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g3201_3300.s3275_k_th_nearest_obstacle_queries.readme.md Maven / Gradle / Ivy

3275\. K-th Nearest Obstacle Queries

Medium

There is an infinite 2D plane.

You are given a positive integer `k`. You are also given a 2D array `queries`, which contains the following queries:

*   `queries[i] = [x, y]`: Build an obstacle at coordinate `(x, y)` in the plane. It is guaranteed that there is **no** obstacle at this coordinate when this query is made.

After each query, you need to find the **distance** of the kth **nearest** obstacle from the origin.

Return an integer array `results` where `results[i]` denotes the kth nearest obstacle after query `i`, or `results[i] == -1` if there are less than `k` obstacles.

**Note** that initially there are **no** obstacles anywhere.

The **distance** of an obstacle at coordinate `(x, y)` from the origin is given by `|x| + |y|`.

**Example 1:**

**Input:** queries = [[1,2],[3,4],[2,3],[-3,0]], k = 2

**Output:** [-1,7,5,3]

**Explanation:**

*   Initially, there are 0 obstacles.
*   After `queries[0]`, there are less than 2 obstacles.
*   After `queries[1]`, there are obstacles at distances 3 and 7.
*   After `queries[2]`, there are obstacles at distances 3, 5, and 7.
*   After `queries[3]`, there are obstacles at distances 3, 3, 5, and 7.

**Example 2:**

**Input:** queries = [[5,5],[4,4],[3,3]], k = 1

**Output:** [10,8,6]

**Explanation:**

*   After `queries[0]`, there is an obstacle at distance 10.
*   After `queries[1]`, there are obstacles at distances 8 and 10.
*   After `queries[2]`, there are obstacles at distances 6, 8, and 10.

**Constraints:**

*   1 <= queries.length <= 2 * 105
*   All `queries[i]` are unique.
*   -109 <= queries[i][0], queries[i][1] <= 109
*   1 <= k <= 105