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

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11 Sep 2026, 9:30 p.m.

20Serious score
01 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

02 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…31. How many values are inspected when searching for 1?
A 2 Does not fit this requirement.
B 5 The midpoint trace reaches 1 after 5 inspection(s).
C 8 Does not fit this requirement.
D 3 Does not fit this requirement.

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

03 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

04 In a directed graph, an edge from u to v
A makes the graph complete Does not fit this requirement.
B does not imply an edge from v to u Direction makes adjacency asymmetric.
C must have weight 1 Does not fit this requirement.
D always implies v to u Does not fit this requirement.

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

05 Which class is best described as problems at least as hard as every problem in NP, without a requirement that they be in NP?
A NP-Complete only Does not fit this requirement.
B P Does not fit this requirement.
C NP-Hard That is the definition of NP-Hard.
D NP only Does not fit this requirement.

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

06 A system groups articles without any supplied category labels. Select the best model or method.
A unsupervised learning unsupervised learning directly matches the stated requirement.
B backtracking Does not fit this requirement.
C binary search Does not fit this requirement.
D PageRank Does not fit this requirement.

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

07 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…255. How many values are inspected when searching for 191?
A 2 Does not fit this requirement.
B 4 Does not fit this requirement.
C 8 The midpoint trace reaches 191 after 8 inspection(s).
D 6 Does not fit this requirement.

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

08 A campus planner needs shortest walking distances between every pair of buildings. Which concept best matches this situation?
A Bellman–Ford algorithm Does not fit this requirement.
B PageRank Does not fit this requirement.
C Prim's algorithm Does not fit this requirement.
D Floyd–Warshall algorithm Floyd–Warshall algorithm directly matches the stated requirement.

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

09 A route finder combines distance travelled with estimated distance remaining. Which concept best matches this situation?
A A* A* directly matches the stated requirement.
B simulated annealing Does not fit this requirement.
C dynamic programming Does not fit this requirement.
D hill climbing Does not fit this requirement.

Written for icaijy.com · Applied · advanced design · answered at 100 ms

10 An organisation names who is responsible for harms caused by its model. What is the most relevant issue?
A memoisation Does not fit this requirement.
B anonymity Does not fit this requirement.
C overfitting Does not fit this requirement.
D accountability The scenario directly illustrates accountability.

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

11 A max-priority queue removes the numerically highest priority first. Which job is removed?
A Job A (priority 5) A higher-priority job is present.
B Job B (priority 2) A higher-priority job is present.
C Job C (priority 8) This has the highest priority.
D Job D (priority 3) A higher-priority job is present.

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

12 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

13 How many edges are in an undirected complete graph with 9 vertices?
A 81 Does not fit this requirement.
B 36 There is one edge for each unordered pair: 9×8/2 = 36.
C 72 Does not fit this requirement.
D 8 Does not fit this requirement.

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

14 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

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

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

16 Which design pattern or algorithm abandons a partial candidate as soon as it cannot lead to a valid solution?
A PageRank Does not fit this requirement.
B hill climbing Does not fit this requirement.
C binary search Does not fit this requirement.
D backtracking This is the defining behaviour of backtracking.

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

17 If one NP-Complete problem is shown to have a polynomial-time algorithm, then
A only that problem enters P Does not fit this requirement.
B P ≠ NP Does not fit this requirement.
C P = NP Every NP problem reduces to that NP-Complete problem.
D all NP-Hard problems become decidable Does not fit this requirement.

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

18 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

19 Ignoring constant factors, approximately how many primitive operations does an \(O(\log_2 n)\) algorithm perform when n = 1,000,000,000?
A about 1 million Does not fit this requirement.
B about 1 thousand Does not fit this requirement.
C about 1 billion Does not fit this requirement.
D about 30 Substitute n into the stated growth function.

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

20 For sufficiently large n, which grows more slowly than \(O(n^3)\)?
A \(O(2^n)\) Does not fit this requirement.
B \(O(n!)\) Does not fit this requirement.
C \(O(n^3)\) Does not fit this requirement.
D \(O(n^2)\) \(O(n^2)\) has the lower asymptotic growth rate.

Written for icaijy.com · U4 AOS1 · Growth rates · answered at 100 ms

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