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would behave more like a queue. The correct end is the top."},{"text":"Either end.","correct":false,"explanation":"A standard stack has one designated access point, so operations cannot occur at either end. Items are added to and removed from the top."},{"text":"The middle.","correct":false,"explanation":"Stack operations do not access the middle, because that would break the ordered LIFO behaviour. Items are both added and removed from the top."}]},{"id":"e972efa7-e202-4c59-94e1-3de59ee16b08","cardType":"cloze","points":null,"front":"A stack follows [ ]: the last item pushed is the first item [ ].","back":"A stack follows LIFO: the last item pushed is the first item popped.","mcqOptions":[{"text":"A stack follows LIFO: the last item pushed is the first item popped.","correct":true,"explanation":"LIFO means Last In, First Out, so the item most recently pushed onto the stack is the first item removed by a pop operation."},{"text":"A stack follows FIFO: the last item pushed is the first item popped.","correct":false,"explanation":"FIFO means the first item added is removed first, so it does not describe a stack. The correct terms are LIFO and popped."},{"text":"A stack follows LIFO: the first item pushed is the first item popped.","correct":false,"explanation":"LIFO removes the last item pushed first, not the first one. The completed rule is that the last item pushed is the first item popped."},{"text":"A stack follows LIFO: the last item pushed is the first item peeked.","correct":false,"explanation":"Peek usually examines the top item without removing it, whereas the operation that removes an item is pop. The correct term here is popped."}]},{"id":"65c391f7-ce9b-4901-a909-5603da8046c2","cardType":"basic","points":1,"front":"If A is pushed, then B is pushed, which item is popped first?","back":"B.","mcqOptions":[{"text":"B.","correct":true,"explanation":"B was pushed after A, so B is at the top of the stack. LIFO means the most recently pushed item is popped first."},{"text":"A.","correct":false,"explanation":"A was pushed first and is below B, so it cannot be popped first. B is on top and is removed before A under LIFO behaviour."},{"text":"A and B.","correct":false,"explanation":"A stack pops one item at a time, not both items together. Since B was pushed last, B is the first item popped."},{"text":"Neither item.","correct":false,"explanation":"The stack contains both items and can pop the item at its top. B was pushed most recently, so it is the first item removed."}]},{"id":"9c7ef39d-a514-4e02-8d5f-1d15619209ec","cardType":"basic","points":1,"front":"What does LIFO stand for?","back":"Last In, First Out.","mcqOptions":[{"text":"Last In, First Out.","correct":true,"explanation":"LIFO expands to Last In, First Out: the most recently added item is the first one removed from the stack."},{"text":"Last In, First Used.","correct":false,"explanation":"The final word describes removal, not general use. LIFO stands for Last In, First Out, meaning the newest item leaves first."},{"text":"Least In, First Out.","correct":false,"explanation":"The I refers to In, not Least. LIFO means Last In, First Out, based on the order in which items enter and leave."},{"text":"First In, Last Out.","correct":false,"explanation":"This reverses the order represented by LIFO and describes queue-like behaviour. LIFO means Last In, First Out."}]},{"id":"602b45ff-f951-4a91-b85f-de7a0f1d89b3","cardType":"basic","points":1,"front":"What does the top of a stack identify?","back":"The item that would be removed next.","mcqOptions":[{"text":"The item that would be removed next.","correct":true,"explanation":"The top identifies the next item available for removal. A pop operation removes this item, preserving the stack's LIFO order."},{"text":"The item that was added first.","correct":false,"explanation":"The first item added is usually at the bottom, not the top, and will leave last. The top identifies the item removed next."},{"text":"The item that would be added next.","correct":false,"explanation":"The top describes the current accessible item, whereas pushing adds a new item above it. The item at the top is removed next."},{"text":"The item with the lowest value.","correct":false,"explanation":"A stack is ordered by insertion time rather than by the values stored in its items. The top identifies the item removed next."}]},{"id":"a4dca3e8-969f-4f83-8093-c95e3e627e29","cardType":"cloze","points":null,"front":"In an array-based stack, topPointer stores the [ ] of the current [ ].","back":"In an array-based stack, topPointer stores the index of the current top item.","mcqOptions":[{"text":"In an array-based stack, topPointer stores the index of the current top item.","correct":true,"explanation":"The pointer records the array position of the current top item, allowing push and pop operations to locate the correct stack element."},{"text":"In an array-based stack, topPointer stores the value of the current top item.","correct":false,"explanation":"The pointer does not store the item's data value; it stores its position in the array. The correct description is the index of the current top item."},{"text":"In an array-based stack, topPointer stores the index of the current bottom item.","correct":false,"explanation":"The bottom item is not what this pointer tracks, even though it also has an array index. It stores the index of the current top item."