rects[index][0]
	return []int{so.rects[index][0] + r%(length+1), so.rects[index][1] + r/(length+1)}
}

/**
 * Your Solution object will be instantiated and called as such:
 * obj := Constructor(rects);
 * param_1 := obj.Pick();
 */