Wiggle Subsequence
A sequence of numbers is called awiggle sequenceif 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
Follow up: Can you do it in O(n) time?
分析
subarray时候 每次都要reset up / down/up&down(==)
2个状态升降 up and down,交替由对方得来
if (nums[i] > nums[i-1]) u = b + 1;
else if (nums[i] < nums[i-1]) b = u + 1;
else 不变
class Solution:
def wiggleMaxLength(self, nums: List[int]) -> int:
n = len(nums)
if n==0:
return n
up=down=1
for i in range(1,n):
if nums[i]>nums[i-1]:
up=down+1
elif nums[i]<nums[i-1]:
down= up+1
return max(up,down)
错位相减得到diff,然后diff错位相乘,计算<0的总数
注意这里float('nan')占位,zip2个数组可以长度不一。
class Solution:
def wiggleMaxLength(self, nums: List[int]) -> int:
c = float('nan')
diffs = [a-b for a,b in zip([c]+nums,nums+[c]) if a-b]
return sum(not a*b>=0 for a,b in zip(diffs,diffs[1:]))
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