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

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 <= 10⁵
• 1 <= obstacles[i] <= 10⁷

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

Yen-Chi ChenSun, 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。
MarsgoatMon, May 8, 2023

Reference

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