pizza-with-3n-slices

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1388. Pizza With 3n Slices (Hard)

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

Related Topics

[Array] [Dynamic Programming] [Greedy] [Heap (Priority Queue)]

Hints

Hint 1

By studying the pattern of the operations, we can find out that the problem is equivalent to: Given an integer array with size 3N, select N integers with maximum sum and any selected integers are not next to each other in the array.

Hint 2

The first one in the array is considered next to the last one in the array. Use Dynamic Programming to solve it.