The keys 10, 20, 30, 40, 50 are inserted in that order into an empty, unbalanced binary search tree. What is the height of the resulting tree, counting edges on the longest path?
Correct answer D. 4
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Programming MCQs
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In the BST built by inserting 50, 30, 70, 20, 40, 60, 80, the root 50 is deleted using its inorder successor. Which key becomes the new root?
Correct answer C. 60
What is the average-case time complexity of searching for a key in a binary search tree built from random insertions?
Correct answer D. O(log n)
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In an AVL tree, which values may the balance factor (height of left subtree minus height of right subtree) of any node take?
Correct answer A. −1, 0 or +1
The keys 10, 20, 30 are inserted in that order into an empty AVL tree. Which rotation restores balance and which key becomes the root?
Correct answer A. A single left rotation; 20 becomes the root
The keys 30, 10, 20 are inserted in that order into an empty AVL tree. Which rotation is needed?
Correct answer B. A left-right double rotation (left rotation at 10, then right rotation at 30)
In a B-tree of order m, where order means the maximum number of children a node may have, what is the maximum number of keys a node can hold?
Correct answer A. m − 1
How does a B+ tree differ from a B-tree?
Correct answer C. All data records are stored in the leaves, and the leaves are linked for sequential access
The keys 10, 4, 7, 1, 8, 3 are inserted one at a time into an empty binary min-heap stored in an array. What is the final array?
Correct answer B. [1, 4, 3, 10, 8, 7]
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The array is turned into a max-heap using the bottom-up build-heap method, sifting down from the last internal node to the root. What is the resulting array?
Correct answer C. [9, 4, 5, 1, 3, 2]
In a binary heap stored in an array with indices starting at 0, what are the indices of the children of the node at index i?
Correct answer A. 2i + 1 and 2i + 2
What is the time complexity of building a binary heap from n unordered elements using the bottom-up heapify method?
Correct answer C. O(n)
The minimum is removed from the min-heap by moving the last element to the root and sifting it down. What is the resulting array?
Correct answer B. [3, 4, 7, 10, 8]
Which data structure does breadth-first search (BFS) use to keep track of vertices still to be explored?
Correct answer D. Queue
Which data structure is used, explicitly or through recursion, to implement depth-first search (DFS)?
Correct answer C. Stack
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What is the space required to store a graph with V vertices and E edges as an adjacency matrix?
Correct answer D. O(V²)
An undirected graph has edges A–B, A–C, B–D, B–E, C–F and E–F, and each adjacency list is kept in alphabetical order. What is the depth-first search order starting from A?
Correct answer D. A, B, D, E, F, C
A directed graph has edges A→B, A→C, B→D, C→D and D→E. Which of these is a valid topological order?
Correct answer B. A, C, B, D, E
For which kind of graph does a topological ordering exist?
Correct answer C. A directed acyclic graph (DAG)
A weighted undirected graph has edges A–B (1), B–C (2), A–C (3), B–D (4), C–D (5), C–E (6) and D–E (7). What is the total weight of its minimum spanning tree found by Kruskal’s algorithm?
Correct answer B. 13