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 ith
obstacle.
For every index i
between 0
and n - 1
(inclusive), find the length of the longest obstacle course in obstacles
such that:
0
and i
inclusive.ith
obstacle in the course.obstacles
.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
1 <= n <= 105
1 <= obstacles[i] <= 107
public class Solution {
public int[] longestObstacleCourseAtEachPosition(int[] obstacles) {
return longestIncreasingSubsequence(obstacles);
}
private int[] longestIncreasingSubsequence(int[] obstacles) {
int len = 1;
int length = obstacles.length;
int[] ans = new int[length];
int[] arr = new int[length];
arr[0] = obstacles[0];
ans[0] = 1;
for (int i = 1; i < length; i++) {
int val = obstacles[i];
if (val >= arr[len - 1]) {
arr[len++] = val;
ans[i] = len;
} else {
int idx = binarySearch(arr, 0, len - 1, val);
arr[idx] = val;
ans[i] = idx + 1;
}
}
return ans;
}
private int binarySearch(int[] arr, int lo, int hi, int val) {
int ans = -1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
if (val >= arr[mid]) {
lo = mid + 1;
} else {
ans = mid;
hi = mid - 1;
}
}
return ans;
}
}