Description#
You are given a 2D integer array rectangles
where rectangles[i] = [li, hi]
indicates that ith
rectangle has a length of li
and a height of hi
. You are also given a 2D integer array points
where points[j] = [xj, yj]
is a point with coordinates (xj, yj)
.
The ith
rectangle has its bottom-left corner point at the coordinates (0, 0)
and its top-right corner point at (li, hi)
.
Return an integer array count
of length points.length
where count[j]
is the number of rectangles that contain the jth
point.
The ith
rectangle contains the jth
point if 0 <= xj <= li
and 0 <= yj <= hi
. Note that points that lie on the edges of a rectangle are also considered to be contained by that rectangle.
Example 1:
![](https://spcdn.pages.dev/leetcode/problems/2250.Count%20Number%20of%20Rectangles%20Containing%20Each%20Point/images/example1.png)
Input: rectangles = [[1,2],[2,3],[2,5]], points = [[2,1],[1,4]]
Output: [2,1]
Explanation:
The first rectangle contains no points.
The second rectangle contains only the point (2, 1).
The third rectangle contains the points (2, 1) and (1, 4).
The number of rectangles that contain the point (2, 1) is 2.
The number of rectangles that contain the point (1, 4) is 1.
Therefore, we return [2, 1].
Example 2:
![](https://spcdn.pages.dev/leetcode/problems/2250.Count%20Number%20of%20Rectangles%20Containing%20Each%20Point/images/example2.png)
Input: rectangles = [[1,1],[2,2],[3,3]], points = [[1,3],[1,1]]
Output: [1,3]
Explanation:
The first rectangle contains only the point (1, 1).
The second rectangle contains only the point (1, 1).
The third rectangle contains the points (1, 3) and (1, 1).
The number of rectangles that contain the point (1, 3) is 1.
The number of rectangles that contain the point (1, 1) is 3.
Therefore, we return [1, 3].
Constraints:
1 <= rectangles.length, points.length <= 5 * 104
rectangles[i].length == points[j].length == 2
1 <= li, xj <= 109
1 <= hi, yj <= 100
- All the
rectangles
are unique. - All the
points
are unique.
Solutions#
Solution 1#
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| class Solution:
def countRectangles(
self, rectangles: List[List[int]], points: List[List[int]]
) -> List[int]:
d = defaultdict(list)
for x, y in rectangles:
d[y].append(x)
for y in d.keys():
d[y].sort()
ans = []
for x, y in points:
cnt = 0
for h in range(y, 101):
xs = d[h]
cnt += len(xs) - bisect_left(xs, x)
ans.append(cnt)
return ans
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| class Solution {
public int[] countRectangles(int[][] rectangles, int[][] points) {
int n = 101;
List<Integer>[] d = new List[n];
Arrays.setAll(d, k -> new ArrayList<>());
for (int[] r : rectangles) {
d[r[1]].add(r[0]);
}
for (List<Integer> v : d) {
Collections.sort(v);
}
int m = points.length;
int[] ans = new int[m];
for (int i = 0; i < m; ++i) {
int x = points[i][0], y = points[i][1];
int cnt = 0;
for (int h = y; h < n; ++h) {
List<Integer> xs = d[h];
int left = 0, right = xs.size();
while (left < right) {
int mid = (left + right) >> 1;
if (xs.get(mid) >= x) {
right = mid;
} else {
left = mid + 1;
}
}
cnt += xs.size() - left;
}
ans[i] = cnt;
}
return ans;
}
}
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| class Solution {
public:
vector<int> countRectangles(vector<vector<int>>& rectangles, vector<vector<int>>& points) {
int n = 101;
vector<vector<int>> d(n);
for (auto& r : rectangles) d[r[1]].push_back(r[0]);
for (auto& v : d) sort(v.begin(), v.end());
vector<int> ans;
for (auto& p : points) {
int x = p[0], y = p[1];
int cnt = 0;
for (int h = y; h < n; ++h) {
auto& xs = d[h];
cnt += xs.size() - (lower_bound(xs.begin(), xs.end(), x) - xs.begin());
}
ans.push_back(cnt);
}
return ans;
}
};
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| func countRectangles(rectangles [][]int, points [][]int) []int {
n := 101
d := make([][]int, 101)
for _, r := range rectangles {
d[r[1]] = append(d[r[1]], r[0])
}
for _, v := range d {
sort.Ints(v)
}
var ans []int
for _, p := range points {
x, y := p[0], p[1]
cnt := 0
for h := y; h < n; h++ {
xs := d[h]
left, right := 0, len(xs)
for left < right {
mid := (left + right) >> 1
if xs[mid] >= x {
right = mid
} else {
left = mid + 1
}
}
cnt += len(xs) - left
}
ans = append(ans, cnt)
}
return ans
}
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| function countRectangles(rectangles: number[][], points: number[][]): number[] {
const n = 101;
let ymap = Array.from({ length: n }, v => []);
for (let [x, y] of rectangles) {
ymap[y].push(x);
}
for (let nums of ymap) {
nums.sort((a, b) => a - b);
}
let ans = [];
for (let [x, y] of points) {
let count = 0;
for (let h = y; h < n; h++) {
const nums = ymap[h];
let left = 0,
right = nums.length;
while (left < right) {
let mid = (left + right) >> 1;
if (x > nums[mid]) {
left = mid + 1;
} else {
right = mid;
}
}
count += nums.length - right;
}
ans.push(count);
}
return ans;
}
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