<p>Given an integer array <code>arr</code>, return <em>the length of a maximum size turbulent subarray of</em> <code>arr</code>.</p>

<p>A subarray is <strong>turbulent</strong> if the comparison sign flips between each adjacent pair of elements in the subarray.</p>

<p>More formally, a subarray <code>[arr[i], arr[i + 1], ..., arr[j]]</code> of <code>arr</code> is said to be turbulent if and only if:</p>

<ul>
	<li>For <code>i &lt;= k &lt; j</code>:

	<ul>
		<li><code>arr[k] &gt; arr[k + 1]</code> when <code>k</code> is odd, and</li>
		<li><code>arr[k] &lt; arr[k + 1]</code> when <code>k</code> is even.</li>
	</ul>
	</li>
	<li>Or, for <code>i &lt;= k &lt; j</code>:
	<ul>
		<li><code>arr[k] &gt; arr[k + 1]</code> when <code>k</code> is even, and</li>
		<li><code>arr[k] &lt; arr[k + 1]</code> when <code>k</code> is odd.</li>
	</ul>
	</li>
</ul>

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

<pre>
<strong>Input:</strong> arr = [9,4,2,10,7,8,8,1,9]
<strong>Output:</strong> 5
<strong>Explanation:</strong> arr[1] &gt; arr[2] &lt; arr[3] &gt; arr[4] &lt; arr[5]
</pre>

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

<pre>
<strong>Input:</strong> arr = [4,8,12,16]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> arr = [100]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 4 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    int dp[40004][3];
    int ans = 1;
    int rec(int i, vector<int> &a, int prev, int len)
    {
        ans = max(ans, len);

        if(i == a.size()) 
            return len;

        if(dp[i][prev]!=-1) 
            return dp[i][prev];
        
        int val = 0;

        if(prev == 0)
        {
            if(a[i] > a[i-1]) 
                val = rec(i+1, a, 2, 2);
            else if(a[i] < a[i-1]) 
                val = rec(i+1, a, 1, 2);
            else 
                val = rec(i+1, a, 0, 0);
        }
        else
        {
            if(prev == 1 && a[i] > a[i-1]) 
                val = rec(i+1, a, 2, len + 1);
            else if(prev == 2 && a[i] < a[i-1]) 
                val = rec(i+1, a, 1, len + 1);
            else if(a[i] > a[i-1]) 
                val = rec(i+1, a, 2, 2);
            else if(a[i] < a[i-1]) 
                val = rec(i+1, a, 1, 2);
            else val = rec(i+1, a, 0, 0);
        }
      
        return dp[i][prev] = val;
    }
    int maxTurbulenceSize(vector<int>& arr) {
        int n = arr.size();
        if(n == 1) return 1;
        memset(dp, -1, sizeof dp);
        rec(1, arr, 0, 0);
        return ans;
    }
};
45000