Are you interested in reducing the time complexity or the space complexity ? The average time complexity can be reduced O(n + d^2), where n is the length of the longer string and d is the edit distance. If you are only interested in the edit distance and not interested in reconstructing the edit sequence, … 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
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
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
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
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
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
Firstly, bear in mind that a language is not the same as the implementation of a language. The call stack size in Python varies by implementation. The limit of 1000 applies to CPython but not necessarily all implementations. Is it reasonable to use recursion to process balanced trees? Recursion is reasonable for balanced trees. As … Read more
Under the assumption numbers less than one are not allowed and there are no duplicates, there is a simple summation identity for this – the sum of numbers from 1 to m in increments of 1 is (m * (m + 1)) / 2. You can then sum the array and use this identity. You … Read more