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Algorithm knowledge check

Ten short questions on sorting, searching, graphs, trees and recursion. Answers are explained after submission.

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01 · SortingWhat is the worst-case time complexity of Bubble Sort?

O(log n)O(n)O(n log n)O(n²)

02 · SortingWhat is the worst-case time complexity of Merge Sort?

O(n log n)O(n²)O(log n)O(1)

03 · SortingWhen can Quick Sort take O(n²) time?

When pivots divide evenlyWhen the pivot is repeatedly an extreme elementWhenever the input is randomOnly for arrays of length two

04 · SearchingWhat must be true for binary search to work correctly?

Values are uniqueValues are sortedValues are positiveArray length is even

05 · GraphsWhich structure naturally supports iterative depth-first search?

QueueMin-heapStackHash set only

06 · GraphsWhich structure naturally supports breadth-first search?

QueueStackBinary search treePriority queue

07 · GraphsWhat restriction applies to Dijkstra’s standard shortest-path algorithm?

No cyclesNo negative edge weightsExactly six nodesEvery edge has equal weight

08 · TreesWhat is the worst-case search time in an unbalanced binary search tree?

O(1)O(log n)O(n)O(n log n)

09 · TreesWhere is the smallest element in a min-heap?

At the rootAt the final leafAlways at the leftmost leafAt an arbitrary position

10 · RecursionWhy does a recursive function need a base case?

To make it asynchronousTo prevent endless recursive callsTo sort its argumentsTo avoid local variables

Complexity quick reference

Worst-case bounds unless a note states otherwise. V = vertices; E = edges.

Algorithm	Time	Extra space	Why it matters
Bubble Sort	O(n²)	O(1)	In-place; optimized early-exit best case O(n).
Merge Sort	O(n log n)	O(n)	Predictable time; auxiliary merge storage.
Quick Sort	O(n²) worst	O(n) worst stack	Average O(n log n); pivot strategy matters.
Binary Search	O(log n)	O(1) iterative	Requires sorted input.
BFS / DFS	O(V + E)	O(V)	Traversal of vertices and edges.
Dijkstra (simple)	O(V² + E)	O(V + E)	This complexity describes a linear-minimum selection implementation.
BST (unbalanced)	O(n) worst	O(n) worst	Balanced trees typically offer O(log n) search.
Min-heap insert/remove	O(log n)	O(1) auxiliary	Finding minimum is O(1).

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