This post presents 50 multiple-choice questions (MCQs) designed for professionals and engineering students to test their understanding of DSA Data Structures and Algorithms. Each question includes an answer and a clear explanation to reinforce key concepts and prepare for exams.
1. Which of the following data structures is used to implement recursion?
Answer:
Explanation:
Recursion is implemented using a stack data structure. Every recursive function call is pushed onto the stack, and when the function returns, it is popped off the stack.
This behavior mimics the Last-In-First-Out (LIFO) nature of stacks. Each function call waits until the next call finishes, and results are returned in reverse order of the calls.
This structure allows recursion to track and maintain the state of each call in memory, preventing overlapping and maintaining execution order.
2. What is the time complexity of searching for an element in a binary search tree (BST) in the average case?
Answer:
Explanation:
In a balanced binary search tree (BST), the average time complexity for searching an element is O(log n). This is because the height of the tree is proportional to log n, and searching involves traversing from the root to a leaf node, which takes log n steps.
In the worst case, if the BST becomes unbalanced (like a linked list), the time complexity degrades to O(n). However, for a well-balanced tree, the search complexity remains O(log n).
Using algorithms like AVL trees or Red-Black trees can help maintain balance in a BST and preserve the O(log n) search complexity.
3. Which of the following is not a self-balancing binary search tree?
Answer:
Explanation:
A Binary Heap is not a self-balancing binary search tree. It is a complete binary tree where each parent node is greater than or equal to (max heap) or less than or equal to (min-heap) its child nodes.
In contrast, AVL Trees, Red-Black Trees, and Splay Trees are all self-balancing binary search trees. They maintain balance during insertions and deletions to ensure that operations like search, insertion, and deletion have logarithmic time complexity.
Binary Heaps are typically used to implement priority queues, whereas self-balancing binary search trees are used for efficient sorted data management.
4. What is the time complexity of accessing an element in an array?
Answer:
Explanation:
Accessing an element in an array is done in constant time O(1), as arrays provide direct access to any element using its index. This makes arrays a very efficient data structure for accessing elements.
The index is used to calculate the memory address of the element, and this operation takes the same amount of time regardless of the size of the array.
However, operations like searching, inserting, or deleting in unsorted arrays can take linear time O(n), depending on the position of the element.
5. In a linked list, how do you insert an element at the beginning of the list?
Answer:
Explanation:
Inserting an element at the beginning of a linked list involves creating a new node, setting its pointer to the current head, and then updating the head pointer to point to the new node. This operation takes constant time O(1).
Unlike arrays, linked lists do not require shifting elements, making insertion at the beginning efficient. This characteristic makes linked lists a good choice when frequent insertions and deletions are needed at the head.
However, insertion at the end or in the middle of a singly linked list requires traversal and takes linear time O(n).
6. What is the main advantage of using a doubly linked list over a singly linked list?
Answer:
Explanation:
The main advantage of a doubly linked list over a singly linked list is that each node contains two pointers: one to the next node and one to the previous node. This allows traversal in both directions, making it more flexible for operations like deletion and insertion at both ends.
However, a doubly linked list uses more memory than a singly linked list due to the additional pointer. Despite this, it is preferred in scenarios where bidirectional traversal is important, such as in certain sorting algorithms.
Searching in a linked list still takes linear time O(n), regardless of whether it is singly or doubly linked.
7. Which of the following data structures is most suitable for implementing a priority queue?
Answer:
Explanation:
A heap is the most suitable data structure for implementing a priority queue because it allows efficient retrieval of the highest (or lowest) priority element. Heaps provide logarithmic time O(log n) for insertion and deletion operations.
In a priority queue, elements are dequeued based on their priority rather than their order of arrival. Heaps are commonly used to maintain such order efficiently.
A binary heap, in particular, is widely used for implementing priority queues due to its structure and the efficiency it provides for maintaining the order of priorities.
8. What is the time complexity of inserting an element into a binary heap?
Answer:
Explanation:
The time complexity of inserting an element into a binary heap is O(log n). This is because after inserting the element at the end, the heap property may need to be restored, which requires traversing up the heap to re-establish the correct order.
This process, called "heapify," ensures that the newly inserted element is correctly placed according to the heap’s properties. Since the height of a binary heap is log n, the heapify process takes O(log n) time.
This efficiency makes heaps ideal for priority queues, where both insertions and deletions are done frequently.
