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

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11 Sep 2026, 9:28 p.m.

20Serious score
01 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

02 In a weighted graph, a weight is usually attached to
A an edge or vertex to represent a quantity Weights encode cost, distance or another quantity.
B only isolated vertices Does not fit this requirement.
C the drawing scale Does not fit this requirement.
D the graph title Does not fit this requirement.

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

03 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 2, h = 14, f = 16 f = 16; another node has a smaller f.
B Node B: g = 5, h = 8, f = 13 f = 13; another node has a smaller f.
C Node C: g = 9, h = 3, f = 12 f = 12; this is minimal.
D Node D: g = 11, h = 2, f = 13 f = 13; another node has a smaller f.

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

04 The negative resolution of the Entscheidungsproblem showed that
A every program can be tested exhaustively Does not fit this requirement.
B all mathematical claims are false Does not fit this requirement.
C NP-Complete problems are undecidable Does not fit this requirement.
D no single algorithm decides validity for every statement in first-order logic The accepted statement is: no single algorithm decides validity for every statement in first-order logic.

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

05 Assume constant-time primitive operations. What is the tightest Big-O bound for: For i from 1 to n: For j from 1 to i: constantWork()
A \(O(n)\) Does not fit this requirement.
B \(O(n^2)\) \(1+\cdots+n\) is quadratic.
C \(O(\log n)\) Does not fit this requirement.
D \(O(n^3)\) Does not fit this requirement.

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

06 A useful dynamic-programming state should contain
A every line of source code Does not fit this requirement.
B enough information to determine future transitions The state summarises relevant history.
C only the final answer Does not fit this requirement.
D a random heuristic Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Advanced design · answered at 100 ms

07 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

08 How many edges are in an undirected complete graph with 4 vertices?
A 16 Does not fit this requirement.
B 6 There is one edge for each unordered pair: 4×3/2 = 6.
C 12 Does not fit this requirement.
D 3 Does not fit this requirement.

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

09 Explore one branch deeply before returning to alternatives. Which algorithm is most fit for purpose?
A PageRank Does not fit this requirement.
B Dijkstra’s algorithm Does not fit this requirement.
C depth-first search DFS follows a branch before backtracking.
D breadth-first search Does not fit this requirement.

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

10 How many edges are in an undirected complete graph with 8 vertices?
A 56 Does not fit this requirement.
B 28 There is one edge for each unordered pair: 8×7/2 = 28.
C 64 Does not fit this requirement.
D 7 Does not fit this requirement.

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

11 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

12 A* uses f(n) = g(n) + h(n). Which frontier node should it expand next?
A Node A: g = 2, h = 8, f = 10 f = 10; another node has a smaller f.
B Node B: g = 3, h = 5, f = 8 f = 8; this is minimal.
C Node C: g = 4, h = 6, f = 10 f = 10; another node has a smaller f.
D Node D: g = 5, h = 3, f = 8 f = 8; another node has a smaller f.

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

13 Use the supplied Master Theorem. What is T(n) if \(T(n)=4T(n/4)+O(n^0)\)?
A \(O(n \log n)\) Does not fit this requirement.
B \(O(n)\) Compare \(a=4\) with \(b^c=1\).
C \(O(n^3)\) 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

14 A form must reject an ID if it is already present. Which concept best matches this situation?
A dictionary Does not fit this requirement.
B priority queue Does not fit this requirement.
C stack Does not fit this requirement.
D set set directly matches the stated requirement.

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

15 An exponential-time algorithm on large inputs illustrates
A an undecidable problem Does not fit this requirement.
B a soft limit of computability The problem is computable but may be impractical.
C a syntax error Does not fit this requirement.
D a violation of Church–Turing Does not fit this requirement.

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

16 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

17 A max-priority queue removes the numerically highest priority first. Which job is removed?
A Job A (priority 17) This has the highest priority.
B Job B (priority 11) A higher-priority job is present.
C Job C (priority 15) A higher-priority job is present.
D Job D (priority 2) A higher-priority job is present.

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

18 Using the usual inclusive low/high implementation, at most how many element inspections can an unsuccessful binary search of 2048 sorted items require?
A 13 Does not fit this requirement.
B 2048 Does not fit this requirement.
C 11 Does not fit this requirement.
D 12 An unsuccessful search may inspect floor(log₂(2048)) + 1 = 12 elements.

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

19 A basic hill-climbing search may stop before the global optimum because of
A the Master Theorem Does not fit this requirement.
B a local optimum No improving neighbour may exist at a non-global optimum.
C a guaranteed negative cycle Does not fit this requirement.
D a queue overflow by definition Does not fit this requirement.

Written for icaijy.com · U4 AOS2 · Advanced design · answered at 100 ms

20 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

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