2210. Count Hills and Valleys in an Array
Description
You are given a 0-indexed integer array nums
. An index i
is part of a hill in nums
if the closest non-equal neighbors of i
are smaller than nums[i]
. Similarly, an index i
is part of a valley in nums
if the closest non-equal neighbors of i
are larger than nums[i]
. Adjacent indices i
and j
are part of the same hill or valley if nums[i] == nums[j]
.
Note that for an index to be part of a hill or valley, it must have a non-equal neighbor on both the left and right of the index.
Return the number of hills and valleys in nums
.
Example 1:
Input: nums = [2,4,1,1,6,5] Output: 3 Explanation: At index 0: There is no non-equal neighbor of 2 on the left, so index 0 is neither a hill nor a valley. At index 1: The closest non-equal neighbors of 4 are 2 and 1. Since 4 > 2 and 4 > 1, index 1 is a hill. At index 2: The closest non-equal neighbors of 1 are 4 and 6. Since 1 < 4 and 1 < 6, index 2 is a valley. At index 3: The closest non-equal neighbors of 1 are 4 and 6. Since 1 < 4 and 1 < 6, index 3 is a valley, but note that it is part of the same valley as index 2. At index 4: The closest non-equal neighbors of 6 are 1 and 5. Since 6 > 1 and 6 > 5, index 4 is a hill. At index 5: There is no non-equal neighbor of 5 on the right, so index 5 is neither a hill nor a valley. There are 3 hills and valleys so we return 3.
Example 2:
Input: nums = [6,6,5,5,4,1] Output: 0 Explanation: At index 0: There is no non-equal neighbor of 6 on the left, so index 0 is neither a hill nor a valley. At index 1: There is no non-equal neighbor of 6 on the left, so index 1 is neither a hill nor a valley. At index 2: The closest non-equal neighbors of 5 are 6 and 4. Since 5 < 6 and 5 > 4, index 2 is neither a hill nor a valley. At index 3: The closest non-equal neighbors of 5 are 6 and 4. Since 5 < 6 and 5 > 4, index 3 is neither a hill nor a valley. At index 4: The closest non-equal neighbors of 4 are 5 and 1. Since 4 < 5 and 4 > 1, index 4 is neither a hill nor a valley. At index 5: There is no non-equal neighbor of 1 on the right, so index 5 is neither a hill nor a valley. There are 0 hills and valleys so we return 0.
Constraints:
3 <= nums.length <= 100
1 <= nums[i] <= 100
Solutions
Solution 1: Traversal
We initialize a pointer $j$ to point to the position with index $0$, and then traverse the array in the range $[1, n-1]$. For each position $i$:
- If $nums[i] = nums[i+1]$, then skip.
- Otherwise, if $nums[i]$ is greater than $nums[j]$ and $nums[i]$ is greater than $nums[i+1]$, then $i$ is a peak; if $nums[i]$ is less than $nums[j]$ and $nums[i]$ is less than $nums[i+1]$, then $i$ is a valley.
- Then, we update $j$ to $i$ and continue to traverse.
After the traversal, we can get the number of peaks and valleys.
The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.
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