Problem Statement
You are given a 0-indexed integer array nums
and an integer threshold
.
Find the length of the longest subarray of nums
starting at index l
and ending at index r
(0 <= l <= r < nums.length
) that satisfies the following conditions:
nums[l] % 2 == 0
(The starting element is even).
- For all indices
i
in the range [l, r - 1]
, nums[i] % 2 != nums[i + 1] % 2
(The elements alternate between even and odd).
- For all indices
i
in the range [l, r]
, nums[i] <= threshold
(Each element is less than or equal to the threshold).
Return the length of the longest such subarray.
Example 1
- Input:
nums = [3,2,5,4]
, threshold = 5
- Output:
3
- Explanation: The subarray
[2,5,4]
satisfies all conditions. The length of this subarray is 3
.
Example 2
- Input:
nums = [1,2]
, threshold = 2
- Output:
1
- Explanation: The subarray
[2]
satisfies all conditions. The length is 1
.
Example 3
- Input:
nums = [2,3,4,5]
, threshold = 4
- Output:
3
- Explanation: The subarray
[2,3,4]
satisfies all conditions. The length is 3
.
Brute Force Approach
a. Approach
- We explore all possible subarrays, checking if each satisfies the required conditions.
- Track the longest valid subarray that meets the conditions.
b. Steps
- Loop through each possible starting index
l
.
- For each
l
, try to extend the subarray to find the longest range [l, r]
that meets the criteria.
- Track the maximum length of any valid subarray found.
c. Time & Space Complexity
- Time Complexity: O(n^2), where
n
is the length of nums
(due to nested loops).
- Space Complexity: O(1), as only variables for tracking the length are used.
d. Code Snippet
e. Dry Run
- For
nums = [3,2,5,4]
and threshold = 5
, the loop finds [2,5,4]
as the longest valid subarray.
Efficient Approach (Sliding Window)
a. Approach
- Use a sliding window technique to dynamically adjust the range
[l, r]
.
- Slide the window to maintain the longest valid subarray that meets the conditions.
b. Steps
- Initialize
l
and r
at the beginning of the array and expand r
.
- If conditions are violated, increment
l
to adjust the window.
- Track the maximum length of any valid window.
c. Time & Space Complexity
- Time Complexity: O(n), as each element is processed at most twice (once by
r
and once by l
).
- Space Complexity: O(1).
d. Code Snippet