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DS:010217A wraparound write fills stale slots; size, not head-equals-tail, decides full versus empty

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DS Circular Buffer Wrap SizeDS Circular Buffer Physical VS Logical

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010218A duplicate minimum must sit on the min-stack, or one pop forgets the other

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DS Min Stack Duplicate RuleDS Min Stack Restore Trace

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010219A two-stack queue is FIFO by an out-then-in reading, and two times in-size pays for every transfer

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DS Two Stack Fifo InvariantDS Two Stack Fifo Potential

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010220A persistent push allocates one node and shares the old spine

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DS Persistent Stack SharingDS Persistent Stack Node Count

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010221A stable in-place list partition relinks existing nodes and does not need a sentinel

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DS Stable List PartitionDS List Partition Node Identity

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010322A two-child BST delete must splice the successor, not promote the right child

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Bst Inorder Successor Two Child DeleteBst Parent Pointer Transplant

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Search trees and balanced treesData Structures · Mixed review

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DS:010323A t=2 B-tree insert splits the full leaf on 40 before writing 35

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Btree Preemptive Full Node SplitBtree Occupancy And Search Path

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Search trees and balanced treesData Structures · Mixed review

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DS:010324Deleting car only clears a terminal; deleting cat prunes a leaf

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Trie Shared Prefix ConstructionTrie Delete Terminal Versus Prune

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Search trees and balanced treesData Structures · Mixed review

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DS:010425A linear-probe delete is a tombstone; insert 45 remembers slot 4

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Linear Probe Wraparound PlacementTombstone Search And Duplicate Safe Insert

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Hash tables and probabilistic performanceData Structures · Mixed review

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DS:010426Three keys that share only A0 and B0 force a cuckoo rehash

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Cuckoo Two Cell Lookup ContractCuckoo Placement Graph Component Bound

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Hash tables and probabilistic performanceData Structures · Mixed review

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DS:010527Bottom-up heap construction is linear because most subtrees are short

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DS Bottom UP Heapify TraceDS Heap Build Linear Height Sum

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010528Decrease-key in an indexed min-heap must restore heap order and the inverse position map

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DS Indexed Decrease Key SiftDS Heap Pos Inverse Identity

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010529Binomial-heap meld adds degree vectors, including a three-tree carry

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DS Binomial Tree BK FactsDS Binomial Meld Three Carry

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010630Multi-source BFS distances depend on the source set, not on parent choices

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DS Multisource Bfs DistanceDS Bfs Mark ON Enqueue

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Graph representations and traversalsData Structures · Mixed review

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DS:010631Recursive DFS is simulated by frames, not by an eager vertex stack

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DS Iterative Dfs FramesDS Dfs Parent Disagreement

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Graph representations and traversalsData Structures · Mixed review

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Adt InvariantsData Structures Problem Solving

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Abstract data types, representation, and invariantsData Structures · Calculation

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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DS:9921011The SortedList ADT maintains a finite multiset of integers and supports: - \mathrm{RankInsert}(x): inserts one occu…

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Adt InvariantsData Structures Problem Solving

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DS:9921012The Deque ADT (double-ended queue) over U has operations \mathrm{NewD}(), \mathrm{PushFront}(d,x), \mathrm{PushBack…

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Adt InvariantsData Structures Problem Solving

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DS:9921013A List ADT object L stores a sequence of n elements and provides a cursor abstraction.

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Adt InvariantsData Structures Problem Solving

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DS:9921014A disjoint-set (Union-Find) structure maintains a partition of the set \{1,\ldots,n\}.

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Adt InvariantsData Structures Problem Solving

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DS:9921015An AVL tree is a BST (as in Problem 6) in which every node u additionally stores an integer u.\mathrm{height}, and…

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Adt InvariantsData Structures Problem Solving

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DS:9921016[Honors] Let T be an AVL tree on n\ge 1 nodes, using the height convention of Problem 15 (h(\mathrm{NIL})=-1).

