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Questions and Answers
What type of algorithm is Quicksort?
What type of algorithm is Quicksort?
The best-case running time of the Quicksort algorithm is $O(n^2)$.
The best-case running time of the Quicksort algorithm is $O(n^2)$.
False
What is the first number in the list that is processed by Quicksort?
What is the first number in the list that is processed by Quicksort?
44
Quicksort requires rearranging elements into two sublists called the first sublist and the ______.
Quicksort requires rearranging elements into two sublists called the first sublist and the ______.
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What is the main characteristic of a stack?
What is the main characteristic of a stack?
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Match the running times of Quicksort to their respective cases:
Match the running times of Quicksort to their respective cases:
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In the third step of the Quicksort algorithm, which number does 44 interchange with?
In the third step of the Quicksort algorithm, which number does 44 interchange with?
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A stack allows elements to be removed from both ends.
A stack allows elements to be removed from both ends.
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In Quicksort, the pivot is always the last number of the list.
In Quicksort, the pivot is always the last number of the list.
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Name the operation used to insert an element into a stack.
Name the operation used to insert an element into a stack.
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When an element is removed from a stack, it is called a _____ operation.
When an element is removed from a stack, it is called a _____ operation.
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How many numbers are initially in the list A?
How many numbers are initially in the list A?
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Match the following stack operations with their descriptions:
Match the following stack operations with their descriptions:
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After the first interchange, the list becomes ______.
After the first interchange, the list becomes ______.
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If the TOP of a stack is equal to MAXSTK, what does this indicate?
If the TOP of a stack is equal to MAXSTK, what does this indicate?
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What determines the final position of the pivot in Quicksort?
What determines the final position of the pivot in Quicksort?
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In a stack, the position of the TOP is always the highest index of the stack array.
In a stack, the position of the TOP is always the highest index of the stack array.
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What is the initial condition of TOP when a stack is empty?
What is the initial condition of TOP when a stack is empty?
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In an empty stack, both TOP and __________ are set to 0.
In an empty stack, both TOP and __________ are set to 0.
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What happens when a pop operation is attempted on an empty stack?
What happens when a pop operation is attempted on an empty stack?
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What is Polish notation also known as?
What is Polish notation also known as?
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Infix notation requires the use of parentheses to define the order of operations.
Infix notation requires the use of parentheses to define the order of operations.
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What is the output of the Postfix expression 'AB+'?
What is the output of the Postfix expression 'AB+'?
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The equivalent Infix expression for the Postfix expression '5 6 2 + * 12 4 / -' is '5 * (6 + 2) - 12 / 4'.
The equivalent Infix expression for the Postfix expression '5 6 2 + * 12 4 / -' is '5 * (6 + 2) - 12 / 4'.
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Match the different notations with their descriptions:
Match the different notations with their descriptions:
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Which of the following correctly represents the transformation of '(A + B) * C' to Polish notation?
Which of the following correctly represents the transformation of '(A + B) * C' to Polish notation?
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One does not need parentheses when using Reverse Polish notation.
One does not need parentheses when using Reverse Polish notation.
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Describe the fundamental property of Polish notation.
Describe the fundamental property of Polish notation.
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In Reverse Polish notation, the expression 'A B +' translates into the Infix expression '______'.
In Reverse Polish notation, the expression 'A B +' translates into the Infix expression '______'.
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Which of the following best describes the transformation of Infix to Postfix?
Which of the following best describes the transformation of Infix to Postfix?
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Study Notes
Stacks
- A stack is a list where elements are inserted and deleted from one end, called the top.
- The last item added is the first removed (LIFO).
- Common operations are "push" (insert) and "pop" (delete).
Basic Operations
- Push: Adds an element to the top of the stack.
- Pop: Removes an element from the top of the stack.
- These operations are unique to stack data structures.
Array Representation of Stacks
- A stack can be implemented using an array.
-
TOPpoints to the top element. -
MAXSTKrepresents the maximum capacity. - An empty stack has
TOP = 0orTOP = NULL.
Push Operation
- Check if the stack is full (TOP=MAXSTK). If full, print "OVERFLOW" and return.
- Increase TOP by 1.
- Insert the new element at STACK[TOP].
- Return.
Pop Operation
- Check if the stack is empty (TOP=0). If empty, print "UNDERFLOW" and return.
- Store the element at STACK[TOP] in ITEM.
- Decrease TOP by 1.
- Return the ITEM.
Arithmetic Expressions: Notation
- Infix Notation: Operator placed between operands (e.g., A + B).
- Polish Notation (Prefix): Operator placed before operands (e.g., +AB).
- Reverse Polish Notation (Postfix): Operator placed after operands (e.g., AB+).
Translation between Notations
- Converting between infix, prefix, and postfix notations requires careful consideration of operator precedence and parentheses.
Quicksort
- Quicksort is a sorting algorithm.
- It rearranges elements of a list.
- It's a divide-and-conquer algorithm.
Quicksort: Reduction Step
- The quicksort algorithm finds a final position for the first element.
- A scan across the list occurs to find the proper location for the initial value.
- This often involves swapping elements.
Quicksort: Complexity
- Worst-case time complexity is O(n²).
- Average-case time complexity is O(n log n).
- Best-case time complexity is O(n log n).
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Description
Test your knowledge on the Quicksort algorithm and fundamental stack operations. This quiz covers the best-case running time, element processing, and characteristics of stacks. Get ready to match descriptions and operations to challenge your understanding of these core computer science concepts.
