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# 題目敘述

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 ith 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 ith 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.

# 解題思路

Using DP.

# Solution

class Solution {
public:
    vector<int> longestObstacleCourseAtEachPosition(vector<int>& obstacles) {
        int n = obstacles.size();
        int length = 0;
        vector<int> result(n);
        vector<int> increasingSubseq(n);
        for (int i = 0; i < n; ++i) {
            int left = 0, right = length;
            while (left < right) {
                int mid = (left + right) / 2;
                if (increasingSubseq[mid] <= obstacles[i])
                    left = mid + 1;
                else
                    right = mid;
            }
            result[i] = left + 1;
            if (length == left)
                length++;
            increasingSubseq[left] = obstacles[i];
        }
        return result;
    }
};
class Solution {
    public int[] longestObstacleCourseAtEachPosition(int[] obstacles) {
        int n = obstacles.length;
        int length = 0;
        int[] result = new int[n];
        int[] sub = new int[n];
        for (int i = 0; i < n; ++i) {
            int left = 0, right = length;
            while (left < right) {
                int mid = left + (right - left) / 2;
                if (sub[mid] <= obstacles[i])
                    left = mid + 1;
                else
                    right = mid;
            }
            result[i] = left + 1;
            if (length == left)
                length++;
            sub[left] = obstacles[i];
        }
        
        return result;
    }
}