<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:
    //starting at index i
    int n;
   
    int dp[40010][4];
    int rec(int level,int prev,vector<int>& arr){
        if(level==n-1) return 1;
        if(dp[level][prev]!=-1) return dp[level][prev];
        int ans=1;
        if(level<n-1){
            int sign=2;
            if(arr[level+1]>arr[level]) sign=1;
            if(arr[level+1]<arr[level]) sign=0;
            if(sign!=2&&(sign!=prev)){
                ans+=rec(level+1,sign,arr);
            }
        }

        return dp[level][prev]=ans;

    }
    int maxTurbulenceSize(vector<int>& arr) {
        n=arr.size();
        memset(dp,-1,sizeof(dp));
        int ans=1;
        for(int i=0;i<n-1;i++){
            int temp=1;
            int sign=2;
            if(arr[i+1]>arr[i]) sign=1;
            if(arr[i+1]<arr[i]) sign=0;
            if(sign!=2) {
                temp+=rec(i+1,sign,arr);
            }

            if(temp>ans) ans=temp;
         }

        return ans;
    }
};
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