9. In a graph, what is the time complexity of searching for an edge in an adjacency matrix representation?
Answer:
Explanation:
In an adjacency matrix representation of a graph, searching for an edge between two vertices can be done in constant time O(1). The adjacency matrix is a 2D array where the presence of an edge between vertices i and j is indicated by the value at index [i][j].
This allows for efficient edge lookups but consumes more memory, especially for sparse graphs, as it stores a matrix of size n^2, where n is the number of vertices.
Adjacency lists, on the other hand, are more memory-efficient for sparse graphs but have slower search times for specific edges.
10. Which of the following sorting algorithms is the fastest in the average case for large datasets?
Answer:
Explanation:
Quick Sort is one of the fastest sorting algorithms in the average case, with a time complexity of O(n log n). It is efficient for large datasets due to its divide-and-conquer approach, where the list is partitioned into smaller sublists and sorted independently.
Although the worst-case time complexity of Quick Sort is O(n^2), this can be avoided with good pivot selection strategies, such as choosing the median or using randomized pivoting.
Bubble Sort, Selection Sort, and Insertion Sort have worse average-case time complexities of O(n^2), making them less suitable for large datasets compared to Quick Sort.
11. What is the time complexity of deleting an element from a doubly linked list?
Answer:
Explanation:
In a doubly linked list, if you have a pointer to the node you want to delete, you can perform the deletion in constant time O(1) by updating the pointers of the adjacent nodes to bypass the deleted node.
This efficiency is due to the fact that a doubly linked list contains both forward and backward links, allowing immediate access to the previous and next nodes without needing to traverse the entire list.
However, finding the node to delete in the first place takes O(n) time in the worst case, as you might need to traverse the list.
12. In a binary search algorithm, what is the time complexity of searching for an element?
Answer:
Explanation:
Binary search is a divide-and-conquer algorithm that splits the search space in half with each comparison, resulting in a time complexity of O(log n). It works efficiently on sorted arrays or lists.
At each step, the algorithm compares the target value with the middle element and discards half of the search space based on the comparison. This ensures that the search process is logarithmic in nature.
Binary search is much faster than linear search O(n) for large datasets, but it requires that the data be sorted beforehand.
13. What is the time complexity of inserting an element at the beginning of an array?
Answer:
Explanation:
Inserting an element at the beginning of an array requires shifting all existing elements one position to the right to make space for the new element, resulting in a time complexity of O(n), where n is the number of elements in the array.
This operation is inefficient compared to inserting at the end of the array, which can be done in O(1) time. For frequent insertions at the beginning, data structures like linked lists are more efficient.
Array operations that involve shifting elements, such as insertion at the start or deletion from the start, have linear time complexity due to the need to move all other elements.
14. Which data structure is most suitable for implementing Breadth-First Search (BFS) in a graph?
Answer:
Explanation:
Breadth-First Search (BFS) is implemented using a queue data structure. BFS explores a graph level by level, visiting all nodes at the current level before moving to the next level.
The queue ensures that nodes are processed in the order they are discovered, maintaining the breadth-first nature of the traversal. Nodes are enqueued when they are first encountered and dequeued for processing in a First-In-First-Out (FIFO) manner.
BFS is commonly used to find the shortest path in an unweighted graph or to explore all connected components of a graph.
15. What is the worst-case time complexity of Quick Sort?
Answer:
Explanation:
Quick Sort has a worst-case time complexity of O(n^2), which occurs when the pivot chosen is always the smallest or largest element in the array. This results in highly unbalanced partitions, causing the algorithm to degrade to quadratic time complexity.
However, with good pivot selection techniques, such as choosing a random pivot or the median, the average-case time complexity of Quick Sort is O(n log n), which makes it very efficient for large datasets.
In practice, Quick Sort is often faster than other O(n log n) algorithms like Merge Sort due to better cache performance and fewer data movements.
16. What data structure is used for Depth-First Search (DFS) in a graph?
Answer:
Explanation:
Depth-First Search (DFS) is implemented using a stack data structure. DFS explores a graph by going as deep as possible along a branch before backtracking, and this is naturally supported by the Last-In-First-Out (LIFO) nature of stacks.
In recursive implementations, DFS uses the call stack implicitly. In iterative implementations, an explicit stack is used to track the vertices that need to be processed.
DFS is useful for applications like topological sorting, detecting cycles in graphs, and solving mazes.
17. In which case does Merge Sort outperform Quick Sort?
Answer:
Explanation:
Merge Sort outperforms Quick Sort in worst-case scenarios, where Quick Sort has a time complexity of O(n^2). Merge Sort guarantees a time complexity of O(n log n) in both the worst and average cases, making it more predictable for large datasets.
