Given an array of integers, find the kth largest element in the array.
Use a min-heap of size k to store the k largest elements encountered so far.
Sort the array and return the element at the kth position from the end.
Use a max-heap to store all the elements and extract the kth largest element.
Use quickselect, a selection algorithm with an average time complexity of O(n).
Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the missing number.
Use the XOR operation to find the missing number.
Use a hash table to store the presence of each number.
Sort the array and find the missing element.
Calculate the sum of all numbers from 0 to n and subtract the sum of the array elements.
You are designing a dynamic array implementation that needs to support efficient insertion at both the beginning and the end. Which of the following underlying data structures would be the MOST suitable to achieve this with optimal time complexity?
Binary Search Tree
Doubly Linked List
Singly Linked List
Circular Buffer
What is a significant disadvantage of using arrays for storing and processing extremely large datasets, particularly in the context of limited memory resources?
Arrays are not suitable for storing structured data, such as key-value pairs.
Arrays have slow access times for individual elements.
Arrays require contiguous blocks of memory, which can be difficult to allocate for massive datasets.
Arrays do not support dynamic resizing, making it challenging to handle growing datasets.
Radix Sort operates by:
Distributing elements into buckets based on individual digits or characters.
Building a binary tree and performing an in-order traversal.
Comparing elements and swapping them based on their values.
Recursively dividing the array and sorting subarrays.
What is the time complexity of Bucket Sort in the average case, assuming uniformly distributed data and a fixed number of buckets?
O(n)
O(n log n)
O(log n)
O(n^2)
You need to sort a massive dataset of social media posts by timestamp. The timestamps are represented as long integers. Which sorting approach is likely the MOST efficient?
Bucket Sort with buckets representing time intervals (e.g., hours, days)
Radix Sort using a base that aligns with the structure of the timestamps
External Merge Sort, as timestamps are naturally comparable
Any of the above would be equally efficient for this scenario
Which of the following array operations has an average-case time complexity that differs from its worst-case time complexity?
Accessing an element at a given index.
Searching for a specific value in a sorted array.
Inserting an element at the beginning of a dynamic array (implemented with reallocation).
Deleting an element from the end of an array.
In the context of external sorting, what does the term 'run' typically refer to?
The number of disk I/O operations performed.
A single pass through the entire dataset.
The process of merging two sorted subarrays.
A sequence of sorted elements that can be held in memory.
In the context of amortized analysis, what is the purpose of the potential function?
To analyze the space complexity of an algorithm.
To optimize the performance of individual array operations.
To calculate the average runtime of a single operation over a sequence of operations.
To determine the maximum possible runtime of a single operation in the worst-case scenario.