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.
Examples:
Input: [1,7,4,9,2,5] Output: 6 The entire sequence is a wiggle sequence. Input: [1,17,5,10,13,15,10,5,16,8] Output: 7 There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8]. Input: [1,2,3,4,5,6,7,8,9] Output: 2
Follow up:
Can you do it in O(n) time?
Can you do it in O(n) time?
The idea is whenever if see a positive difference or a negative difference. We add length by 1. Then skip all consequent numbers with difference of same sign.
public int wiggleMaxLength(int[] nums) { if (nums.length <= 1) { return nums.length; } int fast = 1; int slow = 0; int ans = 1; int n = nums.length; while (fast < n) { if (nums[slow] < nums[fast]) { ans++; while (fast + 1 < n && nums[fast] <= nums[fast + 1]) { fast++; } } else if (nums[slow] > nums[fast]) { ans++; while (fast + 1 < n && nums[fast] >= nums[fast + 1]) { fast++; } } slow = fast; fast++; } return ans; }
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