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 analyze the space complexity of an algorithm.
To calculate the average runtime of a single operation over a sequence of operations.
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?
Any of the above would be equally efficient for this scenario
Radix Sort using a base that aligns with the structure of the timestamps
Bucket Sort with buckets representing time intervals (e.g., hours, days)
External Merge Sort, as timestamps are naturally comparable
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.
Sort the array and calculate the area for each subarray.
Iterate through the array and maintain a stack to track potential rectangle heights.
Use a divide and conquer approach to find the minimum element in each subarray.
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?
Binary Search
Selection Sort
Bubble Sort
Linear Search
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.
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).
Sort the array and return the element at the kth position from the end.
Which of the following factors significantly influences the choice of sorting algorithm for large datasets?
Available memory and storage space
All of the above
Data distribution (uniform, sorted, reverse sorted, etc.)
Stability of the sorting algorithm (whether it maintains relative order of equal elements)
Which sorting algorithm is the MOST suitable for sorting a massive dataset that cannot fit entirely in RAM?
External Merge Sort
Merge Sort
Quick Sort
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.
Calculate the sum of all numbers from 0 to n and subtract the sum of the array elements.
Sort the array and find the missing element.
Use the XOR operation to find the missing number.
In a real-world application, you are using a dynamic array to store a constantly growing dataset. You notice that the performance degrades significantly during the array resizing operations. What strategy could you employ to mitigate this performance bottleneck?
Optimize the algorithm that processes the data to reduce the overall number of insertions into the array.
Implement a custom memory allocator that reserves larger chunks of contiguous memory in advance.
Switch to a linked list data structure, sacrificing some element access speed for better insertion performance.
Increase the frequency of resizing, reallocating the array with smaller size increments.
Given an array of n positive integers and a positive integer s, find the minimal length of a contiguous subarray of which the sum ≥ s. If there isn't one, return 0 instead.
Use binary search to find the minimal length.
Use two nested loops to iterate through all possible subarrays.
Use a sliding window approach to find the minimal length subarray.
Use dynamic programming to store the minimal length for all subarrays ending at each index.