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RUN REVIEW · Algorithmics (HESS) · Units 3 & 4

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11 Sep 2026, 8:51 p.m.

20Serious score
01 Use the supplied Master Theorem. What is T(n) if \(T(n)=2T(n/2)+O(n^1)\)?
A \(O(n^2)\) Does not fit this requirement.
B \(O(n)\) Does not fit this requirement.
C \(O(n \log n)\) Compare \(a=2\) with \(b^c=2\).
D \(O(n^3)\) Does not fit this requirement.

Written for icaijy.com · U4 AOS1 · Recurrence relations · answered at 100 ms

02 A classifier learns from emails already labelled spam or not spam. Which concept best matches this situation?
A backtracking Does not fit this requirement.
B PageRank Does not fit this requirement.
C unsupervised learning Does not fit this requirement.
D supervised learning supervised learning directly matches the stated requirement.

Written for icaijy.com · Applied · data-driven algorithms · answered at 100 ms

03 In the standard model, a Turing machine reads and writes symbols on
A a neural network Does not fit this requirement.
B a finite queue only Does not fit this requirement.
C a weighted graph Does not fit this requirement.
D an unbounded tape divided into cells The accepted statement is: an unbounded tape divided into cells.

Written for icaijy.com · U4 AOS3 · Computability · answered at 100 ms

04 A fare graph includes rebates represented by negative edges and has no negative cycle. Which tool is most fit for purpose?
A Prim's algorithm Does not fit this requirement.
B Bellman–Ford algorithm Bellman–Ford algorithm directly matches the stated requirement.
C Dijkstra’s algorithm Does not fit this requirement.
D PageRank Does not fit this requirement.

Written for icaijy.com · Applied · graph algorithms · answered at 100 ms

05 A transport app must look up a student record using a student ID. Which ADT is most suitable?
A stack Does not fit this requirement.
B set Does not fit this requirement.
C queue Does not fit this requirement.
D dictionary A dictionary maps each key to a value.

Written for icaijy.com · U3 AOS1 · ADTs · answered at 100 ms

06 Which design pattern or algorithm stores solutions of overlapping subproblems to avoid recomputation?
A simulated annealing Does not fit this requirement.
B greedy Does not fit this requirement.
C divide and conquer Does not fit this requirement.
D dynamic programming This is the defining behaviour of dynamic programming.

Written for icaijy.com · U3/U4 · Algorithm design patterns · answered at 100 ms

07 A transport app must undo edits in reverse order. Which ADT is most suitable?
A queue Does not fit this requirement.
B stack A stack provides last-in, first-out access.
C priority queue Does not fit this requirement.
D set Does not fit this requirement.

Written for icaijy.com · U3 AOS1 · ADTs · answered at 100 ms

08 A school system must store a sequence while preserving duplicates and order. Which ADT is most suitable?
A set Does not fit this requirement.
B priority queue Does not fit this requirement.
C list A list preserves sequence and permits repeated values.
D stack Does not fit this requirement.

Written for icaijy.com · U3 AOS1 · ADTs · answered at 100 ms

09 An exponential-time algorithm on large inputs illustrates
A an undecidable problem Does not fit this requirement.
B a soft limit of computability The problem is computable but may be impractical.
C a syntax error Does not fit this requirement.
D a violation of Church–Turing Does not fit this requirement.

Written for icaijy.com · U4 AOS1 · Complexity limits · answered at 100 ms

10 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…31. How many values are inspected when searching for 7?
A 3 Does not fit this requirement.
B 7 Does not fit this requirement.
C 6 Does not fit this requirement.
D 5 The midpoint trace reaches 7 after 5 inspection(s).

Written for icaijy.com · U4 AOS2 · Binary search · answered at 100 ms

11 Memoisation is
A top-down recursion with cached subproblem results Memoisation caches recursive results.
B a greedy proof Does not fit this requirement.
C a graph traversal without storage Does not fit this requirement.
D a hardware optimisation only Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Advanced design · answered at 100 ms

12 A max-priority queue removes the numerically highest priority first. Which job is removed?
A Job A (priority 2) A higher-priority job is present.
B Job B (priority 9) This has the highest priority.
C Job C (priority 5) A higher-priority job is present.
D Job D (priority 7) A higher-priority job is present.

Written for icaijy.com · U3 AOS1 · Priority queues · answered at 100 ms

13 Find a path using the fewest edges in an unweighted graph. Which algorithm is most fit for purpose?
A PageRank Does not fit this requirement.
B breadth-first search BFS explores vertices in increasing edge distance.
C Prim's algorithm Does not fit this requirement.
D depth-first search Does not fit this requirement.

Written for icaijy.com · U3 AOS2 · Graph algorithms · answered at 100 ms

14 A greedy algorithm is claimed to be optimal. Which evidence is strongest?
A It worked on ten random inputs. Does not fit this requirement.
B It uses a priority queue. Does not fit this requirement.
C Its code is short. Does not fit this requirement.
D A proof that every greedy choice can be part of an optimal solution. An exchange-style argument establishes optimality generally.

Written for icaijy.com · U3 AOS2 · Correctness · answered at 100 ms

15 Using the usual inclusive low/high implementation, at most how many element inspections can an unsuccessful binary search of 8 sorted items require?
A 3 Does not fit this requirement.
B 4 An unsuccessful search may inspect floor(log₂(8)) + 1 = 4 elements.
C 8 Does not fit this requirement.
D 5 Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Binary search · answered at 100 ms

16 Using the usual inclusive low/high implementation, at most how many element inspections can an unsuccessful binary search of 4096 sorted items require?
A 4096 Does not fit this requirement.
B 13 An unsuccessful search may inspect floor(log₂(4096)) + 1 = 13 elements.
C 12 Does not fit this requirement.
D 14 Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Binary search · answered at 100 ms

17 Assume constant-time primitive operations. What is the tightest Big-O bound for: For i from 1 to n: j ← 1; While j < n: j ← 2j
A \(O(n \log n)\) A logarithmic loop occurs n times.
B \(O(n^2)\) Does not fit this requirement.
C \(O(n)\) Does not fit this requirement.
D \(O(\log n)\) Does not fit this requirement.

Written for icaijy.com · U4 AOS1 · Time complexity · answered at 100 ms

18 Assume constant-time primitive operations. What is the tightest Big-O bound for: While n > 0: n ← n − 2
A \(O(n)\) Dividing the iteration count by constant 2 keeps it linear.
B \(O(n^2)\) Does not fit this requirement.
C \(O(\log n)\) Does not fit this requirement.
D \(O(1)\) Does not fit this requirement.

Written for icaijy.com · U4 AOS1 · Time complexity · answered at 100 ms

19 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 2, h = 8, f = 10 f = 10; another node has a smaller f.
B Node B: g = 3, h = 5, f = 8 f = 8; this is minimal.
C Node C: g = 4, h = 6, f = 10 f = 10; another node has a smaller f.
D Node D: g = 5, h = 3, f = 8 f = 8; another node has a smaller f.

Written for icaijy.com · U4 AOS2 · A* search · answered at 100 ms

20 Which design pattern or algorithm sometimes accepts a worse move according to a temperature parameter?
A binary search Does not fit this requirement.
B backtracking Does not fit this requirement.
C hill climbing Does not fit this requirement.
D simulated annealing This is the defining behaviour of simulated annealing.

Written for icaijy.com · U3/U4 · Algorithm design patterns · answered at 100 ms

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