How do you solve Fair Distribution of Cookies on LeetCode?

Fair Distribution of Cookies (LeetCode #2305) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(k * 2^n) time complexity and O(n) space complexity. Key insight: Sorting the cookies helps prioritize larger bags, reducing unfairness.

What is the brute force solution for Fair Distribution of Cookies?

The brute force approach for Fair Distribution of Cookies is Brute Force, with O(k^n) time complexity and O(k) space complexity. The brute force approach involves generating all possible distributions of cookie bags to children and calculating the unfairness for each distribution. This method is straightforward but inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(k * 2^n).

What algorithm or data structure is used to solve Fair Distribution of Cookies?

Fair Distribution of Cookies uses the following concepts: Array, Dynamic Programming, Backtracking, Bit Manipulation, Bitmask. The recommended patterns to study are: Backtracking, Greedy, Dynamic Programming.

What are the interview tips for Fair Distribution of Cookies?

Explain your thought process clearly while coding. Discuss edge cases and constraints before diving into the solution. Practice backtracking problems to get comfortable with recursion.

What are common mistakes when solving Fair Distribution of Cookies?

Not considering all children when calculating unfairness. Failing to prune branches in the optimal solution.

#2305

Fair Distribution of Cookies

Medium

ArrayDynamic ProgrammingBacktrackingBit ManipulationBitmaskBacktrackingGreedyDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(k^n)	O(k * 2^n)
Space	O(k)	O(n)

💡

Intuition

Time O(k * 2^n)Space O(n)

The optimal solution uses backtracking with pruning to minimize the search space. By keeping track of the maximum cookies for each child and stopping early when we exceed the current minimum unfairness, we can significantly reduce the number of combinations we explore.

⚙️

Algorithm

4 steps

1Step 1: Sort the cookies array in descending order to prioritize larger bags.
2Step 2: Use a backtracking function to distribute cookies, tracking the current total for each child.
3Step 3: If at any point the maximum cookies for a child exceeds the current minimum unfairness, stop exploring that path.
4Step 4: Update the minimum unfairness whenever a valid distribution is found.

solution.py16 lines

1def distributeCookies(cookies, k):
2    cookies.sort(reverse=True)
3    min_unfairness = float('inf')
4    children = [0] * k
5    def backtrack(index):
6        nonlocal min_unfairness
7        if index == len(cookies):
8            min_unfairness = min(min_unfairness, max(children))
9            return
10        for i in range(k):
11            children[i] += cookies[index]
12            if max(children) < min_unfairness:
13                backtrack(index + 1)
14            children[i] -= cookies[index]
15    backtrack(0)
16    return min_unfairness

ℹ

Complexity note: The time complexity is O(k * 2^n) because we explore each combination of distributing cookies, but we prune branches early when the unfairness exceeds the current minimum. The space complexity is O(n) due to the recursion stack.

1Sorting the cookies helps prioritize larger bags, reducing unfairness.
2Backtracking with pruning significantly reduces the number of combinations explored.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.