What is the time complexity of Bucket Sort in the average case, assuming uniformly distributed data and a fixed number of buckets?
O(log n)
O(n log n)
O(n)
O(n^2)
Imagine you have a sorted array, and you want to find the index of the first element that is greater than a given target value. Which algorithm would provide the most efficient solution?
Bubble Sort
Selection Sort
Linear Search
Binary Search
What is a significant disadvantage of using arrays for storing and processing extremely large datasets, particularly in the context of limited memory resources?
Arrays have slow access times for individual elements.
Arrays are not suitable for storing structured data, such as key-value pairs.
Arrays do not support dynamic resizing, making it challenging to handle growing datasets.
Arrays require contiguous blocks of memory, which can be difficult to allocate for massive datasets.
Which of the following array operations has an average-case time complexity that differs from its worst-case time complexity?
Deleting an element from the end of an array.
Inserting an element at the beginning of a dynamic array (implemented with reallocation).
Accessing an element at a given index.
Searching for a specific value in a sorted array.
When is Bucket Sort LEAST likely to be an efficient sorting algorithm?
The dataset is very large and sparse.
The elements are integers within a known range.
The data is uniformly distributed.
The data is heavily skewed towards a few buckets.
Given an unsorted array of integers, find the length of the longest consecutive sequence.
Use dynamic programming to store the length of the longest consecutive sequence ending at each index.
Sort the array and iterate through it to find the longest consecutive sequence.
Use a sliding window approach to find the longest consecutive sequence.
Use a hash table to store the elements of the array and their visited status.
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.
You are given an array of integers and a target sum. Find all unique quadruplets in the array that sum up to the target sum.
Use four nested loops to iterate through all possible combinations of four elements.
Sort the array and use two pointers to find pairs of elements that sum up to a specific value.
Use a hash table to store the sum of all pairs of elements.
Use a backtracking algorithm to explore all possible combinations of elements.
In the context of amortized analysis, what is the purpose of the potential function?
To determine the maximum possible runtime of a single operation in the worst-case scenario.
To optimize the performance of individual array operations.
To calculate the average runtime of a single operation over a sequence of operations.
To analyze the space complexity of an algorithm.
Given an array of integers, find the subarray with the maximum sum in linear time. The subarray must contain at least one element.
Dynamic programming approach by building a table to store the maximum sum ending at each index.
Kadane's Algorithm, which iterates through the array, keeping track of the maximum sum ending at each index.
Divide and conquer approach by finding the maximum subarray in the left half, right half, and the one crossing the midpoint.
Brute force approach by checking all possible subarrays.