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FIT2004 Algorithms and data structures - S2 2026

FIT2004 Algorithms and data structures - S2 2026

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Consider the undirected graph below and Kruskal's algorithm for computing a minimum spanning tree. In which order are the edges added to the solution?

graph

4th edge

7th edge

5th edge

2nd edge

6th edge

1st edge

8th edge

3rd edge

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Consider the undirected graph below and Prim's algorithm for computing a minimum spanning tree using node S as the source node. In which order are the edges added to the solution?

graph

4th edge

7th edge

5th edge

2nd edge

6th edge

1st edge

8th edge

3rd edge

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A binary search tree holding

n keys, built by inserting the keys in already-sorted order, has height of order:

O(n)

$O(\log n)$ O(\log n)

❌

$O(n \log n)$ O(n \log n)

O(1)

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Using the convention that height is the number of edges on the longest root-to-leaf path: how many nodes in total does a perfect binary tree of height

3 contain?

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Using the convention that height is the number of edges on the longest root-to-leaf path: a perfect binary tree of height

3 has how many LEAF nodes?

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A code has

2 positions, and each position is filled independently by one of

26 symbols (repetition allowed). How many different codes are possible?

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Consider

factorial(k): if

k = 0 return 1, else return $k \cdot factorial(k-1)$ k \cdot factorial(k-1). How many times is factorial invoked in total (counting the initial call and the base-case call) to compute

factorial(7)?

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Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of finding the vertex with the greatest number of edges, counting incoming and outgoing together, if G is implemented using an adjacency matrix?

θ(|E|)

θ(1)

θ(|V|+|E|)

θ(|V|^2)

θ(|V| log |V|)

θ(|E| log |E|)

θ(|E|^2)

θ(|V|)

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of listing all the outgoing edges of the vertex that has the most outgoing edges, if G is implemented using an unsorted adjacency list?

θ(|E|)

θ(1)

θ(|V|+|E|)

θ(|V|^2)

θ(|V| log |V|)

θ(|E| log |E|)

θ(|E|^2)

θ(|V|)

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Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of determining whether G contains an edge between vertices u and v (in either direction), if G is implemented using an unsorted adjacency list?

θ(|E|)

❌

θ(1)

θ(|V|+|E|)

θ(|V|^2)

θ(|V| log |V|)

θ(|E| log |E|)

θ(|E|^2)

θ(|V|)

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