That y8 kid 🤣 - bot · guest · Algorithmics (HESS)

01 Use the supplied Master Theorem. What is T(n) if \(T(n)=9T(n/3)+O(n^1)\)?

A \(O(n^2)\) Compare \(a=9\) with \(b^c=3\).

B \(O(n \log n)\) Does not fit this requirement.

C \(O(\log n)\) Does not fit this requirement.

D \(O(n)\) Does not fit this requirement.

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

02 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

03 How many edges are in an undirected complete graph with 14 vertices?

A 196 Does not fit this requirement.

B 182 Does not fit this requirement.

C 13 Does not fit this requirement.

D 91 There is one edge for each unordered pair: 14×13/2 = 91.

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

04 A school system must access the 18th temperature reading directly. Which ADT is most suitable?

A queue Does not fit this requirement.

B stack Does not fit this requirement.

C array An array supports access by numeric index.

D set Does not fit this requirement.

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

05 A campus planner needs shortest walking distances between every pair of buildings. Which tool is most fit for purpose?

A Floyd–Warshall algorithm Floyd–Warshall algorithm directly matches the stated requirement.

B Prim's algorithm Does not fit this requirement.

C Dijkstra’s algorithm Does not fit this requirement.

D Bellman–Ford algorithm Does not fit this requirement.

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

06 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

07 Assume constant-time primitive operations. What is the tightest Big-O bound for: For i from 1 to n: work(); For j from 1 to n: work()

A \(O(\(2n\)^2)\) Does not fit this requirement.

B \(O(n^2)\) Does not fit this requirement.

C \(O(n)\) Sequential linear loops add, not multiply.

D \(O(1)\) Does not fit this requirement.

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

08 Binary search uses \(\lfloor(low+high)/2\rfloor\) on the sorted integers 1…31. How many values are inspected when searching for 31?

A 3 Does not fit this requirement.

B 5 The midpoint trace reaches 31 after 5 inspection(s).

C 1 Does not fit this requirement.

D 7 Does not fit this requirement.

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

09 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

10 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

11 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

12 A loan applicant is told what major factors affected an automated decision. What is the most relevant issue?

A recursion Does not fit this requirement.

B transparency The scenario directly illustrates transparency.

C graph connectivity Does not fit this requirement.

D data compression Does not fit this requirement.

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

13 For sufficiently large n, which grows more slowly than \(O(n^2)\)?

A \(O(n \log n)\) \(O(n \log n)\) has the lower asymptotic growth rate.

B \(O(2^n)\) Does not fit this requirement.

C \(O(n^2)\) 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

14 Using the usual inclusive low/high implementation, at most how many element inspections can an unsuccessful binary search of 256 sorted items require?

A 8 Does not fit this requirement.

B 256 Does not fit this requirement.

C 9 An unsuccessful search may inspect floor(log₂(256)) + 1 = 9 elements.

D 10 Does not fit this requirement.

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

15 A max-priority queue removes the numerically highest priority first. Which job is removed?

A Job A (priority 25) This has the highest priority.

B Job B (priority 23) A higher-priority job is present.

C Job C (priority 9) A higher-priority job is present.

D Job D (priority 24) A higher-priority job is present.

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

16 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

17 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

18 Which term must be true before an algorithm is executed?

A loop invariant Does not fit this requirement.

B postcondition Does not fit this requirement.

C precondition This describes a precondition.

D heuristic Does not fit this requirement.

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

19 An undirected complete graph with n vertices has

A \(n(n-1)/2\) edges Each unordered pair contributes one edge.

B \(n^2\) edges Does not fit this requirement.

C n(\(n+1\))/2 edges Does not fit this requirement.

D \(2n\) edges Does not fit this requirement.

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

20 For sufficiently large n, which grows more slowly than \(O(n)\)?

A \(O(n!)\) Does not fit this requirement.

B \(O(n)\) Does not fit this requirement.

C \(O(2^n)\) Does not fit this requirement.

D \(O(\log n)\) \(O(\log n)\) has the lower asymptotic growth rate.

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