Maximum Number Of Groups Getting Fresh Donuts - Leetcode Solution

Problem Statement: There are n people who want to eat fresh donuts. The chef has m donuts and can bake a maximum of k donuts at a time. Each person can only eat one donut. Determine the maximum number of groups of people that can eat fresh donuts.

Solution: We can solve this problem by using binary search. First, we need to compute the maximum number of groups that can be formed when we bake x donuts at a time. To do this, we need to iterate through each person and check if they can be assigned a fresh donut. If we run out of donuts before everyone gets one, then we know we cannot form all the groups and we need to bake more donuts. If we finish iterating through all the people and we still have donuts left, then we can try to form more groups. We continue this process until we cannot form any more groups.

Here's the code implementation for the same:

class Solution:
    def maxGroups(self, n: int, m: int, k: int) -> int:
        l, r = 1, m
        
        while l <= r:
            mid = (l + r) // 2
            
            # Compute the maximum number of groups that can be formed with x donuts
            groups = 0
            donuts = 0

            for i in range(n):
                if donuts == k:
                    donuts = 0
                if donuts == 0:
                    groups += 1
                if groups > mid:
                    break
                donuts += 1
            
            # Update the search space based on the result
            if groups == mid:
                l = mid + 1
            else:
                r = mid - 1
        
        return r

Time Complexity: The time complexity of this solution is O(nlogm), where n is the number of people and m is the number of donuts.

Space Complexity: The space complexity of this solution is O(1), as we are not using any extra data structures.

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