<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>

#include <vector>
#include <algorithm>
using namespace std;

class Solution {
public:
    int non_adj(const vector<int>& vi) {
        int n = vi.size();
        vector<vector<int>> dp(n / 3, vector<int>(n, 0));
        dp[0][0] = vi[0];
        for (int i = 1; i < n; ++i) {
            dp[0][i] = max(dp[0][i - 1], vi[i]);
        }
        for (int i = 1; i < n / 3; ++i) {
            for (int j = 2; j < n; ++j) {
                dp[i][j] = max(dp[i - 1][j - 2] + vi[j], dp[i][j - 1]);
            }
        }
        return dp.back().back();
    }

    int maxSizeSlices(vector<int>& slices) {
        int head = slices[0];
        slices[0] = 0;
        int first_ans = non_adj(slices);
        slices[0] = head;
        slices.back() = 0;
        return max(first_ans, non_adj(slices));
    }
};
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