Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. In a binary search implementation, what condition is checked to determine if the search should continue?

A. If the target is less than the middle element
B. If the target is greater than the middle element
C. If the target is equal to the middle element
D. All of the above

Solution

All these conditions are checked to decide whether to continue searching in the left half, right half, or if the target is found.

Correct Answer: D — All of the above

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Q. In a binary search implementation, what happens if the target is less than the mid value?

A. Search the right half
B. Search the left half
C. Return mid
D. End the search

Solution

If the target is less than the mid value, the search continues in the left half of the array.

Correct Answer: B — Search the left half

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Q. In a binary search implementation, what is the condition to continue searching?

A. left <= right
B. left < right
C. left < mid
D. mid < right

Solution

The search continues as long as the left index is less than or equal to the right index.

Correct Answer: A — left <= right

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Q. In a binary search implementation, what is the purpose of the 'mid' variable?

A. To store the maximum value
B. To find the middle index
C. To count iterations
D. To store the minimum value

Solution

'mid' is used to find the middle index of the current search range to compare with the target value.

Correct Answer: B — To find the middle index

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Q. In a binary search implementation, what is the role of the 'low' and 'high' variables?

A. To store the size of the array
B. To track the current search range
C. To count the number of iterations
D. To store the target value

Solution

'low' and 'high' define the current range of indices being searched in the array.

Correct Answer: B — To track the current search range

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Q. In a binary search tree (BST), how does binary search differ from searching in a sorted array?

A. It is slower
B. It requires more comparisons
C. It can be done in O(1)
D. It uses tree properties

Solution

In a binary search tree, the search leverages the tree structure, allowing for efficient searching based on the properties of BSTs.

Correct Answer: D — It uses tree properties

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Q. In a binary search tree, how does binary search help in finding an element?

A. By traversing all nodes
B. By comparing with the root and deciding left or right
C. By using a queue
D. By using a stack

Solution

In a binary search tree, binary search helps by comparing the target with the root and deciding whether to go left or right based on the value.

Correct Answer: B — By comparing with the root and deciding left or right

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Q. In a binary search tree, what is the average time complexity for searching an element?

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

Solution

The average time complexity for searching an element in a balanced binary search tree is O(log n).

Correct Answer: B — O(log n)

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

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

Solution

In a binary search tree, the maximum number of nodes at depth 'd' is 2^d, as each node can have two children.

Correct Answer: A — 2^d

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Q. In a binary search tree, what is the time complexity for inserting an element in the average case?

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

Solution

In a balanced binary search tree, the average-case time complexity for insertion is O(log n).

Correct Answer: B — O(log n)

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

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

Solution

In a balanced binary search tree, the average time complexity for searching an element is O(log n).

Correct Answer: C — O(log n)

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

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

Solution

In a balanced binary search tree, the average time complexity for searching an element is O(log n).

Correct Answer: B — O(log n)

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Q. In a binary search, if the middle element is greater than the target, which half of the array is searched next?

A. Left half
B. Right half
C. Both halves
D. None

Solution

If the middle element is greater than the target, the left half of the array is searched next.

Correct Answer: A — Left half

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Q. In a binary search, if the target is less than the mid value, what should be the next step?

A. Search the right half
B. Search the left half
C. Return the mid index
D. Increase the mid index

Solution

If the target is less than the mid value, the search should continue in the left half of the array.

Correct Answer: B — Search the left half

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Q. In a binary search, if the target value is not found, what will be the return value?

A. -1
B. 0
C. null
D. the index of the closest value

Solution

Typically, binary search returns -1 to indicate that the target value is not present in the array.

Correct Answer: A — -1

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Q. In a binary search, if the target value is not present in the array, what will be the return value?

A. -1
B. 0
C. null
D. the index of the closest value

Solution

Typically, binary search returns -1 to indicate that the target value is not found in the array.

Correct Answer: A — -1

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Q. In a binary tree, how many children can a node have?

