DP31-Wiggle Subsequence.cpp

/*
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?
*/
#include <bits/stdc++.h>
#define ll long long
using namespace std;

//Approach 1: O(N) time and O(N) space
class Solution {
   public:
    int wiggleMaxLength(vector<int>& nums) {
        int n = nums.size();
        if (n == 0) return 0;
        vector<int> up(n, 0), down(n, 0);
        up[0] = down[0] = 1;

        for (int i = 1; i < n; i++) {
            if (nums[i] > nums[i - 1])
                up[i] = down[i - 1] + 1, down[i] = down[i - 1];
            else if (nums[i] < nums[i - 1])
                down[i] = up[i - 1] + 1, up[i] = up[i - 1];
            else
                up[i] = up[i - 1], down[i] = down[i - 1];
        }

        return max(up[n - 1], down[n - 1]);
    }
};

//Approach2: O(N) time O(1) space
class Solution {
   public:
    int wiggleMaxLength(vector<int>& nums) {
        int n = nums.size();
        if (n == 0) return 0;
        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);
    }
};

int main() {
    return 0;
}