There is a pizza with 3n slices of varying size, you and your friends will take slices of pizza as follows:
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.length1 <= slices.length <= 5001 <= slices[i] <= 1000This approach utilizes dynamic programming to solve the problem of selecting non-consecutive maximum slices. Since the pizza is circular, we consider two possible scenarios: including the first slice and excluding the last one, and excluding the first slice and including the last one. We solve both scenarios using a dynamic programming table to store the maximum sum for slices that can be picked.
This C solution defines a helper function solve that uses dynamic programming to calculate the maximum sum for picking non-consecutive slices. The main function maxSizeSlices calls solve for two scenarios to handle the circular nature of the problem, ensuring that slices are not picked consecutively across the cycle.
C++
Java
Python
C#
JavaScript
Time Complexity: O(n^2), where n is the number of slices. Space Complexity: O(n^2) for the DP table.
This approach focuses on optimizing the space used in dynamic programming by maintaining just two previous states rather than a whole table. This can significantly reduce the space complexity from O(n^2) to O(n), improving the practicality of the solution when dealing with larger inputs.
This C solution maintains only two arrays to store results from prior iterations of dynamic programming calculations, effectively reducing space complexity while maintaining the correct logic for slice selection.
C++
Java
Python
C#
JavaScript
Time Complexity: O(n^2), Space Complexity: O(n), where n is the number of slices.
| Approach | Complexity |
|---|---|
| Approach 1: Dynamic Programming - Circular Array | Time Complexity: O(n^2), where n is the number of slices. Space Complexity: O(n^2) for the DP table. |
| Approach 2: Dynamic Programming with Space Optimization | Time Complexity: O(n^2), Space Complexity: O(n), where n is the number of slices. |
Meta's Favorite Coding Question - 3Sum - Leetcode 15 • Greg Hogg • 109,938 views views
Watch 9 more video solutions →Practice Pizza With 3n Slices with our built-in code editor and test cases.
Practice on FleetCodePractice this problem
Open in Editor