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

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11 Sep 2026, 9:29 p.m.

20Serious score
01 Ignoring constant factors, approximately how many primitive operations does an \(O(n)\) algorithm perform when n = 1,000,000?
A about 1 billion Does not fit this requirement.
B about 1 trillion Does not fit this requirement.
C about 1 million Substitute n into the stated growth function.
D about 30 Does not fit this requirement.

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

02 How many edges are in an undirected complete graph with 7 vertices?
A 42 Does not fit this requirement.
B 21 There is one edge for each unordered pair: 7×6/2 = 21.
C 6 Does not fit this requirement.
D 49 Does not fit this requirement.

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

03 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

04 Using the usual inclusive low/high implementation, at most how many element inspections can an unsuccessful binary search of 128 sorted items require?
A 128 Does not fit this requirement.
B 9 Does not fit this requirement.
C 8 An unsuccessful search may inspect floor(log₂(128)) + 1 = 8 elements.
D 7 Does not fit this requirement.

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

05 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 1, h = 12, f = 13 f = 13; another node has a smaller f.
B Node B: g = 3, h = 9, f = 12 f = 12; another node has a smaller f.
C Node C: g = 5, h = 5, f = 10 f = 10; another node has a smaller f.
D Node D: g = 7, h = 2, f = 9 f = 9; this is minimal.

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

06 How many edges are in an undirected complete graph with 17 vertices?
A 272 Does not fit this requirement.
B 136 There is one edge for each unordered pair: 17×16/2 = 136.
C 289 Does not fit this requirement.
D 16 Does not fit this requirement.

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

07 Optimise a timetable while occasionally accepting worse moves early in the search. Choose the best algorithmic description.
A Floyd–Warshall Does not fit this requirement.
B binary search Does not fit this requirement.
C simulated annealing simulated annealing best matches the input and goal.
D hill climbing Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Selecting algorithms · answered at 100 ms

08 How many edges are in an undirected complete graph with 15 vertices?
A 105 There is one edge for each unordered pair: 15×14/2 = 105.
B 210 Does not fit this requirement.
C 14 Does not fit this requirement.
D 225 Does not fit this requirement.

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

09 A school system must undo edits in reverse order. Which ADT is most suitable?
A stack A stack provides last-in, first-out access.
B queue Does not fit this requirement.
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

10 Which class is best described as decision problems whose yes-instances have polynomial-time verifiable certificates?
A NP-Hard only Does not fit this requirement.
B P only Does not fit this requirement.
C undecidable Does not fit this requirement.
D NP That is the definition of NP.

Written for icaijy.com · U4 AOS1 · P, NP and reductions · answered at 100 ms

11 A bank provides understandable reasons for an automated rejection. Select the best model or method.
A privacy Does not fit this requirement.
B time complexity Does not fit this requirement.
C bias Does not fit this requirement.
D transparency transparency directly matches the stated requirement.

Written for icaijy.com · Applied · AI ethics · answered at 100 ms

12 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

13 Which design pattern is most clearly used by the standard earliest-finish-time interval scheduler?
A dynamic programming Does not fit this requirement.
B divide and conquer Does not fit this requirement.
C brute-force search Does not fit this requirement.
D greedy The standard earliest-finish-time interval scheduler uses greedy.

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

14 Find shortest distances between every pair of vertices. Which algorithm is most fit for purpose?
A depth-first search Does not fit this requirement.
B Bellman–Ford algorithm Does not fit this requirement.
C Floyd–Warshall algorithm Floyd–Warshall solves all-pairs shortest paths.
D Prim's algorithm Does not fit this requirement.

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

15 Assume constant-time primitive operations. What is the tightest Big-O bound for: For i from 1 to n: For j from 1 to n: constantWork()
A \(O(n^2)\) There are n × n iterations.
B \(O(n)\) Does not fit this requirement.
C \(O(n \log n)\) Does not fit this requirement.
D \(O(2^n)\) Does not fit this requirement.

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

16 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 5, h = 8, f = 13 f = 13; another node has a smaller f.
B Node B: g = 8, h = 4, f = 12 f = 12; this is minimal.
C Node C: g = 4, h = 10, f = 14 f = 14; another node has a smaller f.
D Node D: g = 9, h = 3, f = 12 f = 12; another node has a smaller f.

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

17 The Halting Problem asks whether
A a program eventually stops on a given input The accepted statement is: a program eventually stops on a given input.
B a graph is connected Does not fit this requirement.
C a model is unbiased Does not fit this requirement.
D two arrays have equal length Does not fit this requirement.

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

18 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…15. How many values are inspected when searching for 3?
A 1 Does not fit this requirement.
B 4 The midpoint trace reaches 3 after 4 inspection(s).
C 6 Does not fit this requirement.
D 7 Does not fit this requirement.

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

19 Assume constant-time primitive operations. What is the tightest Big-O bound for: For i from 1 to n: constantWork()
A \(O(1)\) Does not fit this requirement.
B \(O(n)\) The body runs n times.
C \(O(\log n)\) Does not fit this requirement.
D \(O(n^2)\) Does not fit this requirement.

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

20 Use the supplied Master Theorem. What is T(n) if \(T(n)=9T(n/3)+O(n^1)\)?
A \(O(n^2)\) Compare \(a=9\) with \(b^c=3\).
B \(O(n \log n)\) Does not fit this requirement.
C \(O(\log n)\) Does not fit this requirement.
D \(O(n)\) Does not fit this requirement.

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

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