376. Wiggle Subsequence

Description

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

Tags: Math, String

题意

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

题解

思路1

分别定义上升下降2个状态,分别做判断

376_Wiggle_Subsequence

func wiggleMaxLength(nums []int) int {
    //    序列个数小于二直接是摇摆序列
    if len(nums) < 2 {
        return len(nums)
    }
    //    3种状态
    const BEGIN, UP, DOWN = 0, 1, 2
    //    摇摆序列最小长度至少为1
    STATE, maxLength := BEGIN, 1

    for i := 1; i < len(nums); i++ {
        switch STATE {
        case BEGIN:
            if nums[i-1] < nums[i] {
                STATE = UP
                maxLength++
            } else if nums[i-1] > nums[i] {
                STATE = DOWN
                maxLength++
            }
        case UP:
            if nums[i-1] > nums[i] {
                STATE = DOWN
                maxLength++
            }
        case DOWN:
            if nums[i-1] < nums[i] {
                STATE = UP
                maxLength++
            }
        }
    }
    return maxLength
}

结语

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