How can I minimize the maximum working time for workers in the Find Minimum Time to Finish All Jobs problem?

You can minimize the maximum working time by using dynamic programming combined with bitmasking to explore all possible job assignments while minimizing the maximum workload for each worker.

What is the role of state transitions in the solution for the Find Minimum Time to Finish All Jobs problem?

State transitions allow you to incrementally build job assignments by selecting subsets of jobs for each worker, updating the current state while keeping track of the maximum working time.

What are the most common mistakes when solving the Find Minimum Time to Finish All Jobs problem?

Common mistakes include failing to explore all subsets of jobs, misrepresenting the job assignments with incorrect bitmasks, and not properly optimizing the solution with dynamic programming or backtracking.

What is bitmasking in the context of the Find Minimum Time to Finish All Jobs problem?

Bitmasking is a technique used to represent subsets of jobs as binary numbers, where each bit indicates whether a job is assigned or not. This allows efficient tracking of job assignments in the dynamic programming solution.

How can GhostInterview assist me with the dynamic programming solution for Find Minimum Time to Finish All Jobs?

GhostInterview guides you through the dynamic programming approach, helping you implement bitmasking and state transitions, and offers insight into how to handle job assignments efficiently.

#1723

Hard

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

完成所有工作的最短时间

给你一个整数数组 jobs ，其中 jobs[i] 是完成第 i 项工作要花费的时间。请你将这些工作分配给 k 位工人。所有工作都应该分配给工人，且每项工作只能分配给一位工人。工人的工作时间是完成分配给他们的所有工作花费时间的总和。请你设计一套最佳的工作分配方案，使工人的最大工作时间得以 …

数组动态规划回溯位运算位掩码

题目描述

给你一个整数数组 jobs ，其中 jobs[i] 是完成第 i 项工作要花费的时间。

请你将这些工作分配给 k 位工人。所有工作都应该分配给工人，且每项工作只能分配给一位工人。工人的 工作时间 是完成分配给他们的所有工作花费时间的总和。请你设计一套最佳的工作分配方案，使工人的 最大工作时间 得以 最小化 。

返回分配方案中尽可能最小的 最大工作时间 。

示例 1：

输入：jobs = [3,2,3], k = 3
输出：3
解释：给每位工人分配一项工作，最大工作时间是 3 。

示例 2：

输入：jobs = [1,2,4,7,8], k = 2
输出：11
解释：按下述方式分配工作：
1 号工人：1、2、8（工作时间 = 1 + 2 + 8 = 11）
2 号工人：4、7（工作时间 = 4 + 7 = 11）
最大工作时间是 11 。

提示：

1 <= k <= jobs.length <= 12
1 <= jobs[i] <= 10⁷

lightbulb

解题思路

方法一：DFS + 剪枝

本题与 2305. 公平分发饼干基本一致，不同的地方仅在于 $k$ 值的大小。

剪枝优化：优化分配花费时间较大的工作，因此可以先对 $jobs$ 按照降序排列。

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class Solution:
    def minimumTimeRequired(self, jobs: List[int], k: int) -> int:
        def dfs(i):
            nonlocal ans
            if i == len(jobs):
                ans = min(ans, max(cnt))
                return
            for j in range(k):
                if cnt[j] + jobs[i] >= ans:
                    continue
                cnt[j] += jobs[i]
                dfs(i + 1)
                cnt[j] -= jobs[i]
                if cnt[j] == 0:
                    break

        cnt = [0] * k
        jobs.sort(reverse=True)
        ans = inf
        dfs(0)
        return ans

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Candidates should demonstrate understanding of dynamic programming with bitmasking.
question_mark
Candidates should be able to explain the concept of state transitions and how they apply to this problem.
question_mark
Candidates should discuss how backtracking can optimize the solution and how it interacts with dynamic programming.

warning

常见陷阱

外企场景

error
Not considering all subsets of jobs, leading to suboptimal assignments.
error
Overcomplicating the problem by trying to brute force the solution without using dynamic programming or backtracking.
error
Incorrectly transitioning between states or using the wrong bitmask representation for job assignments.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Increasing the number of workers (k) and ensuring the algorithm still performs efficiently.
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Using additional constraints like worker availability times or different job priorities.
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Considering cases with extremely large job times to test the algorithm’s efficiency.

help

常见问题

外企场景

继续练习

#1655 分配重复整数 #1799 N 次操作后的最大分数和 #1947 最大兼容性评分和