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Adt InvariantsData Structures Problem Solving

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DS:9921017The Graph ADT for a directed graph on a vertex set V=\{1,\ldots,n\} supports: - \mathrm{AddEdge}(u,v): requires u,v…

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Adt InvariantsData Structures Problem Solving

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DS:9921018A PriorityQueue ADT of pairwise-distinct keys from a totally ordered universe supports: - \mathrm{Insert}(x): requi…

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Adt InvariantsData Structures Problem Solving

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DS:9921019A circular doubly linked list with a dummy sentinel S represents a sequence of n integers.

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Adt InvariantsData Structures Problem Solving

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DS:9921020A rooted binary tree is either \mathrm{NIL} or a node with fields \mathrm{left} and \mathrm{right}, each themselves…

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Adt InvariantsData Structures Problem Solving

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DS:9921021The following potential-based accounting is proposed for a stack that supports \mathrm{Push}, \mathrm{Pop}, and \ma…

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Adt InvariantsData Structures Problem Solving

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DS:9921022A hash table with separate chaining as in Problem 9 maintains the invariant that the bucket array length m is alway…

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Adt InvariantsData Structures Problem Solving

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DS:9921023The Sequence ADT (also called Vector or ArrayList) stores a sequence A[0..n-1] of n elements of U and supports: - \…

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Adt InvariantsData Structures Problem Solving

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DS:9921024Let T be a finite BST on pairwise-distinct keys satisfying the invariant of Problem 6.

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Adt InvariantsData Structures Problem Solving

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DS:9921025Let S be the Set ADT of finite sets of elements from a universe U with equality.

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Adt InvariantsData Structures Problem Solving

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DS:9921026[Honors] You must design a data structure that maintains a finite multiset M of integers and supports the following…

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Adt InvariantsData Structures Problem Solving

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DS:9921027Consider two implementations of the List ADT of n integers supporting \mathrm{IndexGet}(i) and \mathrm{IndexSet}(i,…

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Adt InvariantsData Structures Problem Solving

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DS:9921028A binary trie over k-bit keys stores a set S of pairwise-distinct keys from \{0,1\}^k.

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Adt InvariantsData Structures Problem Solving

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DS:9921029In the comparison model, every decision is a comparison of two stored keys, and the only information about keys is…

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Adt InvariantsData Structures Problem Solving

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DS:9921030[Honors] A persistent stack is an ADT whose values are immutable: each operation returns a new stack value, and pre…

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Adt InvariantsData Structures Problem Solving

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DS:9921031Let A be a contiguous array of n elements indexed from 0 to n-1.

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Adt InvariantsData Structures Problem Solving

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DS:9921032An array A of length 8 is initially with valid indices 0 through 7.

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Adt InvariantsData Structures Problem Solving

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DS:9921033Consider `LINEAR-SEARCH(A, n, x)`, which scans A[0],A[1],\ldots in order and returns the smallest index i with A[i]…

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Adt InvariantsData Structures Problem Solving

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DS:9921034A ring buffer (circular array) of fixed capacity C\ge 1 stores a sequence of at most C elements using an underlying…

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Adt InvariantsData Structures Problem Solving

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DS:9921035Let A be an array of n elements.

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Adt InvariantsData Structures Problem Solving

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Problem library

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Problem results

ProblemsBuild a practice set

DS:010217A wraparound write fills stale slots; size, not head-equals-tail, decides full versus empty

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DS Circular Buffer Wrap SizeDS Circular Buffer Physical VS Logical

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010218A duplicate minimum must sit on the min-stack, or one pop forgets the other

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DS Min Stack Duplicate RuleDS Min Stack Restore Trace

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010219A two-stack queue is FIFO by an out-then-in reading, and two times in-size pays for every transfer

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DS Two Stack Fifo InvariantDS Two Stack Fifo Potential

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010220A persistent push allocates one node and shares the old spine

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DS Persistent Stack SharingDS Persistent Stack Node Count

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010221A stable in-place list partition relinks existing nodes and does not need a sentinel

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DS Stable List PartitionDS List Partition Node Identity

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Arrays, linked structures, stacks, queues, and amortizationData Structures · Mixed review

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DS:010322A two-child BST delete must splice the successor, not promote the right child

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Bst Inorder Successor Two Child DeleteBst Parent Pointer Transplant

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Search trees and balanced treesData Structures · Mixed review

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DS:010323A t=2 B-tree insert splits the full leaf on 40 before writing 35

