Leetcode #1388: Pizza With 3n Slices
In this guide, we solve Leetcode #1388 Pizza With 3n Slices in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Greedy, Array, Dynamic Programming, Heap (Priority Queue)
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
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.
Python Solution
class Solution:
def maxSizeSlices(self, slices: List[int]) -> int:
def g(nums: List[int]) -> int:
m = len(nums)
f = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
f[i][j] = max(
f[i - 1][j], (f[i - 2][j - 1] if i >= 2 else 0) + nums[i - 1]
)
return f[m][n]
n = len(slices) // 3
a, b = g(slices[:-1]), g(slices[1:])
return max(a, b)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.