Programming Assignment 2 Due Saturday Nov 17 Noon

Programming Assignment 2due Saturday Nov 17 Noon 2012 the Basic Tas

Programming Assignment 2 due Saturday, Nov. 17, noon, 2012 The basic task is this: implement a stack of float values that has Θ (1) worst case behavior for PUSH, POP, and MEAN, a function returning the mean of the values in the stack. This stack should be wrapped in a user interface that asks the user to choose from POP, PUSH, MEAN, or QUIT at each turn. If the user enters PUSH, the program should read a number from the keyboard. If the user tries POP or MEAN on an empty stack, the program should notify the user of the error, and again prompt the user to choose from POP, PUSH, MEAN, or QUIT. To facilitate testing, please use exactly these commands. preferred in Java using Eclipse IDE

Paper For Above instruction

The task involves designing and implementing a stack data structure for float values in Java that ensures Θ(1) worst-case complexity for its core operations: PUSH, POP, and MEAN. This means each operation should execute in constant time, irrespective of the size of the stack, which necessitates an efficient approach, especially for the MEAN operation that calculates the average of all values in the stack.

To achieve Θ(1) complexity for PUSH and POP, the stack should utilize an array-based structure with a pointer or index to track the current top of the stack. For the MEAN function to also operate in constant time, an auxiliary variable, say 'sum', will be maintained to hold the total of all the values currently in the stack. Whenever a value is pushed onto the stack, 'sum' is incremented by that value, and when a value is popped, 'sum' is decremented accordingly. This approach negates the need to traverse the entire stack to compute the sum, thereby supporting constant-time mean calculation.

The user interface will be a command-line menu, prompting the user to select an operation: POP, PUSH, MEAN, or QUIT. If the user chooses PUSH, the program will read a float value from the input and push it onto the stack, updating the sum accordingly. For POP, the program will remove the top value if the stack is not empty, updating the sum, or notify the user if the stack is empty. The MEAN command will compute and display the mean by dividing 'sum' by the number of elements in the stack, again if not empty. When attempting POP or MEAN on an empty stack, an error message will be displayed.

The solution should be implemented in Java, suitable for development in Eclipse IDE. It should include appropriate error handling and user prompts to facilitate ease of testing and usage.

Paper For Above instruction

The implementation of a stack supporting Θ(1) operations for PUSH, POP, and MEAN involves combining efficient data structure design with auxiliary variables to track the sum of values. The core of this implementation is an array-based stack with an integer index indicating the current top. To support efficient calculation of the mean, an additional variable 'sum' is maintained to keep track of the total sum of all elements in the stack. This approach is grounded in the principle that by maintaining running totals, the need for traversing the entire stack for each mean calculation is eliminated.

In designing the stack, a fixed-size array can be used, with a maximum capacity defined at initialization. The push operation checks for overflow, adding the new value to the top and updating 'sum'. The pop operation removes the top element, decreasing 'sum' correspondingly. The mean operation simply divides 'sum' by the current size of the stack, providing an instantaneous average.

The user interface can be constructed using a while loop that continues until the user chooses to quit. Within each iteration, the program displays a menu and reads the user’s choice. If pushing, the program prompts for a float value, then calls push. If popping, it attempts to remove the top element, and if the stack is empty, it displays an error message. For mean, it calculates if the stack is not empty; otherwise, it reports an error. This design ensures the program handles edge cases gracefully and provides clear feedback to the user.

Overall, this approach demonstrates the practical application of combining data structure design with runtime efficiency considerations, implementing a stack that is both performant and user-friendly within a Java environment using Eclipse IDE.

References

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