1964.Find the Longest Valid Obstacle Course at Each Position
===

###### tags: `Hard`,`Array`,`Binary Search`

[1964. Find the Longest Valid Obstacle Course at Each Position](https://leetcode.com/problems/find-the-longest-valid-obstacle-course-at-each-position/)

### 題目描述

You want to build some obstacle courses. You are given a **0-indexed** integer array `obstacles` of length ``n``, where `obstacles[i]` describes the height of the i^th^ obstacle.

For every index i between `0` and `n - 1` (**inclusive**), find the length of the **longest obstacle course** in `obstacles` such that:

* You choose any number of obstacles between `0` and `i` **inclusive**.
* You must include the i^th^ obstacle in the course.
* You must put the chosen obstacles in the **same order** as they appear in `obstacles`.
* Every obstacle (except the first) is **taller** than or the **same height** as the obstacle immediately before it.

Return *an array* `ans` *of length* `n`, *where* `ans[i]` *is the length of the **longest obstacle course** for index* `i` *as described above*.

### 範例

**Example 1:**

Input: obstacles = [1,2,3,2]
Output: [1,2,3,3]
Explanation: The longest valid obstacle course at each position is:
- i = 0: [1], [1] has length 1.
- i = 1: [1,2], [1,2] has length 2.
- i = 2: [1,2,3], [1,2,3] has length 3.
- i = 3: [1,2,3,2], [1,2,2] has length 3.

**Example 2:**

Input: obstacles = [2,2,1]
Output: [1,2,1]
Explanation: The longest valid obstacle course at each position is:
- i = 0: [2], [2] has length 1.
- i = 1: [2,2], [2,2] has length 2.
- i = 2: [2,2,1], [1] has length 1.

**Example 3:**

Input: obstacles = [3,1,5,6,4,2]
Output: [1,1,2,3,2,2]
Explanation: The longest valid obstacle course at each position is:
- i = 0: [3], [3] has length 1.
- i = 1: [3,1], [1] has length 1.
- i = 2: [3,1,5], [3,5] has length 2. [1,5] is also valid.
- i = 3: [3,1,5,6], [3,5,6] has length 3. [1,5,6] is also valid.
- i = 4: [3,1,5,6,4], [3,4] has length 2. [1,4] is also valid.
- i = 5: [3,1,5,6,4,2], [1,2] has length 2.

**Constraints**:

* `n` == `obstacles.length`
* 1 <= n <= 10^5^
* 1 <= `obstacles[i]` <= 10^7^

### 解答
#### Python

class Solution:
    def longestObstacleCourseAtEachPosition(self, obstacles: List[int]) -> List[int]:
        tmp = []
        ans = []
        for obstacle in obstacles:
            target = bisect_right(tmp, obstacle)
            if target == len(tmp):
                tmp.append(obstacle)
            else:
                tmp[target] = obstacle
            ans.append(target + 1)
        return ans

> [name=Yen-Chi Chen][time=Sun, May 7, 2023]

#### Javascript

import _ from 'lodash';

function longestObstacleCourseAtEachPosition(obstacles) {
  const ans = [];
  const tail = [];
  for (const num of obstacles) {
    const index = _.sortedLastIndex(tail, num);
    tail[index] = num;
    ans.push(index + 1);
  }

  return ans;
}

> 學到很多，其實這題就是找最長非遞減子序列，看答案才恍然大悟，就是LIS的變形而已。
> [name=Marsgoat][time=Mon, May 8, 2023]

### Reference

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