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 iin the range[l, r - 1],nums[i] % 2 != nums[i + 1] % 2(The elements alternate between even and odd).
- For all indices iin 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 is3.
Example 2
- Input: nums = [1,2],threshold = 2
- Output: 1
- Explanation: The subarray [2]satisfies all conditions. The length is1.
Example 3
- Input: nums = [2,3,4,5],threshold = 4
- Output: 3
- Explanation: The subarray [2,3,4]satisfies all conditions. The length is3.
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 nis the length ofnums(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]andthreshold = 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 landrat the beginning of the array and expandr.
- If conditions are violated, increment lto 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 rand once byl).
- Space Complexity: O(1).
d. Code Snippet