HackMD
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 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
0andiinclusive. - 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.
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
