The speaker is wrong in this case. The actual cost is O(n * log(t)). Heapify is called only on the first t elements of the iterable. That’s O(t), but is insignificant if t is much smaller than n. Then all the remaining elements are added to this “little heap” via heappushpop, one at a time. … Read more
O(n) The size, isEmpty, get, set, iterator, and listIterator operations run in constant time. The add operation runs in amortized constant time, that is, adding n elements requires O(n) time. All of the other operations run in linear time (roughly speaking). The constant factor is low compared to that for the LinkedList implementation. http://download.oracle.com/javase/6/docs/api/java/util/ArrayList.html
Asymptotic complexity (which is what both big-O and big-Theta represent) completely ignores the constant factors involved – it’s only intended to give an indication of how running time will change as the size of the input gets larger. So it’s certainly possible that an Θ(n) algorithm can take longer than an Θ(n2) one for some … Read more
From the question itself, we can see that the problem of O(n) operations arises when querying the linked list. Therefore, we need an alternative data structure. We need to be able to update the items’ last access time from the HashMap without searching. We can keep two separate data structures. A HashMap with (Key,Pointer) pairs … Read more
Have you ever written an AI? Isn’t it annoying that you have to thread pruning information (e.g. maximum depth, the minimum cost of an adjacent branch, or other such information) through the tree traversal function? This means you have to write a new tree traversal every time you want to improve your AI. That’s dumb. … Read more
The purpose of the Big-O notation is to find what is the dominant factor in the asymptotic behavior of a function as the value tends towards the infinity. As we walk through the function domain, some factors become more important than others. Imagine f(n) = n^3+n^2. As n goes to infinity, n^2 becomes less and … Read more
Indexes in MongoDB are stored in a B-tree structure, where each index entry points to a specific location on-disk. Using a B-tree structure also means that a MongoDB index is stored in a sorted order, always traversed in-order, and is cheap for MongoDB to fetch a series of documents in a sorted order via indexes. … Read more
This seems to be a question of mislead, because I happened to read that book just now. This part of text in the book is a typo! Here is the context: =================================================================== Question: What is the running time of this code? 1 public String makeSentence(String[] words) { 2 StringBuffer sentence = new StringBuffer(); 3 for … Read more
From the source code of collections.py, we see that if we don’t specify a number of returned elements, most_common returns a sorted list of the counts. This is an O(n log n) algorithm. If we use most_common to return k > 1 elements, then we use heapq.nlargest. This is an O(k) + O((n – k) … Read more
If you want examples of Algorithms/Group of Statements with Time complexity as given in the question, here is a small list – O(1) time Accessing Array Index (int a = ARR[5];) Inserting a node in Linked List Pushing and Poping on Stack Insertion and Removal from Queue Finding out the parent or left/right child of … Read more