},{"text":"In an array-based stack, topPointer stores the number of the current top item.","correct":false,"explanation":"A pointer identifies a location rather than counting the item itself. In this stack representation, it stores the index of the current top item."}]},{"id":"bc916a63-d1c9-4621-b3a0-0d2cda9f6e00","cardType":"basic","points":1,"front":"Using the common convention, what is topPointer when a stack is empty?","back":"-1.","mcqOptions":[{"text":"-1.","correct":true,"explanation":"With zero-based array indexing, -1 represents a position before index 0, so it indicates that an empty stack has no valid top item."},{"text":"0.","correct":false,"explanation":"Using 0 for an empty stack would make the first array position appear to contain the top item. The common convention uses -1 until the first item is pushed."},{"text":"1.","correct":false,"explanation":"Using 1 would imply that the stack begins at the second position in a zero-based array. The empty-state convention is -1."},{"text":"capacity.","correct":false,"explanation":"Capacity represents the number of available positions, not an empty top index. An empty zero-based array stack commonly sets topPointer to -1."}]},{"id":"cd39ba15-7738-47f8-9ebd-83da98c31efc","cardType":"cloze","points":null,"front":"A fixed-size array stack is full when topPointer = [ ].","back":"A fixed-size array stack is full when topPointer = capacity - 1.","mcqOptions":[{"text":"capacity - 1","correct":true,"explanation":"For a zero-based array, the final valid index is one less than its capacity. The stack is full when topPointer reaches that index."},{"text":"capacity","correct":false,"explanation":"Capacity is the number of positions, but it is not a valid zero-based index. The final position is capacity - 1, which marks a full stack."},{"text":"capacity + 1","correct":false,"explanation":"Adding one moves beyond the final array position and would indicate an invalid index rather than a full stack. The correct expression is capacity - 1."},{"text":"0","correct":false,"explanation":"Index 0 is the first position and represents a one-item stack, not a full stack unless capacity is one. Fullness occurs at capacity - 1."}]},{"id":"ceea9f45-0dd9-4037-9e73-9db49063f68f","cardType":"basic","points":1,"front":"Which stack operation adds a new item to the top?","back":"Push.","mcqOptions":[{"text":"Push.","correct":true,"explanation":"Push adds a new item to the top of a LIFO stack, making it the first item that will be accessed or removed."},{"text":"Pop.","correct":false,"explanation":"Pop removes and returns the current top item rather than adding one. Push is the operation used to add a new item to the top."},{"text":"Peek.","correct":false,"explanation":"Peek reads the current top item without changing the stack. Push is the operation that adds a new item to the top."},{"text":"Enqueue.","correct":false,"explanation":"Enqueue adds an item to a queue, not a stack. The corresponding operation for adding an item to the top of a stack is push."}]},{"id":"6cca7687-281e-4251-b697-382f9cb121fd","cardType":"basic","points":1,"front":"Before pushing to a fixed-size stack, what must be checked?","back":"Check the stack is not full.","mcqOptions":[{"text":"Check the stack is not full.","correct":true,"explanation":"A fixed-size stack has limited storage, so it must not be full before a new item is pushed; otherwise, stack overflow occurs."},{"text":"Check the stack is not empty.","correct":false,"explanation":"Checking for an empty stack is required before a pop or peek operation. Before pushing, the stack must be checked to ensure it is not full."},{"text":"Check the item is not null.","correct":false,"explanation":"Whether null values are permitted depends on the implementation and does not determine available capacity. The essential check is that the fixed-size stack is not full."},{"text":"Check the pointer is at zero.","correct":false,"explanation":"A pointer at zero may represent an empty stack or its first occupied position, depending on the implementation. A push specifically requires checking that the stack is not full."}]},{"id":"22f463b2-7cc9-406a-bdca-e248fb0f0c40","cardType":"cloze","points":null,"front":"On a successful push, topPointer is [ ], then the item is stored at [ ].","back":"On a successful push, topPointer is increased by 1, then the item is stored at stack[topPointer].","mcqOptions":[{"text":"On a successful push, topPointer is increased by 1, then the item is stored at stack[topPointer].","correct":true,"explanation":"The pointer is first advanced to the next free position, and the new item is then placed at the array index identified by the updated pointer."},{"text":"On a successful push, topPointer is decreased by 1, then the item is stored at stack[topPointer].","correct":false,"explanation":"Decreasing the pointer moves towards the previous item and is associated with popping. A push increases topPointer by 1 before storing the item at that index."},{"text":"On a successful push, topPointer is increased by 1, then the item is stored at stack[topPointer - 1].","correct":false,"explanation":"This increments the pointer but then writes to the old top position, potentially overwriting an item. The new item must be stored at stack[topPointer]."