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| 1 | +# [376. Wiggle Subsequence][title] |
| 2 | + |
| 3 | +## Description |
| 4 | + |
| 5 | +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. |
| 6 | + |
| 7 | +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. |
| 8 | + |
| 9 | +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. |
| 10 | + |
| 11 | +**Example 1:** |
| 12 | + |
| 13 | +``` |
| 14 | +Input: [1,7,4,9,2,5] |
| 15 | +Output: 6 |
| 16 | +Explanation: The entire sequence is a wiggle sequence. |
| 17 | +``` |
| 18 | + |
| 19 | +**Example 2:** |
| 20 | + |
| 21 | +``` |
| 22 | +Input: [1,17,5,10,13,15,10,5,16,8] |
| 23 | +Output: 7 |
| 24 | +Explanation: There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8]. |
| 25 | +``` |
| 26 | + |
| 27 | +**Example 3:** |
| 28 | + |
| 29 | +``` |
| 30 | +Input: [1,2,3,4,5,6,7,8,9] |
| 31 | +Output: 2 |
| 32 | +``` |
| 33 | + |
| 34 | +**Tags:** Math, String |
| 35 | + |
| 36 | +## 题意 |
| 37 | +>求摇摆序列最长序列,可以转化为数组【上升】【下降】状态的转换 |
| 38 | +
|
| 39 | +<a href="https://github.com/kylesliu/awesome-golang-leetcode/tree/master/assets/images/376_Wiggle_Subsequence.jpg"> |
| 40 | + <img src="https://github.com/kylesliu/awesome-golang-leetcode/tree/master/assets/images/376_Wiggle_Subsequence.jpg" /> |
| 41 | +</a> |
| 42 | + |
| 43 | +## 题解 |
| 44 | + |
| 45 | +### 思路1 |
| 46 | +> 按照小学算数那么来做,用 `carry` 表示进位,从后往前算,依次往前,每算出一位就插入到最前面即可,直到把两个二进制串都遍历完即可。 |
| 47 | +
|
| 48 | +```go |
| 49 | +func wiggleMaxLength(nums []int) int { |
| 50 | + // 序列个数小于二直接是摇摆序列 |
| 51 | + if len(nums) < 2 { |
| 52 | + return len(nums) |
| 53 | + } |
| 54 | + // 3种状态 |
| 55 | + const BEGIN, UP, DOWN = 0, 1, 2 |
| 56 | + // 摇摆序列最小长度至少为1 |
| 57 | + STATE, maxLength := BEGIN, 1 |
| 58 | + |
| 59 | + for i := 1; i < len(nums); i++ { |
| 60 | + switch STATE { |
| 61 | + case BEGIN: |
| 62 | + if nums[i-1] < nums[i] { |
| 63 | + STATE = UP |
| 64 | + maxLength++ |
| 65 | + } else if nums[i-1] > nums[i] { |
| 66 | + STATE = DOWN |
| 67 | + maxLength++ |
| 68 | + } |
| 69 | + case UP: |
| 70 | + if nums[i-1] > nums[i] { |
| 71 | + STATE = DOWN |
| 72 | + maxLength++ |
| 73 | + } |
| 74 | + case DOWN: |
| 75 | + if nums[i-1] < nums[i] { |
| 76 | + STATE = UP |
| 77 | + maxLength++ |
| 78 | + } |
| 79 | + } |
| 80 | + } |
| 81 | + return maxLength |
| 82 | +} |
| 83 | + |
| 84 | +``` |
| 85 | + |
| 86 | +### 思路2 |
| 87 | +> 思路2 |
| 88 | +```go |
| 89 | + |
| 90 | +``` |
| 91 | + |
| 92 | +## 结语 |
| 93 | + |
| 94 | +如果你同我一样热爱数据结构、算法、LeetCode,可以关注我 GitHub 上的 LeetCode 题解:[awesome-golang-leetcode][me] |
| 95 | + |
| 96 | +[title]: https://leetcode.com/problems/wiggle-subsequence/ |
| 97 | +[me]: https://github.com/kylesliu/awesome-golang-leetcode |
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