<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 solve(vector<vector<int>> &dp, vector<int>& arr, int idx, int prev, int state){
        if(idx >= arr.size()){
            return 0;
        }
        if(dp[state][idx] != 0){
            return dp[state][idx];
        }

        
        if(state == 0){
            // down
            if(arr[idx] < prev){
                dp[state][idx] = 1 + solve(dp, arr, idx+1, arr[idx], 1);
            }
        }
        else if(state == 1){
            if(arr[idx] > prev){
                dp[state][idx] = 1 + solve(dp, arr, idx+1, arr[idx], 0);
            }
        }
        return dp[state][idx];
    }

    int maxTurbulenceSize(vector<int>& arr) {
        int n = arr.size();
        vector<vector<int>> dp(2, vector<int>(n, 0));
        // dp[0][n-1] = 1;
        // dp[1][n-1] = 1;
        int res = 1;

        for(int i=0; i<n-1; i++){
            dp[0][i] = 1 + solve(dp, arr, i+1, arr[i], 0);
            dp[1][i] = 1 + solve(dp, arr, i+1, arr[i], 1);  
            res = max(res, dp[0][i]);     
            res = max(res, dp[1][i]);     
        }
        /*
        for(int i=0; i<n; i++){
            cout << dp[0][i] << " "; 
        }
        cout << '\n';
        for(int i=0; i<n; i++){
            cout << dp[1][i] << " "; 
        }
        cout << '\n';
        */
        return res;
    }
};
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