1388. Pizza With 3n Slices

Problem

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

• You will pick any pizza slice.

• Your friend Alice will pick the next slice in the anti-clockwise direction of your pick.

• Your friend Bob will pick the next slice in the clockwise direction of your pick.

• Repeat until there are no more slices of pizzas.

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

  Example 1:

Input: slices = [1,2,3,4,5,6]
Output: 10
Explanation: 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.

Example 2:

Input: slices = [8,9,8,6,1,1]
Output: 16
Explanation: Pick pizza slice of size 8 in each turn. If you pick slice with size 9 your partners will pick slices of size 8.

  Constraints:

• 3 * n == slices.length

• 1 <= slices.length <= 500

• 1 <= slices[i] <= 1000

Solution

class Solution {
    public int maxSizeSlices(int[] slices) {
        int n = slices.length;
        int third = n / 3;
        return Math.max(
                maxSizeSlices(slices, 0, n - 2, third), maxSizeSlices(slices, 1, n - 1, third));
    }

    private int maxSizeSlices(int[] slices, int start, int end, int parts) {
        int[] dp = new int[slices.length];
        int res = 0;
        for (int i = 0; i < parts; i++) {
            int prev = 0;
            int prevPrev = 0;
            for (int j = end; j >= start; j--) {
                int curr = dp[j];
                dp[j] = slices[j] + prevPrev;
                prevPrev = prev;
                prev = Math.max(curr, prev);
                res = Math.max(res, dp[j]);
            }
        }
        return res;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).