<p>There is a pizza with <code>3n</code> slices of varying size, you and your friends will take slices of pizza as follows:</p>

<ul>
	<li>You will pick <strong>any</strong> pizza slice.</li>
	<li>Your friend Alice will pick the next slice in the anti-clockwise direction of your pick.</li>
	<li>Your friend Bob will pick the next slice in the clockwise direction of your pick.</li>
	<li>Repeat until there are no more slices of pizzas.</li>
</ul>

<p>Given an integer array <code>slices</code> that represent the sizes of the pizza slices in a clockwise direction, return <em>the maximum possible sum of slice sizes that you can pick</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_3_1723.png" style="width: 500px; height: 266px;" />
<pre>
<strong>Input:</strong> slices = [1,2,3,4,5,6]
<strong>Output:</strong> 10
<strong>Explanation:</strong> Pick pizza slice of size 4, Alice and Bob will pick slices with size 3 and 5 respectively. Then Pick slices with size 6, finally Alice and Bob will pick slice of size 2 and 1 respectively. Total = 4 + 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_4_1723.png" style="width: 500px; height: 299px;" />
<pre>
<strong>Input:</strong> slices = [8,9,8,6,1,1]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Pick pizza slice of size 8 in each turn. If you pick slice with size 9 your partners will pick slices of size 8.
</pre>

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

<ul>
	<li><code>3 * n == slices.length</code></li>
	<li><code>1 &lt;= slices.length &lt;= 500</code></li>
	<li><code>1 &lt;= slices[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int solve(int index,int end,vector<int>&slices,int n){
        if(n==0|| index>end){
            return 0;
        }
        int include=slices[index]+solve(index+2,end,slices,n-1);
        int exclude=solve(index+1,end,slices,n);
        return max(include,exclude);
    }
    int solvemem(int index,int end,vector<int>&slices,int n,vector<vector<int>>&dp){
        if(n==0|| index>end){
            return 0;
        }
        if(dp[index][n]!=-1){
            return dp[index][n];
        }
        int include=slices[index]+solvemem(index+2,end,slices,n-1,dp);
        int exclude=solvemem(index+1,end,slices,n,dp);
        dp[index][n]=max(include,exclude);
        return dp[index][n];
    }
    int solvetab(vector<int>&slices){
        int k=slices.size();
        vector<vector<int>>dp1(k+2,vector<int>(k+2,0));
        vector<vector<int>>dp2(k+2,vector<int>(k+2,0));
        for(int index=k-2;index>=0;index--){
            for(int n=1;n<=k/3;n++){
                int include=slices[index]+dp1[index+2][n-1];
                int exclude=dp1[index+1][n];
                dp1[index][n]=max(include,exclude);
            }
        }
        int case1= dp1[0][k/3];
        for(int index=k-1;index>=0;index--){
            for(int n=1;n<=k/3;n++){
                int include=slices[index]+dp2[index+2][n-1];
                int exclude=dp2[index+1][n];
                dp2[index][n]=max(include,exclude);
            }
        }
        int case2= dp2[1][k/3];
        return max(case1,case2);
    }
    int maxSizeSlices(vector<int>& slices) {
        //int k=slices.size();
        //vector<vector<int>>dp1(k,vector<int>(k,-1));
        //int first=solvemem(0,k-2,slices,k/3,dp1);
        //vector<vector<int>>dp2(k,vector<int>(k,-1));
        //int second=solvemem(1,k-1,slices,k/3,dp2);
        //return max(first,second);
        return solvetab(slices);
    }
};
25600