},{"text":"On a successful push, topPointer is left unchanged, then the item is stored at stack[topPointer + 1].","correct":false,"explanation":"Writing to the next position without updating the pointer leaves the stack's recorded top incorrect. The pointer must increase by 1, followed by storage at stack[topPointer]."}]},{"id":"be2997d4-126d-41b6-be84-3a656756cdce","cardType":"basic","points":1,"front":"Which stack operation removes and returns the top item?","back":"Pop.","mcqOptions":[{"text":"Pop.","correct":true,"explanation":"Pop accesses the item currently at the top of the stack, removes it by updating the top position, and returns its value."},{"text":"Peek.","correct":false,"explanation":"Peek returns the top item but deliberately leaves it on the stack. Pop both removes the top item and returns its value."},{"text":"Push.","correct":false,"explanation":"Push adds an item to the top rather than removing one. Pop is the stack operation that removes and returns the current top item."},{"text":"Dequeue.","correct":false,"explanation":"Dequeue removes an item from a queue, normally from its front. The operation that removes and returns the top stack item is pop."}]},{"id":"1dac2fa6-3dba-41bc-9b7f-ac149c69b730","cardType":"basic","points":2,"front":"Why must a pop read the old top item before moving the pointer down?","back":"So the removed item can be returned.","mcqOptions":[{"text":"So the removed item can be returned.","correct":true,"explanation":"The pointer identifies the current top item, so its value must be read before the pointer moves down and identifies the next item instead."},{"text":"So the pointer can be decremented.","correct":false,"explanation":"The pointer can be decremented without reading the item, but doing so first loses its identified top position. The old top is read so the removed item can be returned."},{"text":"So the empty slot can be reused.","correct":false,"explanation":"Moving the pointer down makes the old array position available for a later push regardless of whether it was read. Reading first allows the removed item to be returned."},{"text":"So the stack can be searched.","correct":false,"explanation":"Pop does not search through the stack; it accesses only the current top. The old top value is read before moving the pointer so it can be returned."}]},{"id":"609f13a3-8545-4599-a416-167aeb46f751","cardType":"cloze","points":null,"front":"A [ ] happens when pushing onto a full stack; a [ ] happens when popping from an empty stack.","back":"A stack overflow happens when pushing onto a full stack; a stack underflow happens when popping from an empty stack.","mcqOptions":[{"text":"A stack overflow happens when pushing onto a full stack; a stack underflow happens when popping from an empty stack.","correct":true,"explanation":"Overflow occurs when a push exceeds the stack's storage capacity, while underflow occurs when a pop requests an item even though the stack contains none."},{"text":"A stack underflow happens when pushing onto a full stack; a stack underflow happens when popping from an empty stack.","correct":false,"explanation":"Underflow correctly describes attempting to pop from an empty stack, but pushing onto a full stack is stack overflow because the operation exceeds the available capacity."},{"text":"A stack overflow happens when pushing onto a full stack; a stack overflow happens when popping from an empty stack.","correct":false,"explanation":"Overflow correctly describes pushing beyond capacity, but popping from an empty stack is underflow because the operation attempts to access an item that does not exist."},{"text":"A stack underflow happens when pushing onto a full stack; a stack overflow happens when popping from an empty stack.","correct":false,"explanation":"The two errors are reversed. Pushing onto a full stack causes overflow, whereas popping from an empty stack causes underflow."}]},{"id":"f199eb8e-dc3d-4542-ac0a-37a860d0ad14","cardType":"basic","points":1,"front":"Which stack operation returns the top item without removing it?","back":"Peek or top.","mcqOptions":[{"text":"Peek or top.","correct":true,"explanation":"Peek, sometimes named top, reads and returns the item at the top of the stack while leaving the pointer and stack contents unchanged."},{"text":"Pop or remove.","correct":false,"explanation":"Pop removes the top item as it returns it, so the stack changes. Peek, also called top, returns the top item without removing it."},{"text":"Push or insert.","correct":false,"explanation":"Push inserts a new item and therefore changes the stack. Peek, or top, returns the existing top item without adding or removing anything."},{"text":"Size or length.","correct":false,"explanation":"Size or length reports how many items the stack contains rather than returning its top item. Peek, or top, provides the top item without removing it."}]},{"id":"0612c7fa-a5a2-4468-bfae-03ffb9d151c2","cardType":"basic","points":1,"front":"Before peek() or top(), what must be checked?","back":"Check the stack is not empty.","mcqOptions":[{"text":"Check the stack is not empty.","correct":true,"explanation":"Peek or top must have an existing item to return. Checking that the stack is not empty prevents an attempt to access a nonexistent top item."},{"text":"Check the stack is not full.","correct":false,"explanation":"A not-full check is needed before pushing because pushing requires spare capacity. Peek only reads the top item, so it requires the stack to be not empty."