However, Merge Sort requires additional memory for the merge step, whereas Quick Sort works in-place. Despite this, Merge Sort is stable, which means it preserves the relative order of equal elements.
Merge Sort is commonly used in applications where stability and predictable performance are important, such as external sorting with large datasets.
18. Which data structure is used to implement a breadth-first search in a tree?
Answer:
Explanation:
Breadth-First Search (BFS) in a tree is implemented using a queue data structure. BFS explores the tree level by level, starting from the root and visiting all nodes at the current level before moving to the next.
The queue allows nodes to be processed in the order they are discovered, ensuring that all children of a node are visited before moving deeper into the tree.
BFS is useful for finding the shortest path in unweighted trees or graphs and for level-order traversal of a tree.
19. Which of the following algorithms is not stable?
Answer:
Explanation:
Quick Sort is not a stable sorting algorithm, meaning it does not guarantee that two equal elements will retain their relative order after sorting. The order of equal elements can change depending on the partitioning.
In contrast, Merge Sort, Bubble Sort, and Insertion Sort are stable algorithms that preserve the relative order of equal elements during sorting.
Stability is important in certain applications, such as when sorting a list of records based on multiple fields. For example, you may want to sort by one field while maintaining the order of another field that is already sorted.
20. What is the maximum number of children a node can have in a binary tree?
Answer:
Explanation:
In a binary tree, each node can have at most two children: a left child and a right child. This structure is what defines a binary tree, as the "binary" in the name refers to two possible child nodes.
Binary trees are used in various applications such as searching (binary search trees), sorting (heap sort), and representing hierarchical structures. The properties of binary trees make them a fundamental data structure in computer science.
A full binary tree is a binary tree in which each node has either zero or two children, while a complete binary tree is a binary tree in which all levels are fully filled except possibly the last level, which is filled from left to right.
21. What is the height of a complete binary tree with n nodes?
Answer:
Explanation:
The height of a complete binary tree with n nodes is O(log n). In a complete binary tree, all levels except possibly the last are completely filled, and the last level is filled from left to right.
The height of a complete binary tree is determined by the number of levels, which is proportional to log n, where n is the total number of nodes in the tree.
This logarithmic height allows efficient searching, insertion, and deletion operations in binary trees, particularly in balanced binary trees such as AVL and Red-Black trees.
22. Which of the following data structures is best suited for implementing a circular queue?
Answer:
Explanation:
A circular queue is best implemented using an array. In a circular queue, the positions in the array are reused by wrapping around when the end of the array is reached. This allows for efficient use of space and prevents the need to shift elements.
In a normal queue, once the end of the array is reached, no more elements can be inserted, even if there are free spaces at the beginning. A circular queue overcomes this limitation by linking the end of the array back to the beginning.
Both enqueue and dequeue operations in a circular queue take constant time O(1), making it an efficient data structure for scenarios where a fixed-size buffer is required.
23. In an AVL tree, what is the maximum difference in height between the left and right subtrees of a node?
Answer:
Explanation:
In an AVL tree, the maximum difference in height between the left and right subtrees of any node is 1. This condition ensures that the tree remains balanced, keeping the height logarithmic with respect to the number of nodes.
When the balance factor of a node (the difference in heights of its subtrees) exceeds 1, the tree is rebalanced using rotations. These rotations restore the balance factor to either 0, -1, or 1.
The AVL tree provides logarithmic time complexity for insertion, deletion, and search operations, making it efficient for maintaining sorted data.
24. Which of the following graph traversal algorithms uses recursion implicitly?
Answer:
Explanation:
Depth-First Search (DFS) uses recursion implicitly through the system's call stack. The algorithm explores as far as possible along each branch before backtracking, which is a natural fit for recursive function calls.
While DFS can also be implemented iteratively using an explicit stack, the recursive implementation is more intuitive as the function calls inherently handle the backtracking process.
DFS is widely used in applications such as detecting cycles in graphs, solving mazes, and performing topological sorting in directed acyclic graphs (DAGs).
25. In a priority queue, which data structure is typically used to ensure efficient access to the highest (or lowest) priority element?
Answer:
Explanation:
A binary heap is commonly used to implement a priority queue. In a binary heap, the highest (or lowest) priority element is always at the root, allowing for efficient access in O(1) time. Insertion and deletion operations in a heap take O(log n) time, making it well-suited for priority queues.
