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In this approach, we maintain a greedy solution by keeping track of directions of the growing and shrinking sequences. We scan through the array, checking the differences between consecutive numbers. Whenever a change in the sign is detected, it contributes to a count of the longest wiggle sequence.
This approach efficiently computes in O(n) time by scanning the list only once.
Time Complexity: O(n).
Space Complexity: O(1).
1def wiggleMaxLength(nums):
2 if len(nums) < 2:
3 return len(nums)
4 up = down = 1
5 for i in range(1, len(nums)):
6 if nums[i] > nums[i - 1]:
7 up = down + 1
8 elif nums[i] < nums[i - 1]:
9 down = up + 1
10 return max(up, down)
11
12nums = [1, 7, 4, 9, 2, 5]
13print(wiggleMaxLength(nums))The Python solution follows the greedy strategy approach to determine the maximum length of a wiggle subsequence. Using two counters up and down, we iterate through each element and update these counters based on the observed differences.
This solution involves using dynamic programming to keep track of two arrays - up[i] and down[i] where up[i] and down[i] indicate the longest wiggle subsequence ending at index i with an upward or downward difference respectively.
This allows evaluating the longest wiggle subsequence leading to a time complexity of O(n^2), given we evaluate each index pair combination.
Time Complexity: O(n^2).
Space Complexity: O(n).
1
public class Solution {
public int WiggleMaxLength(int[] nums) {
if (nums.Length < 2) return nums.Length;
int[] up = new int[nums.Length];
int[] down = new int[nums.Length];
Array.Fill(up, 1);
Array.Fill(down, 1);
for (int i = 1; i < nums.Length; i++) {
for (int j = 0; j < i; j++) {
if (nums[i] > nums[j])
up[i] = Math.Max(up[i], down[j] + 1);
else if (nums[i] < nums[j])
down[i] = Math.Max(down[i], up[j] + 1);
}
}
return Math.Max(up[nums.Length - 1], down[nums.Length - 1]);
}
public static void Main() {
Solution sol = new Solution();
int[] nums = {1, 7, 4, 9, 2, 5};
Console.WriteLine(sol.WiggleMaxLength(nums));
}
}In C#, this dynamic programming approach utilizes two arrays up and down to track subsequence lengths, analyzing each elements relationship to previous elements to determine growth in subsequence length.