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Btree Preemptive Full Node SplitBtree Occupancy And Search Path

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Search trees and balanced treesData Structures · Mixed review

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DS:010324Deleting car only clears a terminal; deleting cat prunes a leaf

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Trie Shared Prefix ConstructionTrie Delete Terminal Versus Prune

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Search trees and balanced treesData Structures · Mixed review

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DS:010425A linear-probe delete is a tombstone; insert 45 remembers slot 4

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Linear Probe Wraparound PlacementTombstone Search And Duplicate Safe Insert

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Hash tables and probabilistic performanceData Structures · Mixed review

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DS:010426Three keys that share only A0 and B0 force a cuckoo rehash

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Cuckoo Two Cell Lookup ContractCuckoo Placement Graph Component Bound

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Hash tables and probabilistic performanceData Structures · Mixed review

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DS:010527Bottom-up heap construction is linear because most subtrees are short

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DS Bottom UP Heapify TraceDS Heap Build Linear Height Sum

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010528Decrease-key in an indexed min-heap must restore heap order and the inverse position map

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DS Indexed Decrease Key SiftDS Heap Pos Inverse Identity

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010529Binomial-heap meld adds degree vectors, including a three-tree carry

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DS Binomial Tree BK FactsDS Binomial Meld Three Carry

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Heaps, priority queues, and disjoint setsData Structures · Mixed review

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DS:010630Multi-source BFS distances depend on the source set, not on parent choices

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DS Multisource Bfs DistanceDS Bfs Mark ON Enqueue

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Graph representations and traversalsData Structures · Mixed review

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DS:010631Recursive DFS is simulated by frames, not by an eager vertex stack

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DS Iterative Dfs FramesDS Dfs Parent Disagreement

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Graph representations and traversalsData Structures · Mixed review

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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Adt InvariantsData Structures Problem Solving

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DS:9921011The SortedList ADT maintains a finite multiset of integers and supports: - \mathrm{RankInsert}(x): inserts one occu…

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Adt InvariantsData Structures Problem Solving

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DS:9921012The Deque ADT (double-ended queue) over U has operations \mathrm{NewD}(), \mathrm{PushFront}(d,x), \mathrm{PushBack…

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Adt InvariantsData Structures Problem Solving

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DS:9921013A List ADT object L stores a sequence of n elements and provides a cursor abstraction.

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Adt InvariantsData Structures Problem Solving

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DS:9921014A disjoint-set (Union-Find) structure maintains a partition of the set \{1,\ldots,n\}.

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Adt InvariantsData Structures Problem Solving

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DS:9921015An AVL tree is a BST (as in Problem 6) in which every node u additionally stores an integer u.\mathrm{height}, and…

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Adt InvariantsData Structures Problem Solving

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DS:9921016[Honors] Let T be an AVL tree on n\ge 1 nodes, using the height convention of Problem 15 (h(\mathrm{NIL})=-1).

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Adt InvariantsData Structures Problem Solving

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DS:9921017The Graph ADT for a directed graph on a vertex set V=\{1,\ldots,n\} supports: - \mathrm{AddEdge}(u,v): requires u,v…

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Adt InvariantsData Structures Problem Solving

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DS:9921018A PriorityQueue ADT of pairwise-distinct keys from a totally ordered universe supports: - \mathrm{Insert}(x): requi…

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Adt InvariantsData Structures Problem Solving

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DS:9921019A circular doubly linked list with a dummy sentinel S represents a sequence of n integers.

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Adt InvariantsData Structures Problem Solving

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DS:9921020A rooted binary tree is either \mathrm{NIL} or a node with fields \mathrm{left} and \mathrm{right}, each themselves…

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Adt InvariantsData Structures Problem Solving

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DS:9921021The following potential-based accounting is proposed for a stack that supports \mathrm{Push}, \mathrm{Pop}, and \ma…

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Adt InvariantsData Structures Problem Solving

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DS:9921022A hash table with separate chaining as in Problem 9 maintains the invariant that the bucket array length m is alway…

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Adt InvariantsData Structures Problem Solving

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DS:9921023The Sequence ADT (also called Vector or ArrayList) stores a sequence A[0..n-1] of n elements of U and supports: - \…

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Adt InvariantsData Structures Problem Solving

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DS:9921024Let T be a finite BST on pairwise-distinct keys satisfying the invariant of Problem 6.

