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Structure{{ resultsReady ? simulation.mode_label : '—' }} Outcome{{ resultsReady ? currentState.outcome_label : '—' }} Invariant{{ resultsReady ? (simulation.invariant_valid ? 'Holds' : 'Failed') : '—' }}

Structure visual unavailable.

The accepted operation language changes with the selected structure.
Queue and deque arrays retain logical order while front and rear indices wrap.
Enter up to 10 comma-separated labels. Leave blank to test an empty structure.
Choose 3–10 physical slots.
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Samples replace the initial values and operation script with an editable lesson.
{{ resultsReady ? `${effectiveTraceStep} / ${operationCount}` : '—' }}
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Move through operations
The neutral default is off.
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State
Empty structure
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Pointer evidence
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The chart renderer is unavailable. Every size transition remains available in the operation ledger.

StepOperationOutcomeSizeComplexityExplanationCopy
{{ row.step }}{{ row.operation }}{{ row.outcome }}{{ row.size }}{{ row.complexity }}{{ row.detail }}
BST Operations Simulator Trace BST operations from insertion and search through deletion and traversal across ordinary, AVL or red-black trees with invariant checks and replay.
Heap Operations Simulator Build min or max heaps and trace insert, peek, and extract operations with synchronized array and tree views plus comparison and swap counts.
Hash Table Operations Simulator Trace hash-table insert, search, and delete operations across chaining and probing strategies with collision and tombstone evidence.
Recursion & Backtracking Simulator Trace four recursion and backtracking presets step by step with synchronized call stacks, branch choices and clear return and undo events.

Linear data structures keep items in a sequence, but they do not all expose that sequence in the same way. A list supports positions, a stack restricts routine access to the top, a queue separates the entry and removal ends, and a deque allows work at both ends.

Structure Accessible ends or positions Ordering idea
Linked list Head, tail, or an indexed position Nodes follow links in logical order.
Stack Top Last in, first out.
Queue Rear for insertion, front for removal First in, first out.
Deque Front and back Insertion and removal are allowed at either end.

Representation matters as much as the abstract structure. Linked nodes express order through next links and, for a doubly linked list, previous links. A bounded array stores values in physical slots. Circular arrays let queue and deque endpoints wrap from the last slot to the first without changing logical order.

Underflow, overflow, and an invalid position are meaningful outcomes rather than crashes. Removing from an empty structure produces underflow. Adding to a full bounded array produces overflow. Position-based list operations reject an index outside the current insertion or removal range and leave the sequence unchanged.

A trace is most useful when logical order is compared with physical evidence. The same queue may read A, B, C from front to rear even when those values occupy slots near both ends of a circular array. Confusing slot order with queue order is a common programming error.

How to Use This Tool:

Choose the abstract structure first because it determines the available representations and operation language.

  1. Select a singly linked list, doubly linked list, circular linked list, stack, queue, or deque.
  2. Choose the available representation. Lists use linked nodes; stacks can use linked nodes or a bounded array; queues and deques can use linked nodes or a bounded circular array.
  3. Enter up to 10 comma-separated initial values. For an array representation, set a capacity from 3 to 10 that can hold every initial value.
  4. Enter 1 to 12 operations using the syntax shown for the selected structure. List operations accept head, tail, position, and search actions; stacks, queues, and deques accept only their own endpoint actions.
  5. Move Trace position through the script. Check logical order, endpoint or index labels, operation outcome, and the invariant status at the selected step.

Interpreting Results:

State review shows the sequence after the selected operation prefix. The final values summarize the whole script, so they may differ when the trace is paused at an earlier step.

  • Success means the operation completed; a successful peek or search can leave size unchanged.
  • Underflow, Overflow, Invalid position, and Not found are non-mutating outcomes that need attention but do not corrupt the next state.
  • Size path records logical item count after each operation. It does not show memory consumption.
  • Invariant holds confirms unique node identities, legal size and capacity, and a valid circular-array front index for the generated states.
  • Pointer evidence explains the selected representation. It is hidden by default because logical order is enough for many first comparisons.

Technical Details:

The simulation applies every operation to one canonical logical sequence, then derives linked-node arrows or array slots from that state. This keeps logical behavior consistent while making representation-specific endpoints visible.

Mechanism Core:

Representation State rule Boundary behavior
Singly linked Each node points to the next; the tail points to null. Removing the tail requires a walk from the head.
Doubly linked Each node records next and previous neighbors. Head has no previous node and tail has no next node.
Circular linked The tail’s next link returns to the head. An empty structure still terminates at null in the evidence view.
Bounded stack array Logical top is the first displayed item; physical slots store the reversed logical sequence. Insertion stops when item count equals capacity.
Bounded circular array Logical item i occupies slot (front + i) modulo capacity. Front advances after front removal and moves backward after a deque front insertion.

Rule Core:

Each operation either changes the logical sequence or records a non-mutating outcome. The trace labels search, insertion at a position, and removal at a position as O(n). Removing the tail of a singly linked list is also O(n); the remaining supported endpoint operations are labeled O(1).

Condition Outcome State change
Remove or peek from empty Underflow None
Insert into a full array Overflow None
Insert at position p Valid when 0 ≤ p ≤ size New value becomes position p
Remove at position p Valid when 0 ≤ p < size Existing position p is removed
Search missing value Not found None

Model Limits:

The O(1) and O(n) labels describe the modeled access path, not measured runtime. They assume endpoint references are already available and omit allocation costs, cache effects, language overhead, resizing, concurrency, and garbage collection. Linked representations also stop at a 10-item visualization limit even though a real linked structure is not normally bounded that way.

References: