<p>A <strong>wiggle sequence</strong> is a sequence where 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 one element and a sequence with two non-equal elements are trivially wiggle sequences.</p>

<ul>
	<li>For example, <code>[1, 7, 4, 9, 2, 5]</code> is a <strong>wiggle sequence</strong> because the differences <code>(6, -3, 5, -7, 3)</code> alternate between positive and negative.</li>
	<li>In contrast, <code>[1, 4, 7, 2, 5]</code> and <code>[1, 7, 4, 5, 5]</code> are not wiggle sequences. The first is not because its first two differences are positive, and the second is not because its last difference is zero.</li>
</ul>

<p>A <strong>subsequence</strong> is obtained by deleting some elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.</p>

<p>Given an integer array <code>nums</code>, return <em>the length of the longest <strong>wiggle subsequence</strong> of </em><code>nums</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,7,4,9,2,5]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The entire sequence is a wiggle sequence with differences (6, -3, 5, -7, 3).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,17,5,10,13,15,10,5,16,8]
<strong>Output:</strong> 7
<strong>Explanation:</strong> There are several subsequences that achieve this length.
One is [1, 17, 10, 13, 10, 16, 8] with differences (16, -7, 3, -3, 6, -8).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8,9]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> Could you solve this in <code>O(n)</code> time?</p>

int dp[1001][1002][2];
class Solution {
public:
    int sol(int i, int prv, int j, int n, vector<int>&a){
        if(i==n) return 0;
        if(dp[i][prv][j]!=-1) return dp[i][prv][j];
        if(j==0){
            int ans = sol(i+1,prv,j,n,a);
            if(prv==0||a[i]<a[prv-1]) ans = max(ans, 1+sol(i+1,i+1,1,n,a));
            return dp[i][prv][j]= ans;
        }
        else{
            int ans = sol(i+1,prv,j,n,a);
            if(prv==0||a[i]>a[prv-1]) ans = max(ans, 1+sol(i+1,i+1,0,n,a));
            return dp[i][prv][j]= ans;
        }
    }
    int wiggleMaxLength(vector<int>& nums) {
        memset(dp,-1,sizeof(dp));
        return max(sol(0,0,0,nums.size(),nums),sol(0,0,1,nums.size(),nums));
    }
};
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