A binary heap can be implemented as a max-heap or min-heap, depending on whether the priority queue is meant to retrieve the maximum or minimum element.
Other data structures, like unsorted arrays or linked lists, are less efficient for priority queues because they require linear time to find the element with the highest priority.
26. What is the best case time complexity for bubble sort?
Answer:
Explanation:
The best case time complexity for bubble sort is O(n). This occurs when the input array is already sorted, so no swaps are needed, and the algorithm only makes one pass through the array to verify that no further sorting is required.
In contrast, the average and worst-case time complexities for bubble sort are O(n^2) because, in those cases, the algorithm may need to perform multiple passes and swaps to sort the elements.
Bubble sort is simple to implement but inefficient for large datasets, so it is mainly used for educational purposes or when the dataset is small and almost sorted.
27. Which of the following data structures is non-linear?
Answer:
Explanation:
A graph is a non-linear data structure consisting of nodes (also called vertices) and edges connecting the nodes. It is used to represent networks, such as social networks or communication networks, where relationships between entities are not hierarchical or sequential.
In contrast, arrays, linked lists, and stacks are linear data structures because their elements are arranged sequentially, and each element is directly accessible in a specific order.
Graphs are widely used in algorithms for network analysis, shortest path calculations, and finding connected components in a system.
28. What is the time complexity of inserting an element into an unsorted array?
Answer:
Explanation:
Inserting an element into an unsorted array can be done in constant time O(1) by simply placing the new element at the end of the array. This operation does not require shifting any elements or searching for a specific position.
However, if the array is full and needs to be resized, the time complexity will be O(n), as copying all elements to a new array takes linear time. Resizing typically happens in amortized constant time for dynamically sized arrays.
Although insertion is fast, searching in an unsorted array takes linear time O(n) because elements are not ordered.
29. What is a complete graph?
Answer:
Explanation:
A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge. If a complete graph has n vertices, it will have n(n-1)/2 edges.
In a complete graph, each vertex is adjacent to every other vertex, meaning that the graph is highly connected. Complete graphs are often used in network theory to represent fully connected systems.
A complete graph with n vertices is denoted by K_n, and it is an important concept in graph theory for studying various properties of connectivity and traversal.
30. Which data structure is used to find the shortest path in an unweighted graph?
Answer:
Explanation:
Breadth-First Search (BFS), which uses a queue, is used to find the shortest path in an unweighted graph. BFS explores all vertices at the current level before moving on to the next, ensuring that the shortest path is found in terms of the number of edges.
BFS works efficiently for unweighted graphs because it treats each edge as having equal weight. As it explores each node level by level, the first time a node is reached, the shortest path to that node is guaranteed.
In weighted graphs, algorithms like Dijkstra’s algorithm, which uses a priority queue, are more suitable for finding the shortest path.
31. What is the time complexity of searching for an element in a hash table with n elements?
Answer:
Explanation:
The time complexity of searching for an element in a hash table is O(1) on average. This is because hash tables use a hash function to compute an index at which the data is stored, allowing for constant-time access.
However, in the worst case, when there are many collisions, the time complexity can degrade to O(n). To minimize collisions, good hash functions and collision resolution techniques like chaining or open addressing are used.
Hash tables are widely used in situations where fast data retrieval is critical, such as in databases and caching mechanisms.
32. What is the primary difference between a stack and a queue?
Answer:
Explanation:
The primary difference between a stack and a queue is the order in which elements are processed. A stack follows Last In, First Out (LIFO) order, meaning the last element added is the first to be removed.
On the other hand, a queue follows First In, First Out (FIFO) order, meaning the first element added is the first to be removed. This makes queues suitable for tasks like scheduling or buffering, where the order of elements matters.
Stacks are commonly used in recursion, backtracking algorithms, and expression evaluation, while queues are used in breadth-first search and task scheduling.
33. Which of the following algorithms is used to detect a cycle in a graph?
Answer:
Explanation:
Depth-First Search (DFS) is commonly used to detect cycles in a graph. By tracking visited nodes and using a recursive or iterative approach, DFS can identify back edges, which indicate a cycle in the graph.
In an undirected graph, a cycle is detected when DFS encounters a vertex that has already been visited and is not the parent of the current vertex. In a directed graph, a cycle is found when DFS encounters a vertex that is still in the recursion stack.
Cycle detection is important in algorithms for topological sorting, deadlock detection, and graph traversal.
