#2365

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Task Scheduler II

Complete tasks in the optimal number of days by considering breaks and task type constraints.

Problem Statement

You are given an array of tasks that need to be completed in order, where each task is represented by an integer. You are also provided with a number 'space' which indicates the minimum number of days required between performing the same task. The goal is to determine the minimum number of days needed to complete all the tasks, ensuring that no two tasks of the same type are completed within the given space constraint.

Each day, you can either complete a task or take a break. Your challenge is to optimally place breaks between tasks so that no two tasks of the same type violate the space constraint. Return the minimum number of days required to complete all tasks, taking into account the necessary breaks for task type separation.

Examples

Example 1

Input: tasks = [1,2,1,2,3,1], space = 3

Output: 9

One way to complete all tasks in 9 days is as follows: Day 1: Complete the 0th task. Day 2: Complete the 1st task. Day 3: Take a break. Day 4: Take a break. Day 5: Complete the 2nd task. Day 6: Complete the 3rd task. Day 7: Take a break. Day 8: Complete the 4th task. Day 9: Complete the 5th task. It can be shown that the tasks cannot be completed in less than 9 days.

Example 2

Input: tasks = [5,8,8,5], space = 2

Output: 6

One way to complete all tasks in 6 days is as follows: Day 1: Complete the 0th task. Day 2: Complete the 1st task. Day 3: Take a break. Day 4: Take a break. Day 5: Complete the 2nd task. Day 6: Complete the 3rd task. It can be shown that the tasks cannot be completed in less than 6 days.

Constraints

1 <= tasks.length <= 105
1 <= tasks[i] <= 109
1 <= space <= tasks.length

Solution Approach

Array Scanning with Hash Table Lookup

The most efficient approach for this problem involves scanning the tasks array while maintaining a hash table to track when the last occurrence of each task was completed. For each new task, check if the task type can be completed without violating the spacing constraint. If it cannot, insert the appropriate number of break days before continuing. This ensures that task types are spaced apart correctly.

Greedy Strategy for Task Scheduling

A greedy approach can be applied where you try to place breaks as late as possible while ensuring the space constraint is met. By always waiting until the last possible moment to take a break, you reduce the total number of days. The key trade-off is balancing break days with the need to maintain task spacing.

Efficient Time Complexity Management

To solve the problem efficiently, aim for a time complexity of O(n) by leveraging a hash map that stores the last occurrence of each task. Each task in the array is processed once, and hash lookups are constant time, ensuring the solution scales well even for large inputs.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of the solution is O(n), where n is the number of tasks. Each task is processed once, and each hash map lookup or update is O(1). The space complexity is O(k), where k is the number of distinct tasks, as the hash map needs to store the last occurrence of each task type.

What Interviewers Usually Probe

Look for the candidate's ability to optimize task scheduling by minimizing break days.
Evaluate their understanding of hash map operations and how it ties into scheduling tasks efficiently.
Assess their ability to handle edge cases, such as tasks with large gaps or very small space constraints.

Common Pitfalls or Variants

Common pitfalls

Failing to correctly handle the spacing constraint by not taking breaks at the optimal times.
Overcomplicating the solution with unnecessary nested loops or excessive time complexity.
Misunderstanding the nature of breaks and underestimating the importance of placing them strategically.

Follow-up variants

What if the space constraint varies between different tasks? This could require a more complex strategy to handle multiple constraints.
Consider what happens if tasks are already spaced appropriately. This could result in fewer breaks or days.
What if there are only one or two types of tasks? This could simplify the problem, as fewer space checks are needed.

FAQ

What is the primary strategy to solve Task Scheduler II?

The main strategy involves scanning through the task array and using a hash map to track the last completion time for each task type, ensuring spacing constraints are met.

How can I optimize the solution for Task Scheduler II?

Optimizing involves using a greedy approach where breaks are taken as late as possible, minimizing unnecessary days while maintaining the task spacing constraints.

What time complexity should I expect for Task Scheduler II?

The optimal solution should run in O(n) time, where n is the length of the tasks array, leveraging hash map lookups for efficient processing.

Can Task Scheduler II be solved without using a hash map?

While it is possible to solve the problem without a hash map, it would likely result in higher time complexity, especially for larger inputs. A hash map is essential for efficient tracking of task types.

How can I handle edge cases in Task Scheduler II?

Edge cases, like tasks with large gaps or multiple tasks of the same type, should be handled by ensuring breaks are placed optimally according to the space constraint, and the hash map is updated accordingly.

terminal

Solution

Solution 1: Hash Table + Simulation

We can use a hash table $day$ to record the next time each task can be executed. Initially, all values in $day$ are $0$. We use a variable $ans$ to record the current time.

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class Solution:
    def taskSchedulerII(self, tasks: List[int], space: int) -> int:
        day = defaultdict(int)
        ans = 0
        for task in tasks:
            ans += 1
            ans = max(ans, day[task])
            day[task] = ans + space + 1
        return ans

Continue Practicing

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