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

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11 Sep 2026, 8:58 p.m.

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

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

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

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

03 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

04 Which design pattern or algorithm repeatedly moves to a neighbouring state with a better heuristic value?
A divide and conquer Does not fit this requirement.
B dynamic programming Does not fit this requirement.
C breadth-first search Does not fit this requirement.
D hill climbing This is the defining behaviour of hill climbing.

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

05 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

06 Which term best matches a system that makes predictions by following feature-based branches?
A decision tree This describes decision tree.
B neural network Does not fit this requirement.
C support vector machine Does not fit this requirement.
D Turing machine Does not fit this requirement.

Written for icaijy.com · U4 AOS3 · Data-driven algorithms · answered at 100 ms

07 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

08 A route finder combines distance travelled with estimated distance remaining. Select the best model or method.
A simulated annealing Does not fit this requirement.
B A* A* directly matches the stated requirement.
C hill climbing Does not fit this requirement.
D dynamic programming Does not fit this requirement.

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

09 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 2, h = 10, f = 12 f = 12; another node has a smaller f.
B Node B: g = 6, h = 5, f = 11 f = 11; another node has a smaller f.
C Node C: g = 9, h = 1, f = 10 f = 10; this is minimal.
D Node D: g = 4, h = 8, f = 12 f = 12; another node has a smaller f.

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

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

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

11 Find shortest distances from one depot when all edge weights are non-negative. Which algorithm is most fit for purpose?
A PageRank Does not fit this requirement.
B Floyd–Warshall algorithm Does not fit this requirement.
C Dijkstra’s algorithm Dijkstra solves non-negative single-source shortest paths.
D Prim's algorithm Does not fit this requirement.

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

12 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

13 Estimate a web page’s importance from links made by other pages. Which algorithm is most fit for purpose?
A PageRank PageRank estimates importance from incoming links.
B Prim's algorithm Does not fit this requirement.
C binary search Does not fit this requirement.
D Floyd–Warshall algorithm Does not fit this requirement.

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

14 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

15 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

16 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

17 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

18 Use the supplied Master Theorem. What is T(n) if \(T(n)=1T(n/3)+O(n^0)\)?
A \(O(n)\) Does not fit this requirement.
B \(O(\log n)\) Compare \(a=1\) with \(b^c=1\).
C \(O(n^2)\) 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

19 A research program must serve customers in the order in which they arrived. Which ADT is most suitable?
A stack Does not fit this requirement.
B queue A queue provides first-in, first-out access.
C set Does not fit this requirement.
D dictionary Does not fit this requirement.

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

20 How many edges are in an undirected complete graph with 16 vertices?
A 240 Does not fit this requirement.
B 120 There is one edge for each unordered pair: 16×15/2 = 120.
C 256 Does not fit this requirement.
D 15 Does not fit this requirement.

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

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