34. In a min-heap, where is the minimum element located?
Answer:
Explanation:
In a min-heap, the minimum element is always located at the root. This is because a min-heap is a binary tree in which each parent node is less than or equal to its child nodes, ensuring that the root contains the smallest value.
When extracting the minimum element, the root is removed, and the heap is restructured (heapified) to maintain the heap property. This allows for efficient access to the minimum element in O(1) time.
Min-heaps are commonly used in priority queues and algorithms like Dijkstra's shortest path algorithm.
35. What is a strongly connected component in a directed graph?
Answer:
Explanation:
A strongly connected component (SCC) in a directed graph is a maximal subgraph where every vertex is reachable from every other vertex within that subgraph. In other words, there is a path from each vertex to every other vertex in the component.
SCCs can be identified using algorithms like Kosaraju’s or Tarjan’s algorithm, which traverse the graph and group vertices into strongly connected components.
SCCs are important in many graph-based algorithms, including those used for analyzing dependencies and detecting cycles in directed graphs.
36. Which data structure is used to implement a LIFO (Last In, First Out) buffer?
Answer:
Explanation:
A stack is used to implement a LIFO (Last In, First Out) buffer, meaning the last element added to the stack is the first to be removed. This structure is used in various algorithms where backtracking is needed, such as in recursion and depth-first search (DFS).
The two main operations of a stack are push() (to add an element) and pop() (to remove the most recently added element). These operations have constant time complexity O(1).
Stacks are commonly used in applications such as expression evaluation, function call management (system call stack), and reversing sequences.
37. Which sorting algorithm is considered a comparison-based sort?
Answer:
Explanation:
Quick Sort is a comparison-based sorting algorithm, meaning it sorts elements by comparing them to one another. The efficiency of Quick Sort is based on how well the pivot element is chosen and how the partitioning step divides the list.
In contrast, non-comparison-based algorithms like Radix Sort and Counting Sort use other properties of the elements (such as their digit values or frequencies) rather than comparisons to sort them.
Comparison-based algorithms have a lower bound of O(n log n) for time complexity, which applies to sorting algorithms like Quick Sort, Merge Sort, and Heap Sort.
38. What is a spanning tree of a graph?
Answer:
Explanation:
A spanning tree of a graph is a subgraph that includes all the vertices of the original graph and is a tree, meaning it is connected and has no cycles. A spanning tree has exactly n-1 edges, where n is the number of vertices in the graph.
Spanning trees are important in network design and optimization problems. In weighted graphs, the minimum spanning tree (MST) is the spanning tree with the smallest possible sum of edge weights.
Algorithms like Kruskal's and Prim's are used to find the minimum spanning tree in weighted graphs.
39. What is the time complexity of inserting an element into a sorted linked list?
Answer:
Explanation:
Inserting an element into a sorted linked list has a time complexity of O(n) because it requires traversing the list to find the correct insertion point. Once the correct position is found, the insertion itself takes constant time O(1).
This linear time traversal is necessary because linked lists do not provide direct access to their elements, unlike arrays, which allow access via index in constant time.
Sorted linked lists are used in applications where frequent insertions and deletions are needed while maintaining sorted order, such as in priority queues.
40. Which of the following algorithms is used to find the shortest path in a graph with negative weights?
Answer:
Explanation:
The Bellman-Ford algorithm is used to find the shortest path in graphs with negative weights. Unlike Dijkstra's algorithm, Bellman-Ford can handle negative weight edges and detect negative weight cycles.
Bellman-Ford works by relaxing edges repeatedly, allowing it to update the shortest path distances from the source vertex to all other vertices. If a negative weight cycle is detected, the algorithm reports that no shortest path exists.
Although Bellman-Ford has a higher time complexity of O(V * E), it is more versatile than Dijkstra's algorithm, which is limited to graphs with non-negative weights.
41. What is a deque (double-ended queue)?
Answer:
Explanation:
A deque (double-ended queue) is a data structure that allows insertion and deletion of elements from both the front and the rear. This makes it more flexible than a regular queue, which only allows operations at one end.
Deques are used in various algorithms that require access to both ends of the sequence, such as in certain sliding window problems or in breadth-first search (BFS) with priority constraints.
Deques can be implemented using arrays or linked lists, and they support O(1) operations for insertion and deletion at both ends.
42. What is a red-black tree?
Answer:
Explanation:
A red-black tree is a self-balancing binary search tree in which each node has an extra color attribute, either red or black. The tree is balanced by maintaining specific properties, such as the rule that no two red nodes can be adjacent and that every path from the root to a leaf must have the same number of black nodes.
