Introduction

In this blog post, we will explore how to solve the LeetCode problem "2305" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer array cookies, where cookies[i] denotes the number of cookies in the ith bag. You are also given an integer k that denotes the number of children to distribute all the bags of cookies to. All the cookies in the same bag must go to the same child and cannot be split up. The unfairness of a distribution is defined as the maximum total cookies obtained by a single child in the distribution. Return the minimum unfairness of all distributions. Example 1: Input: cookies = [8,15,10,20,8], k = 2 Output: 31 Explanation: One optimal distribution is [8,15,8] and [10,20] - The 1st child receives [8,15,8] which has a total of 8 + 15 + 8 = 31 cookies. - The 2nd child receives [10,20] which has a total of 10 + 20 = 30 cookies. The unfairness of the distribution is max(31,30) = 31. It can be shown that there is no distribution with an unfairness less than 31. Example 2: Input: cookies = [6,1,3,2,2,4,1,2], k = 3 Output: 7 Explanation: One optimal distribution is [6,1], [3,2,2], and [4,1,2] - The 1st child receives [6,1] which has a total of 6 + 1 = 7 cookies. - The 2nd child receives [3,2,2] which has a total of 3 + 2 + 2 = 7 cookies. - The 3rd child receives [4,1,2] which has a total of 4 + 1 + 2 = 7 cookies. The unfairness of the distribution is max(7,7,7) = 7. It can be shown that there is no distribution with an unfairness less than 7. Constraints: 2 <= cookies.length <= 8 1 <= cookies[i] <= 105 2 <= k <= cookies.length

Explanation

Here's the solution:

• Binary Search: Perform a binary search on the possible range of unfairness (from the maximum cookie bag size to the total sum of cookies).
• Feasibility Check: For a given mid-value during the binary search, check if it's possible to distribute the cookies among k children such that no child receives more than mid cookies. We achieve this by recursively exploring all possible assignments of cookie bags to children.

• Optimization: Utilize backtracking to efficiently explore the possible distributions.

• Runtime Complexity: O(kⁿ log(sum of cookies)), where n is the number of cookie bags and k is the number of children.

• Storage Complexity: O(k + n), due to the recursion depth and the array of child cookie sums.

Code

    def distributeCookies(cookies, k):
    n = len(cookies)
    total_sum = sum(cookies)
    low = max(cookies)
    high = total_sum
    ans = high

    def is_possible(mid):
        child_sums = [0] * k

        def backtrack(index):
            if index == n:
                return True

            for i in range(k):
                if child_sums[i] + cookies[index] <= mid:
                    child_sums[i] += cookies[index]
                    if backtrack(index + 1):
                        return True
                    child_sums[i] -= cookies[index]
                    if child_sums[i] == 0:
                        break  # Optimization: No need to try empty assignment again
            return False

        return backtrack(0)

    while low <= high:
        mid = (low + high) // 2
        if is_possible(mid):
            ans = mid
            high = mid - 1
        else:
            low = mid + 1

    return ans