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Formatted question description: https://leetcode.ca/all/497.html

497. Random Point in Non-overlapping Rectangles (Medium)

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.

 

Related Topics:
Binary Search, Random

Similar Questions:

// OJ: https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/
// Time:
//      Solution: O(N)
//      pick: O(logN)
// Space: O(N)
class Solution {
    vector<vector<int>> A;
    vector<int> size;
    int total = 0;
public:
    Solution(vector<vector<int>>& rects) : A(rects) {
        for (auto &r : A) size.push_back(total += (r[3] - r[1] + 1) * (r[2] - r[0] + 1));
    }
    vector<int> pick() {
        int r = rand() % total;
        int i = upper_bound(begin(size), end(size), r) - begin(size);
        r -= i > 0 ? size[i - 1] : 0;
        int w = A[i][3] - A[i][1] + 1;
        return { A[i][0] + r / w, A[i][1] + r % w };
    }
};

  • class Solution {
    int rectsCount;
    int[][] rects;
    int[] accumulatedPoints;
    int pointsCount;

    public Solution(int[][] rects) {
        rectsCount = rects.length;
        this.rects = rects;
        accumulatedPoints = new int[rectsCount];
        for (int i = 0; i < rectsCount; i++) {
            int[] rect = rects[i];
            int points = (rect[2] - rect[0] + 1) * (rect[3] - rect[1] + 1);
            accumulatedPoints[i] = points;
            pointsCount += points;
        }
        for (int i = 1; i < rectsCount; i++)
            accumulatedPoints[i] += accumulatedPoints[i - 1];
    }
    
    public int[] pick() {
        int pointsPosition = (int) (Math.random() * pointsCount);
        int index = 0;
        for (int i = 0; i < rectsCount; i++) {
            if (accumulatedPoints[i] > pointsPosition) {
                index = i;
                break;
            }
        }
        int[] rect = rects[index];
        int xMin = rect[0], xMax = rect[2];
        int yMin = rect[1], yMax = rect[3];
        int randomX = xMin + (int) (Math.random() * (xMax - xMin + 1));
        int randomY = yMin + (int) (Math.random() * (yMax - yMin + 1));
        int[] randomPoint = {randomX, randomY};
        return randomPoint;
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(rects);
 * int[] param_1 = obj.pick();
 */
############

class Solution {
    private int[] s;
    private int[][] rects;
    private Random random = new Random();

    public Solution(int[][] rects) {
        int n = rects.length;
        s = new int[n + 1];
        for (int i = 0; i < n; ++i) {
            s[i + 1] = s[i] + (rects[i][2] - rects[i][0] + 1) * (rects[i][3] - rects[i][1] + 1);
        }
        this.rects = rects;
    }

    public int[] pick() {
        int n = rects.length;
        int v = 1 + random.nextInt(s[n]);
        int left = 0, right = n;
        while (left < right) {
            int mid = (left + right) >> 1;
            if (s[mid] >= v) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        int[] rect = rects[left - 1];
        return new int[] {rect[0] + random.nextInt(rect[2] - rect[0] + 1),
            rect[1] + random.nextInt(rect[3] - rect[1] + 1)};
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(rects);
 * int[] param_1 = obj.pick();
 */

  • // OJ: https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/
// Time:
//      Solution: O(N)
//      pick: O(logN)
// Space: O(N)
class Solution {
    vector<vector<int>> A;
    vector<int> size;
    int total = 0;
public:
    Solution(vector<vector<int>>& rects) : A(rects) {
        for (auto &r : A) size.push_back(total += (r[3] - r[1] + 1) * (r[2] - r[0] + 1));
    }
    vector<int> pick() {
        int r = rand() % total;
        int i = upper_bound(begin(size), end(size), r) - begin(size);
        r -= i > 0 ? size[i - 1] : 0;
        int w = A[i][3] - A[i][1] + 1;
        return { A[i][0] + r / w, A[i][1] + r % w };
    }
};

  • class Solution:
    def __init__(self, rects: List[List[int]]):
        self.rects = rects
        self.s = [0] * len(rects)
        for i, (x1, y1, x2, y2) in enumerate(rects):
            self.s[i] = self.s[i - 1] + (x2 - x1 + 1) * (y2 - y1 + 1)

    def pick(self) -> List[int]:
        v = random.randint(1, self.s[-1])
        idx = bisect_left(self.s, v)
        x1, y1, x2, y2 = self.rects[idx]
        return [random.randint(x1, x2), random.randint(y1, y2)]


# Your Solution object will be instantiated and called as such:
# obj = Solution(rects)
# param_1 = obj.pick()

############

class Solution(object):

    def __init__(self, rects):
        """
        :type rects: List[List[int]]
        """
        self.rects = rects
        self.N = len(rects)
        areas = [(x2 - x1 + 1) * (y2 - y1 + 1) for x1, y1, x2, y2 in rects]
        self.preSum = [0] * self.N
        self.preSum[0] = areas[0]
        for i in range(1, self.N):
            self.preSum[i] = self.preSum[i - 1] + areas[i]
        self.total = self.preSum[-1]

    def pickRect(self):
        rand = random.randint(0, self.total - 1)
        return bisect.bisect_right(self.preSum, rand)

    def pickPoint(self, rect):
        x1, y1, x2, y2 = rect
        x = random.randint(x1, x2)
        y = random.randint(y1, y2)
        return x, y
        
    def pick(self):
        """
        :rtype: List[int]
        """
        rectIndex = self.pickRect()
        rect = self.rects[rectIndex]
        return self.pickPoint(rect)
        


# Your Solution object will be instantiated and called as such:
# obj = Solution(rects)
# param_1 = obj.pick()

  • type Solution struct {
	s     []int
	rects [][]int
}

func Constructor(rects [][]int) Solution {
	n := len(rects)
	s := make([]int, n+1)
	for i, v := range rects {
		s[i+1] = s[i] + (v[2]-v[0]+1)*(v[3]-v[1]+1)
	}
	return Solution{s, rects}
}

func (this *Solution) Pick() []int {
	n := len(this.rects)
	v := 1 + rand.Intn(this.s[len(this.s)-1])
	left, right := 0, n
	for left < right {
		mid := (left + right) >> 1
		if this.s[mid] >= v {
			right = mid
		} else {
			left = mid + 1
		}
	}
	rect := this.rects[left-1]
	x, y := rect[0]+rand.Intn(rect[2]-rect[0]+1), rect[1]+rand.Intn(rect[3]-rect[1]+1)
	return []int{x, y}
}

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