卖萌的弱渣

I am stupid, I am hungry.

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.

Examples:

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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?

Solution

  • 构造法:
  • up: 结尾是wiggle up 的序列的长度
  • down: 结尾是wiggle down的序列的长度
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if nums[i]>nums[i-1]; down[i] = up[i-1]+1
if nums[i]<nums[i-1]; up[i] = down[i-1]+1
(Wiggle-Subsequence.py) download
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class Solution(object):
    def wiggleMaxLength(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        if not nums:
            return 0

        n = len(nums)


        up = [1]*n
        down = [1] * n

        for i in range(1,n):
            if nums[i] == nums[i-1]:
                up[i] = up[i-1]
                down[i] = down[i-1]
            # wiggle down, we need to find the length of last wiggle up
            elif nums[i] < nums[i-1]:
                down[i] = up[i-1] + 1
                up[i] = up[i-1]
            # wiggle up, we need to find the length of last wiggle down
            else:
                up[i] = down[i-1]+1
                down[i] = down[i-1]
        return max(max(up),max(down))