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

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11 Sep 2026, 8:55 p.m.

20Serious score
01 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 3, h = 15, f = 18 f = 18; another node has a smaller f.
B Node B: g = 7, h = 6, f = 13 f = 13; another node has a smaller f.
C Node C: g = 10, h = 2, f = 12 f = 12; this is minimal.
D Node D: g = 12, h = 1, f = 13 f = 13; another node has a smaller f.

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

02 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

03 Use the supplied Master Theorem. What is T(n) if \(T(n)=4T(n/2)+O(n^1)\)?
A \(O(\log n)\) Does not fit this requirement.
B \(O(n^2)\) Compare \(a=4\) with \(b^c=2\).
C \(O(n)\) Does not fit this requirement.
D \(O(n^3)\) Does not fit this requirement.

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

04 The Church–Turing thesis informally claims that
A every true statement is provable Does not fit this requirement.
B every effectively calculable function can be computed by a Turing machine The accepted statement is: every effectively calculable function can be computed by a Turing machine.
C P equals NP Does not fit this requirement.
D all programs halt Does not fit this requirement.

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

05 A max-priority queue removes the numerically highest priority first. Which job is removed?
A Job A (priority 7) A higher-priority job is present.
B Job B (priority 14) This has the highest priority.
C Job C (priority 11) A higher-priority job is present.
D Job D (priority 13) A higher-priority job is present.

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

06 A bank provides understandable reasons for an automated rejection. Which tool is most fit for purpose?
A privacy Does not fit this requirement.
B transparency transparency directly matches the stated requirement.
C bias Does not fit this requirement.
D time complexity Does not fit this requirement.

Written for icaijy.com · Applied · AI ethics · 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 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

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

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

10 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

11 Worst-case time complexity gives
A the average over one dataset Does not fit this requirement.
B an upper bound over all inputs of a given size Worst case considers the most costly input of each size.
C the exact time on every device Does not fit this requirement.
D the memory used by the best input Does not fit this requirement.

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

12 Patients must be treated according to changing urgency scores. Which concept best matches this situation?
A priority queue priority queue directly matches the stated requirement.
B queue Does not fit this requirement.
C stack Does not fit this requirement.
D set Does not fit this requirement.

Written for icaijy.com · Applied · ADTs · answered at 100 ms

13 To show new problem X is NP-Hard using known NP-Hard problem Y, the required polynomial reduction direction is
A P → Y Does not fit this requirement.
B Y → X Solving X would then solve Y.
C X → Y Does not fit this requirement.
D X → P Does not fit this requirement.

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

14 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…127. How many values are inspected when searching for 127?
A 3 Does not fit this requirement.
B 8 Does not fit this requirement.
C 7 The midpoint trace reaches 127 after 7 inspection(s).
D 4 Does not fit this requirement.

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

15 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

16 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

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

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

18 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 3, h = 7, f = 10 f = 10; this is minimal.
B Node B: g = 5, h = 6, f = 11 f = 11; another node has a smaller f.
C Node C: g = 7, h = 3, f = 10 f = 10; another node has a smaller f.
D Node D: g = 8, h = 2, f = 10 f = 10; another node has a smaller f.

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

19 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

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

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

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