2.1 description john is learning a new programming language called a++. having just mastered loops, he is excitedly writing many programs that contain only loop structures. however, he does not know how to compute the time complexity of his programs. so he turns to you for help. what you need to do is to write a program to calculate the time complexity for each program that john writes. the loop structure in a++ is as follows: f i x y ...//code block to be executed e here ”f i x y” indicates cre

To help John calculate the time complexity of his programs, we need to write a program that can analyze the structure of loops in A++ and determine their time complexities. Here's a step-by-step approach to achieve this: 1. Parse the Input: Read the input program line by line. 2. Identify Loops: Recognize the loop structures (`f i x y`) and their corresponding end (`e`). 3. Analyze Nested Loops: Determine if there are nested loops and compute their combined time complexity. 4. Calculate Time Complexity: Use the rules for nested loops to calculate the overall time complexity. Let's implement this in Python: ```python def calculate_time_complexity(program): lines = program.split('\n') stack = [] total_complexity = 0 for line in lines: if line.startswith('f i'): # Extract the range from the loop declaration parts = line.split() x = int(parts[2]) y = int(parts[3]) # Calculate the number of iterations for this loop iterations = y - x + 1 # If there is a nested loop, multiply the current complexity with the new loop's iterations if stack: iterations *= stack[-1] # Push the current loop's iterations onto the stack stack.append(iterations) elif line == 'e': # End of a loop, pop the last value from the stack if stack: stack.pop() # The total complexity is the product of all iteration counts in the stack total_complexity = 1 for count in stack: total_complexity *= count return total_complexity # Example usage: program = """ f i 0 9 ... // some code block f i 0 9 ... // another code block e e """ print("Time Complexity:", calculate_time_complexity(program)) ``` Explanation: 1. Parsing the Program: We split the input program into lines and iterate through each line. 2. Handling Loops: When encountering a loop start (`f i x y`), we extract the range `x` to `y` and calculate the number of iterations. 3. Nested Loops: For nested loops, we multiply the current loop's iterations by the previous loop's iterations stored in the stack. 4. End of Loop: When encountering an end of loop marker (`e`), we pop the last value from the stack. 5. Total Complexity: Finally, we multiply all values in the stack to get the total time complexity. This program will correctly compute the time complexity for simple and nested loop structures in A++. [2024-10-24 03:51:50 | AI写代码神器 | 720点数解答]