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1388. Pizza With 3n Slices

Difficulty Topics

Description

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

pizza-with-3n-slices.py
class Solution:
    def maxSizeSlices(self, slices: List[int]) -> int:

        @cache
        def go(i, j, k):
            if k == 1: return max(slices[i : j + 1])

            if j - i + 1 < k * 2 - 1: return float('-inf')

            return max(go(i + 2, j, k - 1) + slices[i], go(i + 1, j, k))

        n = len(slices)

        return max(go(0, n - 2, n // 3), go(1, n - 1, n // 3))