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Answer questions and provide explanations Question 1 (18 marks) Suppose there ar...

May 11, 2024

Answer questions and provide explanations

Question 1

python

Explanation

The function "calculate_min_time_and_path" calculates the minimum time and path through the assembly lines using dynamic programming. It initializes the tables for minimum time and path, sets the base case for the first station, and iterates through each station to calculate the minimum time and path. The main function "main" tests the function with two use cases to ensure correctness.

Step-by-step Instruction

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Initialize the tables for minimum time `fi` and path `path`

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Set the base case for the first station in each line

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Iterate through each station starting from the second one to calculate the minimum time and path

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Define the main function `main` to test the `calculate_min_time_and_path` function with use cases

Time Complexity

The time complexity is O(n) where n is the number of stations, as the function iterates through each station once.

Space Complexity

The space complexity is O(n) for storing the minimum time and path for each station.

Question 2 To find the minimum time

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needed to get through the assembly line, we can look at the last station of both lines and take the minimum of the two values calculated by the "calculate_min_time_and_path" function.

python

Explanation

The function "find_min_time" calculates the minimum time needed to get through the assembly line by taking the minimum of the last station's time in both lines. The main function "main" tests the function with two use cases.

Step-by-step Instruction

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Return the minimum time of the last station in both lines

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Define the main function `main` to test the `find_min_time` function with use cases

Time Complexity

The time complexity is O(1) as it only compares two values.

Space Complexity

The space complexity is O(1) as no additional space is required.

Question 3 To find the fastest way through the assembly line, we can trace back the path from the last station to the first station using the path table calculated by the "calculate_min_time_and_path" function.

python

Explanation

The function "find_fastest_path" calculates the fastest way through the assembly line by tracing back the path from the last station to the first station. The main function "main" tests the function with two use cases.

Step-by-step Instruction

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Trace back the path from the last station to the first station

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Reverse the path to start from the first station

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Define the main function `main` to test the `find_fastest_path` function with use cases

Time Complexity

The time complexity is O(n) where n is the number of stations, as it traces back the path from the last station to the first station.

Space Complexity

The space complexity is O(n) for storing the fastest path.

Provide the above Chinese explanation

python

Answer the question and provide an explanation (provide a Chinese translation below the English answer)

python

Explanation

The function "calculate_min_time_and_path" calculates the minimum time and path through the assembly lines using dynamic programming. It initializes tables for storing the minimum time "f" and the path "l", sets the base cases for the first station, and iterates through each station to fill in the tables. The main function "main" tests this function with two use cases and asserts the expected results.

Step-by-step Instruction

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Initialize tables for minimum time and path, and set base cases for the first station

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Iterate through each station to fill in the tables with the minimum time and path

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Define concrete use cases and testing cases for the function: when user calls calculate_min_time_and_path() with specific assembly and transfer times, it should return the correct minimum time and path

Time Complexity

The time complexity is O(n) where n is the number of stations, as the function iterates through each station once.

Space Complexity

The space complexity is O(n) due to the storage of two tables with size proportional to the number of stations.

Answer the question and provide an explanation (provide a Chinese translation below the English answer)

python

Explanation

The function "assembly_line_scheduling" computes the minimum time and path through an assembly line using dynamic programming. It initializes tables for tracking the minimum time and the line of the station just before the current one. It then iterates through each station, calculating the minimum time to reach that station from both the same line and the other line, and chooses the minimum. Finally, it backtracks to determine the path taken. The "main" function tests this with two use cases.

Step-by-step Instruction

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Initialize tables for minimum time and line tracking, and set base cases for the first station on each line

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Iterate through each station, calculating the minimum time to reach that station from both the same line and the other line, and choose the minimum

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Compute the minimum time to finish the process and backtrack to find the path taken

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Define concrete use cases and testing cases for the function: test with given assembly and transfer times, and assert the expected minimum time and path

Time Complexity

The time complexity is O(n) where n is the number of stations, as the algorithm iterates through each station once.

Space Complexity

The space complexity is O(n) due to the storage of minimum times and paths for each station on each line.

--- 由于您的问题是关于动态规划的，下面我将提供中文翻译：

解释

函数"assembly_line_scheduling"使用动态规划计算通过装配线的最小时间和路径。它初始化用于跟踪最小时间和当前站点之前站点线路的表格。然后它遍历每个站点，计算从同一线路和其他线路到达该站点的最小时间，并选择最小值。最后，它回溯确定所采取的路径。"main"函数使用两个用例进行测试。

逐步指导

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初始化最小时间和线路跟踪表，并为每条线上的第一个站点设置基本情况。

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遍历每个站点，计算从同一线路和其他线路到达该站点的最小时间，并选择最小值。

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计算完成过程的最小时间并回溯找到所采取的路径。

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为函数定义具体的用例和测试案例：使用给定的装配和转移时间进行测试，并断言预期的最小时间和路径。

时间复杂度

时间复杂度为O(n)，其中n是站点的数量，因为算法只遍历每个站点一次。

空间复杂度

空间复杂度为O(n)，因为需要为每条线上的每个站点存储最小时间和路径。