Red-black trees provide logarithmic time complexity for search, insertion, and deletion operations, making them efficient for use in databases and memory management systems.
The balancing of a red-black tree is less strict than that of an AVL tree, making red-black trees slightly faster in practice for insertion and deletion operations.
43. In a linked list, what is the time complexity of accessing an element by its index?
Answer:
Explanation:
Accessing an element by its index in a linked list takes O(n) time because linked lists do not provide direct access to elements. To access the i-th element, you need to traverse the list from the head node, which requires linear time.
This is in contrast to arrays, which allow O(1) access to elements by their index. However, linked lists are more efficient than arrays for insertions and deletions, especially at the beginning or middle of the list.
Linked lists are often used when dynamic memory allocation and frequent insertions and deletions are required.
44. What is a perfect binary tree?
Answer:
Explanation:
A perfect binary tree is a binary tree in which all internal nodes have exactly two children, and all leaf nodes are at the same level. In other words, every level of the tree is completely filled with nodes.
Perfect binary trees have a well-defined structure, and their height is minimal given the number of nodes. For a perfect binary tree with height h, the number of nodes is 2^(h+1) - 1.
Perfect binary trees are used in algorithms and applications where the structure needs to be balanced and evenly distributed, such as in heap-based priority queues.
45. What is a hash collision in a hash table?
Answer:
Explanation:
A hash collision occurs in a hash table when two different keys produce the same hash value, meaning they are mapped to the same index. Since a hash table uses hash values to determine where to store or find data, collisions must be handled properly to avoid data loss.
Common techniques to handle hash collisions include chaining (storing multiple elements in the same index using a linked list) and open addressing (finding the next available slot in the table).
Good hash functions minimize the number of collisions by distributing keys uniformly across the hash table.
46. What is the space complexity of Merge Sort?
Answer:
Explanation:
The space complexity of Merge Sort is O(n) because it requires additional space for the temporary arrays used to merge the sorted subarrays. During the merging process, the algorithm creates a new array to hold the merged results.
While Merge Sort has a time complexity of O(n log n), the extra space required for merging makes it less space-efficient compared to in-place sorting algorithms like Quick Sort.
Despite its higher space complexity, Merge Sort is stable and performs well for large datasets, especially when external memory is used for sorting (e.g., in external sorting).
47. What is the in-order traversal of a binary search tree (BST)?
Answer:
Explanation:
In-order traversal of a binary search tree (BST) visits nodes in the following order: left subtree, root, and then right subtree. This traversal results in visiting the nodes in ascending order of their values, making it particularly useful for BSTs.
In-order traversal can be implemented recursively or iteratively using a stack. It is commonly used to retrieve all the elements of a BST in sorted order.
Other types of tree traversal include pre-order (Root, Left, Right) and post-order (Left, Right, Root), each serving different purposes in tree operations.
48. What is the main advantage of a doubly linked list over a singly linked list?
Answer:
Explanation:
The main advantage of a doubly linked list over a singly linked list is that it allows for traversal in both directions. Each node in a doubly linked list contains two pointers: one to the next node and one to the previous node, enabling movement forward and backward through the list.
While doubly linked lists require more memory than singly linked lists due to the additional pointer, they are more flexible for operations like deletion and insertion, especially when the list is traversed in both directions.
Doubly linked lists are used in scenarios where bidirectional traversal is important, such as in certain types of caches or navigation systems.
49. Which algorithm is used to detect a negative cycle in a graph?
Answer:
Explanation:
The Bellman-Ford algorithm is used to detect negative weight cycles in a graph. By running the algorithm for one additional iteration beyond the number of vertices, any negative cycle can be detected if the shortest path estimate is updated again.
If a negative cycle exists, the algorithm will indicate that there is no solution for the shortest path, as paths that involve the negative cycle can reduce the path length indefinitely.
While Bellman-Ford can handle negative weights and cycles, Dijkstra’s algorithm cannot. This makes Bellman-Ford a more versatile option for graphs with negative weights.
50. What is a balanced binary search tree?
Answer:
Explanation:
A balanced binary search tree is a binary search tree where the height of the left and right subtrees of every node differ by no more than one. This ensures that the tree remains balanced, leading to logarithmic time complexity O(log n) for search, insertion, and deletion operations.
Examples of balanced binary search trees include AVL trees and Red-Black trees, which use various balancing techniques to maintain this height property.
Balanced trees are crucial in maintaining the efficiency of operations in scenarios where the tree can become skewed, such as in databases and search algorithms.
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