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 2 3 4 5 6 7 8 9 10
Input: [1,7,4,9,2,5] Output: 6 Explanation: The entire sequence is a wiggle sequence.
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].
// time:O(n) space:O(n) publicintwiggleMaxLength2(int[] nums){ if (nums == null || nums.length == 0) return0; int n = nums.length; int[] up = newint[n]; int[] down = newint[n]; up[0] = 1; down[0] = 1; for (int i = 1; i < n; i++) { if (nums[i] > nums[i - 1]) { // up up[i] = down[i - 1] + 1; down[i] = down[i - 1]; } elseif (nums[i] < nums[i - 1]) { // down down[i] = up[i - 1] + 1; up[i] = up[i - 1]; } else { down[i] = down[i - 1]; up[i] = up[i - 1]; } } return Math.max(down[n - 1], up[n - 1]); }
// time:O(n) space:O(1) 优化空间,因为只是依赖前后的值 publicintwiggleMaxLength3(int[] nums){ if (nums == null || nums.length == 0) return0; int n = nums.length; int up = 1; int down = 1; for (int i = 1; i < n; i++) { if (nums[i] > nums[i - 1]) { // up up = down + 1; } elseif (nums[i] < nums[i - 1]) { // down down = up + 1; } } return Math.max(down, up); }