Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. In a binary tree, what does it mean if a node has two children?

A. It is a leaf node
B. It is a full node
C. It is a parent node
D. It is a root node

Solution

A node with two children is referred to as a full node, as it has both left and right children.

Correct Answer: B — It is a full node

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Q. In a binary tree, what does the term 'height' refer to?

A. Number of nodes
B. Number of edges
C. Maximum depth of a node
D. Minimum depth of a node

Solution

The height of a binary tree is defined as the maximum depth of any node, which is the longest path from the root to a leaf.

Correct Answer: C — Maximum depth of a node

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Q. In a binary tree, what does the term 'leaf node' refer to?

A. A node with two children
B. A node with one child
C. A node with no children
D. A node that is the root

Solution

A leaf node is defined as a node that has no children.

Correct Answer: C — A node with no children

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Q. In a binary tree, what is the height of a tree with only one node?

A. 0
B. 1
C. 2
D. Undefined

Solution

The height of a tree with only one node is 0, as height is defined as the number of edges on the longest path from the root to a leaf.

Correct Answer: A — 0

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Q. In a binary tree, what is the in-order traversal of the nodes?

A. Visit left subtree, root, right subtree
B. Visit root, left subtree, right subtree
C. Visit left subtree, right subtree, root
D. Visit right subtree, root, left subtree

Solution

In in-order traversal, the nodes are visited in the order: left subtree, root, right subtree.

Correct Answer: A — Visit left subtree, root, right subtree

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Q. In a binary tree, what is the in-order traversal of the tree with nodes 1, 2, 3?

A. [1, 2, 3]
B. [2, 1, 3]
C. [1, 3, 2]
D. [3, 2, 1]

Solution

In-order traversal visits the left subtree, then the root, and then the right subtree. For a tree with nodes 1, 2, 3, the in-order traversal is [2, 1, 3].

Correct Answer: B — [2, 1, 3]

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Q. In a binary tree, what is the in-order traversal of the tree with nodes A, B, C, D arranged as follows: A is the root, B is the left child of A, and C is the right child of A, with D as the left child of C?

A. A, B, C, D
B. B, A, D, C
C. B, A, C, D
D. B, D, A, C

Solution

The in-order traversal visits the left subtree, then the root, and then the right subtree, resulting in B, A, C, D.

Correct Answer: C — B, A, C, D

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Q. In a binary tree, what is the in-order traversal of the tree with nodes A, B, C?

A. A, B, C
B. B, A, C
C. B, C, A
D. C, B, A

Solution

In in-order traversal, the left subtree is visited first, then the root, and finally the right subtree. For a tree with nodes A (root), B (left), and C (right), the traversal is B, A, C.

Correct Answer: B — B, A, C

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Q. In a binary tree, what is the in-order traversal of the tree with root 1, left child 2, and right child 3?

A. 1, 2, 3
B. 2, 1, 3
C. 3, 1, 2
D. 1, 3, 2

Solution

The in-order traversal visits the left child first, then the root, and finally the right child, resulting in 2, 1, 3.

Correct Answer: B — 2, 1, 3

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Q. In a binary tree, what is the maximum height of a tree with n nodes?

A. n
B. n/2
C. log n
D. n-1

Solution

The maximum height of a binary tree with n nodes occurs when the tree is skewed, resulting in a height of n-1.

Correct Answer: D — n-1

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Q. In a binary tree, what is the maximum number of children a node can have?

A. One
B. Two
C. Three
D. Unlimited

Solution

In a binary tree, each node can have at most two children, typically referred to as the left and right child.

Correct Answer: B — Two

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Q. In a binary tree, what is the maximum number of leaf nodes possible?

A. n
B. n/2
C. 2^h
D. 2^(h+1) - 1

Solution

The maximum number of leaf nodes in a binary tree of height h is 2^h, as each level can have twice the number of nodes as the previous level.

Correct Answer: C — 2^h

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Q. In a binary tree, what is the maximum number of leaf nodes?

A. n
B. n/2
C. 2^(h-1)
D. 2^h

Solution

In a binary tree of height h, the maximum number of leaf nodes is 2^(h-1), which occurs in a complete binary tree.

Correct Answer: C — 2^(h-1)

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Q. In a binary tree, what is the maximum number of nodes at depth d?

A. d
B. 2^d
C. 2^(d+1) - 1
D. d^2

Solution

The maximum number of nodes at depth d in a binary tree is 2^d.

Correct Answer: B — 2^d

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Q. In a binary tree, what is the maximum number of nodes at level 'h'?

A. h
B. 2^h
C. 2^(h+1)-1
D. h^2

Solution

The maximum number of nodes at level 'h' in a binary tree is 2^h.

