Leetcode: Wiggle Subsequence

2024年6月11日 155次阅读

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:
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

Solution:

class Solution {
public:
    void _wiggleMaxLength(vector<int>& nums, int idx, int result[2]) {
        result[0] = result[1] = 1;

        if (idx == nums.size() - 1) {
            return;
        }

        if (idx == nums.size() - 2) {
            if (nums[idx] < nums[idx + 1]) {
                result[0] = 2;
            } else if (nums[idx] > nums[idx + 1]) {
                result[1] = 2;
            }

            return;
        }

        _wiggleMaxLength(nums, idx + 1, result);
        if (nums[idx] < nums[idx + 1]) {
            result[0] = result[1] + 1;
        } else if (nums[idx] > nums[idx + 1]) {
            result[1] = result[0] + 1;
        }
    }

    int wiggleMaxLength(vector<int>& nums) {
        if (nums.empty())
            return 0;

        int result[2] = {0};
        _wiggleMaxLength(nums, 0, result);

        return std::max(result[0], result[1]);
    }
};

动态规划，时间复杂度：O(n)

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