External Merge Sort is particularly well-suited for scenarios where:
The elements are already nearly sorted.
Real-time sorting is required.
The data is stored on a slow, disk-based storage device.
The dataset is small and fits entirely in memory.
Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the missing number.
Sort the array and find the missing element.
Use a hash table to store the presence of each number.
Use the XOR operation to find the missing number.
Calculate the sum of all numbers from 0 to n and subtract the sum of the array elements.
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.
When is Bucket Sort LEAST likely to be an efficient sorting algorithm?
The data is heavily skewed towards a few buckets.
The data is uniformly distributed.
The dataset is very large and sparse.
The elements are integers within a known range.
Given an array of n integers, find three elements in the array such that the sum is closest to a given target number. Return the sum of the three integers.
Sort the array and use two pointers to find pairs of elements with a sum close to the target minus the current element.
Use dynamic programming to store the closest sum for all subarrays of size three.
Use three nested loops to iterate through all possible triplets.
Given an array of integers, find the kth largest element in the array.
Use a max-heap to store all the elements and extract the kth largest element.
Sort the array and return the element at the kth position from the end.
Use a min-heap of size k to store the k largest elements encountered so far.
Use quickselect, a selection algorithm with an average time complexity of O(n).
Which of the following factors significantly influences the choice of sorting algorithm for large datasets?
Available memory and storage space
All of the above
Stability of the sorting algorithm (whether it maintains relative order of equal elements)
Data distribution (uniform, sorted, reverse sorted, etc.)
Given an unsorted array of integers, find the length of the longest consecutive sequence.
Sort the array and iterate through it to find the longest consecutive sequence.
Use dynamic programming to store the length of the longest consecutive sequence ending at each index.
Use a hash table to store the elements of the array and their visited status.
Use a sliding window approach to find the longest consecutive sequence.
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?
Linear Search
Bubble Sort
Selection Sort
Binary Search
In the context of amortized analysis, what is the purpose of the potential function?
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.
To analyze the space complexity of an algorithm.
To optimize the performance of individual array operations.