One of the major factors is that quicksort has better locality of reference — the next thing to be accessed is usually close in memory to the thing you just looked at. By contrast, heapsort jumps around significantly more. Since things that are close together will likely be cached together, quicksort tends to be faster. … Read more
Under the appropriate assumptions on the hash function being used, we can say that hash table lookups take expected O(1) time (assuming you’re using a standard hashing scheme like linear probing or chained hashing). This means that on average, the amount of work that a hash table does to perform a lookup is at most … Read more
map, set, multimap, and multiset These are implemented using a red-black tree, a type of balanced binary search tree. They have the following asymptotic run times: Insertion: O(log n) Lookup: O(log n) Deletion: O(log n) hash_map, hash_set, hash_multimap, and hash_multiset These are implemented using hash tables. They have the following runtimes: Insertion: O(1) expected, O(n) … Read more
You’re going to want to read up on Order of complexity. http://en.wikipedia.org/wiki/Big_O_notation In short, O(1) means that it takes a constant time, like 14 nanoseconds, or three minutes no matter the amount of data in the set. O(n) means it takes an amount of time linear with the size of the set, so a set … 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
To directly answer your question: Your sorting algorithm is technically not O(n) but rather O(n + max), since you need to create an array of size max, which takes O(max) time. This isn’t a problem; in fact, it’s a special case of a well-known sorting algorithm that breaks the Ω(n log n) barrier. So what … Read more
The complexity of a naive recursive fibonacci is indeed 2ⁿ. T(n) = T(n-1) + T(n-2) = T(n-2) + T(n-3) + T(n-3) + T(n-4) = = T(n-3) + T(n-4) + T(n-4) + T(n-5) + T(n-4) + T(n-5) + T(n-5) + T(n-6) = … In each step you call T twice, thus will provide eventual asymptotic barrier … Read more
Worst case should be O(n) (copying all n-1 elements to new array). A linked list would be O(1) for a single deletion. For those interested I’ve made this lazily-crafted benchmark. (Please don’t run on Windows XP/Vista). As you can see from this though, it looks fairly constant (i.e. O(1)), so who knows what they’re doing … Read more
It’s O(n), also check out: http://wiki.python.org/moin/TimeComplexity This page documents the time-complexity (aka “Big O” or “Big Oh”) of various operations in current CPython. Other Python implementations (or older or still-under development versions of CPython) may have slightly different performance characteristics. However, it is generally safe to assume that they are not slower by more than … Read more
Finally! Following up leads in sdcvvc’s answer, we have it: the O(n log n) algorithm for the problem! It is simple too, after you understand it. Those who guessed FFT were right. The problem: we are given a binary string S of length n, and we want to find three evenly spaced 1s in it. … Read more