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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 \(T(n)=3T(n/3)+O(n^1)\)?
A \(O(n \log n)\) Compare \(a=3\) with \(b^c=3\).
B \(O(n^2)\) Does not fit this requirement.
C \(O(n^2 \log n)\) Does not fit this requirement.
D \(O(\log n)\) Does not fit this requirement.

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

02 A council must connect all suburbs while minimising total new cable. Select the best model or method.
A Bellman–Ford algorithm Does not fit this requirement.
B Prim's algorithm Prim's 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

03 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…127. How many values are inspected when searching for 31?
A 7 The midpoint trace reaches 31 after 7 inspection(s).
B 3 Does not fit this requirement.
C 2 Does not fit this requirement.
D 5 Does not fit this requirement.

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

04 Which design pattern or algorithm splits a problem into independent smaller instances and combines their answers?
A greedy Does not fit this requirement.
B hill climbing Does not fit this requirement.
C divide and conquer This is the defining behaviour of divide and conquer.
D brute-force search Does not fit this requirement.

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

05 Which design pattern is most clearly used by mergesort?
A brute-force search Does not fit this requirement.
B greedy Does not fit this requirement.
C divide and conquer Mergesort uses divide and conquer.
D dynamic programming Does not fit this requirement.

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

06 A transport app must always process the waiting job with the highest urgency. Which ADT is most suitable?
A stack Does not fit this requirement.
B priority queue A priority queue removes the highest-priority item.
C queue Does not fit this requirement.
D set Does not fit this requirement.

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

07 Which signature best specifies the lookup operation?
A key → dictionary Does not fit this requirement.
B dictionary × key → value Lookup maps a supplied key to its value.
C dictionary → key × value Does not fit this requirement.
D dictionary × value → key Does not fit this requirement.

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

08 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…127. How many values are inspected when searching for 1?
A 5 Does not fit this requirement.
B 3 Does not fit this requirement.
C 7 The midpoint trace reaches 1 after 7 inspection(s).
D 6 Does not fit this requirement.

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

09 A research program must always process the waiting job with the highest urgency. Which ADT is most suitable?
A set Does not fit this requirement.
B priority queue A priority queue removes the highest-priority item.
C queue Does not fit this requirement.
D stack Does not fit this requirement.

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

10 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

11 A subgraph may contain
A edges absent from the original graph Does not fit this requirement.
B new vertices only Does not fit this requirement.
C every original edge only Does not fit this requirement.
D subsets of the original vertices and edges A subgraph uses only original vertices and edges.

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

12 The general Halting Problem is
A linear time Does not fit this requirement.
B undecidable The accepted statement is: undecidable.
C NP-Complete Does not fit this requirement.
D solved by binary search Does not fit this requirement.

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

13 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

14 Use the supplied Master Theorem. What is T(n) if \(T(n)=8T(n/2)+O(n^2)\)?
A \(O(n)\) Does not fit this requirement.
B \(O(n^2 \log n)\) Does not fit this requirement.
C \(O(n^2)\) Does not fit this requirement.
D \(O(n^3)\) Compare \(a=8\) with \(b^c=4\).

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

15 A school system must test quickly whether a username has already been used. Which ADT is most suitable?
A stack Does not fit this requirement.
B queue Does not fit this requirement.
C priority queue Does not fit this requirement.
D set A set models unique membership.

Written for icaijy.com · U3 AOS1 · ADTs · 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 Which signature best specifies the insert operation?
A set × set → item Does not fit this requirement.
B item → set × set Does not fit this requirement.
C set → item Does not fit this requirement.
D set × item → set Insert adds one item to the set.

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

18 A face-recognition model works poorly for a group scarcely represented in its training set. What is the most relevant issue?
A guaranteed neutrality Does not fit this requirement.
B a faster runtime Does not fit this requirement.
C a proof of correctness Does not fit this requirement.
D bias from unrepresentative data The scenario directly illustrates bias from unrepresentative data.

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

19 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

20 Which term must be true when a correct algorithm terminates?
A recurrence Does not fit this requirement.
B precondition Does not fit this requirement.
C counterexample Does not fit this requirement.
D postcondition This describes a postcondition.

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

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