3n 块披萨

/*
 * Problem: You are given a pizza with 3n slices of different sizes. You, Alice, and Bob
 * need to take turns picking slices according to the rules:
 * - You pick any slice.
 * - Alice picks the next slice counterclockwise.
 * - Bob picks the next slice clockwise.
 * - Repeat until all slices are taken.
 * The goal is to maximize the total size of slices you can collect.
 */
import java.util.stream.IntStream;

public class Solution {
    public int maxSizeSlices(int[] slices) {
        int n = slices.length / 3;
        return Math.max(maxSizeSlicesHelper(slices, 0, slices.length - 2, n),
                        maxSizeSlicesHelper(slices, 1, slices.length - 1, n));
    }
    
    private int maxSizeSlicesHelper(int[] slices, int start, int end, int n) {
        int[][] dp = new int[end - start + 2][n + 1];
        IntStream.range(1, end - start + 2).forEach(i ->
            IntStream.range(1, n + 1).forEach(j ->
                dp[i][j] = Math.max(dp[i - 1][j], (i >= 2 ? dp[i - 2][j - 1] : 0) + slices[start + i - 1])
            )
        );
        return dp[end - start + 1][n];
    }
}