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

Hard

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 <code>i^th</code> 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 <code>i^th</code> 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.

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

• <code>1 <= n <= 10⁵</code>

• <code>1 <= obstaclesi<= 10⁷</code>