Formatted question description: https://leetcode.ca/all/376.html
376 Wiggle Subsequence A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two elements is trivially a wiggle sequence. For example, [1,7,4,9,2,5] is a wiggle sequence because the differences (6,-3,5,-7,3) are alternately positive and negative. In contrast, [1,4,7,2,5] and [1,7,4,5,5] are not wiggle sequences, the first because its first two differences are positive and the second because its last difference is zero. Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order. Example 1: Input: [1,7,4,9,2,5] Output: 6 Explanation: The entire sequence is a wiggle sequence. Example 2: Input: [1,17,5,10,13,15,10,5,16,8] Output: 7 Explanation: There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8]. Example 3: Input: [1,2,3,4,5,6,7,8,9] Output: 2 Follow up: Can you do it in O(n) time? @tag-dp
We maintain two dp arrays p and q,
p[i]indicates the maximum length of the swing subsequence with a positive first difference when the position i is reached
q[i]indicates the maximum length of the wobble sub-sequence with a negative first difference when reaching the i position
We traverse the array from i=1, and then for each traversed number, traverse to this number from the beginning position, then compare nums[i] and nums[j], and update the corresponding positions respectively.
Maintain two variables p and q, and then traverse the array
- If the current number is greater than the previous number, then
- If the current number is smaller than the previous number, then
Finally, compare the larger value of p and q with n, and choose the smaller one.