A. 1
B. 2
C. 3
D. None

Solution

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

Correct Answer: B — 2

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Q. In a binary tree, how many edges are there if there are n nodes?

A. n-1
B. n
C. n+1
D. 2n

Solution

In a binary tree, the number of edges is always one less than the number of nodes, hence there are n-1 edges for n nodes.

Correct Answer: A — n-1

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Q. In a binary tree, how many leaf nodes can there be at maximum if there are n internal nodes?

A. n + 1
B. n
C. 2n
D. n - 1

Solution

In a binary tree, the maximum number of leaf nodes is n + 1, where n is the number of internal nodes.

Correct Answer: A — n + 1

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Q. In a binary tree, how many nodes can be at the maximum level 'h'?

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

Solution

The maximum number of nodes at level 'h' in a binary tree is 2^h, as each node can have two children.

Correct Answer: A — 2^h

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Q. In a binary tree, if a node has only one child, which traversal will still visit all nodes?

A. In-order
B. Pre-order
C. Post-order
D. All of the above

Solution

All traversal methods (in-order, pre-order, post-order) will visit all nodes even if a node has only one child.

Correct Answer: D — All of the above

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Q. In a binary tree, if a node has two children, how many leaf nodes can it have at maximum?

A. 1
B. 2
C. 3
D. 4

Solution

If a node has two children, it can lead to a maximum of 3 leaf nodes in its subtree, assuming each child has at least one leaf.

Correct Answer: C — 3

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Q. In a binary tree, if a node has two children, how many nodes are there in its subtree?

A. 1
B. 2
C. 3
D. 4

Solution

If a node has two children, there are at least 3 nodes in its subtree (the node itself and its two children).

Correct Answer: C — 3

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Q. In a binary tree, if a node has two children, how many nodes are there in the subtree rooted at that node?

A. 1
B. 2
C. 3
D. 4

Solution

If a node has two children, there are 3 nodes in the subtree rooted at that node (the node itself and its two children).

Correct Answer: C — 3

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Q. In a binary tree, if a node has two children, how many nodes can be at the next level?

A. 1
B. 2
C. 3
D. 4

Solution

If a node has two children, it can lead to a maximum of 4 nodes at the next level (2 children for each of the 2 children).

Correct Answer: D — 4

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Q. In a binary tree, if the in-order and post-order traversals are given, how can you reconstruct the tree?

A. Using only in-order
B. Using only post-order
C. Using both in-order and post-order
D. Using pre-order and in-order

Solution

To reconstruct a binary tree, both in-order and post-order traversals are needed.

Correct Answer: C — Using both in-order and post-order

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Q. In a binary tree, if the in-order traversal yields the sequence [D, B, E, A, F, C], what is the pre-order traversal?

A. [A, B, D, E, C, F]
B. [A, B, E, D, C, F]
C. [A, C, B, D, E, F]
D. [A, B, D, C, E, F]

Solution

The pre-order traversal can be derived from the in-order traversal and the structure of the tree, yielding [A, B, D, E, C, F].

Correct Answer: A — [A, B, D, E, C, F]

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Q. In a binary tree, what does a level-order traversal use to keep track of nodes?

A. Stack
B. Queue
C. Array
D. Linked List

Solution

Level-order traversal uses a queue to keep track of nodes at each level as it processes them.

Correct Answer: B — Queue

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Q. In a binary tree, what does a null left child indicate?

A. The node is a leaf
B. The node has only a right child
C. The node has no children
D. The node is the root

Solution

A null left child indicates that the node is a leaf node, meaning it has no children.

Correct Answer: A — The node is a leaf

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Q. In a binary tree, what does it mean if a node has both left and right children?

A. It is a leaf node
B. It is a full node
C. It is a complete node
D. It is a balanced node

Solution

A node with both left and right children is referred to as a full node in the context of binary trees.

Correct Answer: B — It is a full node

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Data Structures & Algorithms

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