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Adt InvariantsData Structures Problem Solving

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DS:9921025Let S be the Set ADT of finite sets of elements from a universe U with equality.

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Adt InvariantsData Structures Problem Solving

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DS:9921026[Honors] You must design a data structure that maintains a finite multiset M of integers and supports the following…

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Adt InvariantsData Structures Problem Solving

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DS:9921027Consider two implementations of the List ADT of n integers supporting \mathrm{IndexGet}(i) and \mathrm{IndexSet}(i,…

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Adt InvariantsData Structures Problem Solving

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DS:9921028A binary trie over k-bit keys stores a set S of pairwise-distinct keys from \{0,1\}^k.

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Adt InvariantsData Structures Problem Solving

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DS:9921029In the comparison model, every decision is a comparison of two stored keys, and the only information about keys is…

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Adt InvariantsData Structures Problem Solving

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DS:9921030[Honors] A persistent stack is an ADT whose values are immutable: each operation returns a new stack value, and pre…

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Adt InvariantsData Structures Problem Solving

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DS:9921031Let A be a contiguous array of n elements indexed from 0 to n-1.

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Adt InvariantsData Structures Problem Solving

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DS:9921032An array A of length 8 is initially with valid indices 0 through 7.

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Adt InvariantsData Structures Problem Solving

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DS:9921033Consider `LINEAR-SEARCH(A, n, x)`, which scans A[0],A[1],\ldots in order and returns the smallest index i with A[i]…

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Adt InvariantsData Structures Problem Solving

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DS:9921034A ring buffer (circular array) of fixed capacity C\ge 1 stores a sequence of at most C elements using an underlying…

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Adt InvariantsData Structures Problem Solving

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DS:9921035Let A be an array of n elements.

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Adt InvariantsData Structures Problem Solving

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Problem results

DS:9921001The Stack ADT over a universe U is specified by the following operations and contracts.

DS:9921002A singly linked list representation of a finite sequence of integers uses nodes with fields \mathrm{data} (an integ…

DS:9921003A bounded queue of integers is stored in an array A[0..n-1] with n = 6, together with integers \mathrm{front}, \mat…

DS:9921004Let V be a dynamic array of n elements stored in a buffer of capacity c, with the invariant 0 \le n \le c and c \ge 1.

DS:9921005Design a representation of the Queue ADT that uses two Stack ADT objects \mathrm{In} and \mathrm{Out} as its only a…

DS:9921006A binary search tree (BST) T stores pairwise-distinct keys from a totally ordered universe.

DS:9921007A binary min-heap of n pairwise-distinct integers is stored in an array H[1..n] (1-based) satisfying two invariants…

DS:9921008Let H[1..n] be an array.

DS:9921009Consider a hash table that resolves collisions by separate chaining.

DS:9921010An open-address hash table stores keys from U \cup \{\mathrm{EMPTY},\mathrm{DELETED}\} in an array T[0..m-1], with…

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Problem results

DS:9921001The Stack ADT over a universe U is specified by the following operations and contracts.

DS:9921002A singly linked list representation of a finite sequence of integers uses nodes with fields \mathrm{data} (an integ…

DS:9921003A bounded queue of integers is stored in an array A[0..n-1] with n = 6, together with integers \mathrm{front}, \mat…

DS:9921004Let V be a dynamic array of n elements stored in a buffer of capacity c, with the invariant 0 \le n \le c and c \ge 1.

DS:9921005Design a representation of the Queue ADT that uses two Stack ADT objects \mathrm{In} and \mathrm{Out} as its only a…

DS:9921006A binary search tree (BST) T stores pairwise-distinct keys from a totally ordered universe.

DS:9921007A binary min-heap of n pairwise-distinct integers is stored in an array H[1..n] (1-based) satisfying two invariants…

DS:9921008Let H[1..n] be an array.

DS:9921009Consider a hash table that resolves collisions by separate chaining.

DS:9921010An open-address hash table stores keys from U \cup \{\mathrm{EMPTY},\mathrm{DELETED}\} in an array T[0..m-1], with…