2420. Find All Good Indices
Description
You are given a 0-indexed integer array nums
of size n
and a positive integer k
.
We call an index i
in the range k <= i < n - k
good if the following conditions are satisfied:
- The
k
elements that are just before the indexi
are in non-increasing order. - The
k
elements that are just after the indexi
are in non-decreasing order.
Return an array of all good indices sorted in increasing order.
Example 1:
Input: nums = [2,1,1,1,3,4,1], k = 2 Output: [2,3] Explanation: There are two good indices in the array: - Index 2. The subarray [2,1] is in non-increasing order, and the subarray [1,3] is in non-decreasing order. - Index 3. The subarray [1,1] is in non-increasing order, and the subarray [3,4] is in non-decreasing order. Note that the index 4 is not good because [4,1] is not non-decreasing.
Example 2:
Input: nums = [2,1,1,2], k = 2 Output: [] Explanation: There are no good indices in this array.
Constraints:
n == nums.length
3 <= n <= 105
1 <= nums[i] <= 106
1 <= k <= n / 2
Solutions
Solution 1: Recursion
We define two arrays decr
and incr
, which represent the longest non-increasing and non-decreasing subarray lengths from left to right and from right to left, respectively.
We traverse the array, updating the decr
and incr
arrays.
Then we sequentially traverse the index $i$ (where $k\le i \lt n - k$), if $decr[i] \geq k$ and $incr[i] \geq k$, then $i$ is a good index.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array.
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