Correct Answer: B — 2^h

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Q. In a binary tree, what is the maximum number of nodes at level 'l'?

A. 2^l
B. l^2
C. l
D. 2^(l+1)

Solution

The maximum number of nodes at level 'l' in a binary tree is 2^l.

Correct Answer: A — 2^l

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Q. In a binary tree, what is the maximum number of nodes at level k?

A. k
B. 2^k
C. 2^(k+1)
D. k^2

Solution

In a binary tree, the maximum number of nodes at level k is 2^k, as each node can have two children.

Correct Answer: B — 2^k

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Q. In a binary tree, what is the minimum number of nodes required to have a height of h?

A. h
B. h + 1
C. 2^h
D. 2^(h+1) - 1

Solution

The minimum number of nodes required to have a height of h in a binary tree is h, which occurs in a skewed tree.

Correct Answer: A — h

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Q. In a binary tree, what is the time complexity of finding the height of the tree?

A. O(n)
B. O(log n)
C. O(n log n)
D. O(1)

Solution

The time complexity of finding the height of a binary tree is O(n) because we may need to visit all nodes.

Correct Answer: A — O(n)

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Q. In a binary tree, what is the time complexity of searching for an element in the worst case?

A. O(log n)
B. O(n)
C. O(n log n)
D. O(1)

Solution

In the worst case, searching for an element in a binary tree can take O(n) time, especially if the tree is unbalanced.

Correct Answer: B — O(n)

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Q. In a binary tree, what is the time complexity of traversing all nodes using in-order traversal?

A. O(1)
B. O(n)
C. O(log n)
D. O(n log n)

Solution

In-order traversal visits each node exactly once, resulting in a time complexity of O(n).

Correct Answer: B — O(n)

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Q. In a binary tree, which traversal method is most similar to DFS?

A. Level-order traversal
B. In-order traversal
C. Breadth-first traversal
D. Random traversal

Solution

In-order traversal is a type of DFS as it explores the left subtree, then the node, and finally the right subtree.

Correct Answer: B — In-order traversal

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Q. In a case study involving a city map, which application of Dijkstra's algorithm is most relevant?

A. Finding the fastest route between two locations
B. Calculating the total distance of all roads
C. Determining the longest path in the city
D. Finding all intersections in the map

Solution

In a city map scenario, Dijkstra's algorithm is most relevant for finding the fastest route between two locations.

Correct Answer: A — Finding the fastest route between two locations

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Q. In a circular linked list, what is the main characteristic?

A. Last node points to null
B. First node points to last node
C. All nodes are connected in a circle
D. None of the above

Solution

In a circular linked list, the last node points back to the first node, forming a circle.

Correct Answer: C — All nodes are connected in a circle

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Q. In a circular queue implemented using an array, what is the time complexity of the enqueue operation?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

The enqueue operation in a circular queue can be performed in constant time O(1) as long as there is space available.

Correct Answer: A — O(1)

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Q. In a circular queue, what condition indicates that the queue is full?

A. front == rear
B. rear == (front + 1) % size
C. front == (rear + 1) % size
D. rear == front

Solution

In a circular queue, the condition rear == (front + 1) % size indicates that the queue is full, as it means there is no space left for new elements.

Correct Answer: B — rear == (front + 1) % size

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Q. In a circular queue, what happens when the rear pointer reaches the end of the array?

A. It resets to the beginning of the array
B. It stops accepting new elements
C. It throws an error
D. It moves to the next available position

Solution

In a circular queue, when the rear pointer reaches the end of the array, it resets to the beginning of the array to utilize the available space.

Correct Answer: A — It resets to the beginning of the array

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Q. In a complete binary tree, how many nodes are there at height 'h'?

A. h + 1
B. 2^h
C. 2^(h+1) - 1
D. h^2

Solution

In a complete binary tree, the number of nodes at height 'h' is 2^(h+1) - 1.

Correct Answer: C — 2^(h+1) - 1

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Q. In a complete binary tree, how many nodes are there at level k?

A. 2^k
B. 2^(k+1)
C. 2^(k-1)
D. k^2

Solution

In a complete binary tree, the number of nodes at level k is given by 2^k, where k starts from 0 for the root level.

Correct Answer: A — 2^k

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Q. In a complete binary tree, how many nodes are there at the last level if the total number of levels is 'h'?

A. 2^(h-1)
B. 2^h
C. 2^(h+1)
D. 2^(h-1) - 1

Solution

In a complete binary tree, the last level can have up to 2^(h-1) nodes, where h is the total number of levels.

Correct Answer: A — 2^(h-1)

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Data Structures & Algorithms

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