Leetcode #1815: Maximum Number of Groups Getting Fresh Donuts
In this guide, we solve Leetcode #1815 Maximum Number of Groups Getting Fresh Donuts 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 donuts shop that bakes donuts in batches of batchSize. They have a rule where they must serve all of the donuts of a batch before serving any donuts of the next batch.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Bit Manipulation, Memoization, Array, Dynamic Programming, Bitmask
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: batchSize = 3, groups = [1,2,3,4,5,6]
Output: 4
Explanation: You can arrange the groups as [6,2,4,5,1,3]. Then the 1st, 2nd, 4th, and 6th groups will be happy.
Python Solution
class Solution:
def maxHappyGroups(self, batchSize: int, groups: List[int]) -> int:
def dfs(state, mod):
res = 0
x = int(mod == 0)
for i in range(1, batchSize):
if state >> (i * 5) & 31:
t = dfs(state - (1 << (i * 5)), (mod + i) % batchSize)
res = max(res, t + x)
return res
state = ans = 0
for v in groups:
i = v % batchSize
ans += i == 0
if i:
state += 1 << (i * 5)
ans += dfs(state, 0)
return ans
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
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.