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
Follow up:
Can you do it in O(n) time?
Approach #1: C++.
class Solution {
public:
int wiggleMaxLength(vector<int>& nums) {
int size = nums.size();
if (size == 0) return 0;
int old_slope = 0;
int new_slope = 0;
int ans = 1;
for (int i = 1; i < size; ++i) {
new_slope = (nums[i] - nums[i-1]) > 0 ? 1 : (nums[i] - nums[i-1]) < 0 ? -1 : 0;
if (new_slope == 0) continue;
if (new_slope == 1 && old_slope == -1 || new_slope == -1 && old_slope == 1)
ans++;
old_slope = new_slope;
}
if (old_slope == 0 && new_slope == 0) return ans;
return ans + 1;
}
};