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.
Use dynamic programming to store the closest sum for all subarrays of size three.
Sort the array and use two pointers to find pairs of elements with a sum close to the target minus the current element.
Use three nested loops to iterate through all possible triplets.
Use a hash table to store the sum of all pairs of elements.
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)
External Merge Sort is particularly well-suited for scenarios where:
The data is stored on a slow, disk-based storage device.
The dataset is small and fits entirely in memory.
Real-time sorting is required.
The elements are already nearly sorted.
You are given an unsorted array of integers where each element represents the height of a bar in a histogram. Find the largest rectangular area in the histogram.
Use dynamic programming to store the maximum area ending at each index.
Iterate through the array and maintain a stack to track potential rectangle heights.
Sort the array and calculate the area for each subarray.
Use a divide and conquer approach to find the minimum element in each subarray.
You need to perform matrix multiplication on two large matrices, A and B, where A is of size M x N and B is of size N x P. You have multiple machines available for distributed computing. Which approach would likely yield the BEST performance improvement?
Divide matrix A into row blocks and distribute each block with a copy of B to different machines.
Divide both matrices A and B into smaller, equally sized submatrices and distribute the computation of these submatrices across the machines.
Performing the matrix multiplication sequentially on a single machine without any distribution.
Divide matrix B into column blocks and distribute each block with a copy of A to different machines.
Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, 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.
Use the XOR operation to find the missing number.
What is a significant disadvantage of using arrays for storing and processing extremely large datasets, particularly in the context of limited memory resources?
Arrays do not support dynamic resizing, making it challenging to handle growing datasets.
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.
In the context of amortized analysis, what is the purpose of the potential function?
To analyze the space complexity of an algorithm.
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 optimize the performance of individual array operations.
Given an unsorted array of integers, find the length of the longest consecutive sequence.
Use a hash table to store the elements of the array and their visited status.
Use dynamic programming to store the length of the longest consecutive sequence ending at each index.
Use a sliding window approach to find the longest consecutive sequence.
Sort the array and iterate through it to find the longest consecutive sequence.
Which data structure would be the MOST suitable for implementing a sparse matrix efficiently, where most elements are zero, to save memory and potentially improve computation speed?
Multidimensional Array
Linked List
Hash Table
Binary Tree