},{"text":"Check the pointer is at maximum.","correct":false,"explanation":"A maximum pointer suggests the stack may be full and is relevant to capacity checks. Before peeking, the required condition is that the stack is not empty."},{"text":"Check the item is not null.","correct":false,"explanation":"The value stored at the top may legitimately be null in some implementations. The essential check is that the stack itself is not empty before accessing its top."}]},{"id":"8c31eeda-1139-464a-85b2-a4f374308a81","cardType":"cloze","points":null,"front":"After peek(), the stack contents are [ ] and topPointer is [ ].","back":"After peek(), the stack contents are unchanged and topPointer is unchanged.","mcqOptions":[{"text":"After peek(), the stack contents are unchanged and topPointer is unchanged.","correct":true,"explanation":"The peek() operation reads the top item without removing it, so neither the stored elements nor the pointer identifying the top position changes."},{"text":"After peek(), the stack contents are unchanged and topPointer is decremented.","correct":false,"explanation":"Decrementing the pointer is part of a typical pop() operation, not peek(). A peek only reads the top item, leaving both the contents and topPointer unchanged."},{"text":"After peek(), the stack contents are missing the top item and topPointer is unchanged.","correct":false,"explanation":"Removing the top item confuses peek() with pop(). A peek returns the top item without altering the stack contents or changing topPointer."},{"text":"After peek(), the stack contents are missing the top item and topPointer is decremented.","correct":false,"explanation":"This describes the effects of pop(), which removes an item and adjusts the pointer. The correct result of peek() is that both contents and topPointer remain unchanged."}]},{"id":"f6af3791-5025-4a49-ae26-26daa45083d3","cardType":"basic","points":2,"front":"Starting empty: push(3), push(7), pop(), push(9). What is the final stack, bottom to top?","back":"3, 9.","mcqOptions":[{"text":"3, 9.","correct":true,"explanation":"Pushing 3 then 7 gives 3, 7; pop() removes 7, and pushing 9 places it above 3. Bottom to top is therefore 3, 9."},{"text":"3, 7, 9.","correct":false,"explanation":"This result overlooks the pop() operation. The pop removes 7 before 9 is pushed, so the final stack from bottom to top is 3, 9."},{"text":"3, 7.","correct":false,"explanation":"This result omits the final push(9). After 7 is popped, 3 remains, and pushing 9 makes the final bottom-to-top order 3, 9."},{"text":"9, 3.","correct":false,"explanation":"This reverses the requested bottom-to-top order. The value 3 was pushed first and remains at the bottom, while 9 is pushed last and sits on top."}]},{"id":"54f7e74c-a1f3-424f-aa36-badd2a005f39","cardType":"basic","points":1,"front":"What is the time complexity of push, pop, and peek with a top pointer?","back":"$O(1)$.","mcqOptions":[{"text":"$O(1)$.","correct":true,"explanation":"A top pointer gives direct access to the relevant stack position. Each operation performs a fixed number of reads, writes, or pointer updates regardless of stack size."},{"text":"$O(n)$.","correct":false,"explanation":"Linear time would require traversing a number of items proportional to the stack size. A top pointer avoids traversal, making push, pop, and peek $O(1)$."},{"text":"$O(\\log n)$.","correct":false,"explanation":"Logarithmic time is associated with repeatedly reducing a search space, as in binary search. Stack operations directly access the top, so their complexity is $O(1)$."},{"text":"$O(n^2)$.","correct":false,"explanation":"Quadratic time normally involves nested processing across the data structure. These stack operations perform only direct top access and fixed pointer updates, so they are $O(1)$."}]},{"id":"b9fb3b0b-4792-4f00-8946-34506fc46f70","cardType":"basic","points":2,"front":"Why are typical stack operations constant time?","back":"They access the top pointer directly, with no search.","mcqOptions":[{"text":"They access the top pointer directly, with no search.","correct":true,"explanation":"The pointer identifies the current top position, allowing an operation to read, insert, or remove there immediately. No traversal depends on the number of stored items."},{"text":"They access every stored item sequentially, requiring a full search.","correct":false,"explanation":"Sequentially checking all stored items would make an operation linear, not constant time. Typical stack operations instead use the top pointer directly and require no search."},{"text":"They perform a binary search to locate the top item.","correct":false,"explanation":"Binary search applies to ordered searchable data and has logarithmic complexity. Stack operations do not search for values; they directly access the position identified by the top pointer."},{"text":"They sort the stack contents before each operation.","correct":false,"explanation":"Sorting the stack would take more than constant time and would also disrupt its last-in, first-out order. Operations are constant because they directly access the top pointer."}]}]}],"examCountdown":{"examDate":"2027-05-11","paperLabel":"Paper 1"},"heading":"Stacks","title":"Stacks Flashcards","topbar":{"backHref":"/as-level/computer-science/aqa/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"b621650c-235b-5edd-9a63-325c853ec06e","walled":"$L38"}],"$L39","$L3a"]