376. Swing sequence - LeetCode
If the difference between consecutive numbers alternates strictly between positive and negative numbers, the sequence of numbers is called a wobble sequence. The first difference (if present) may be positive or negative. Sequences with only one element or two unequal elements are also considered wobble sequences.
-
For example,
[1, 7, 4, 9, 2, 5]it is a swing sequence because the differences(6, -3, 5, -7, 3)alternate between positive and negative values. - In contrast, the sum is
[1, 4, 7, 2, 5]not[1, 7, 4, 5, 5]a oscillating sequence, the first one because its first two differences are both positive, and the second one because its last difference is zero.
A subsequence can be obtained by deleting some (or not) elements from the original sequence, leaving the remaining elements in their original order.
Given an array of integers nums , return the length of the longest subsequencenums in the wobble sequence .
Example 1:
Input: nums = [1,7,4,9,2,5] Output: 6 Explanation: The entire sequence is a swing sequence, and the difference between each element is (6, -3, 5, -7, 3) .
Example 2:
Input: nums = [1,17,5,10,13,15,10,5,16,8] Output: 7 Explanation: This sequence contains several wobble sequences of length 7. One of them is [1, 17, 10, 13, 10, 16, 8], and the difference between the elements is (16, -7, 3, -3, 6, -8).
Example 3:
Input: nums = [1,2,3,4,5,6,7,8,9] Output: 2
>>Ideas and analysis
Official solution 376. Swinging sequence - LeetCode and this article 376. Swinging sequence - LeetCode
Summary and summary of the ideas for solving the given problem
- An element in a sequence is called a "peak" if and only if the adjacent elements on both sides of the element are smaller than it. For example, 3 in the sequence [1,3,2,4] is a "peak"
- An element in a sequence is called a "valley" if and only if the adjacent elements on both sides of the element are larger than it. For example, 2 in the sequence [1,3,2,4] is a "valley"
- In particular, for elements located at both ends of the sequence, only the adjacent elements on one side are smaller or larger than it, which is also called a "peak" or "valley" . For example , in the sequence [1,3,2,4] , 1 is also a "valley" and 4 is a "peak"
Status definition:
- up[i]: The longest rising swing sequence in the array nums[0...i]
- down[i]: the longest descending swing sequence in the array nums[0...i]
State transfer:
- nums[i] > nums[i-1]: up[i] = down[i-1] + 1; down[i] = down[i-1]
- nums[i] < nums[i-1]: up[i] = up[i-1]; down[i] = up[i-1] + 1
class Solution {
public:
int wiggleMaxLength(vector<int>& nums) {
int n = nums.size();
if (n < 2) {
return n;
}
int up = 1, down = 1;
for (int i = 1; i < n; i++) {
if (nums[i] > nums[i - 1]) {
up = down + 1;
} else if (nums[i] < nums[i - 1]) {
down = up + 1;
}
}
return max(up, down);
}
};
// 作者：力扣官方题解
// 链接：https://leetcode.cn/problems/wiggle-subsequence/solutions/805292/python3-yi-tu-sheng-qian-yan-by-v12de-ao-72b1/
// 来源：力扣（LeetCode）
// 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。My previous articles: leetCode 376. Swinging Sequence Greedy Algorithm_Heheda(￣▽￣)"'s blog-CSDN blog
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