Using linear algebra, there exist algorithms that achieve better complexity than the naive O(n3). Solvay Strassen algorithm achieves a complexity of O(n2.807) by reducing the number of multiplications required for each 2×2 sub-matrix from 8 to 7. The fastest known matrix multiplication algorithm is Coppersmith-Winograd algorithm with a complexity of O(n2.3737). Unless the matrix is … Read more
It’s written in the documentation for Dictionary… The Dictionary generic class provides a mapping from a set of keys to a set of values. Each addition to the dictionary consists of a value and its associated key. Retrieving a value by using its key is very fast, close to O(1), because the Dictionary class is … Read more
It will have to go through all the elements in the array to do this. Array is a unique data structure where you have to specify a size when you initialize it. Order would be the source array’s size or in Big O terms its O(length). Infact this happens internally in an ArrayList. ArrayList wraps … Read more
The trick is to figure out a way to categorize the possible solutions and come up with a linear-time constant-space solution for each. Consider the three ranges X = (0,2/3), Y = [2/3,1], Z = (1,2). At most one value can come from Z (if two values came from Z, then the sum would exceed … Read more
Yes, in your case*1 string concatenation requires all characters to be copied, this is a O(N+M) operation (where N and M are the sizes of the input strings). M appends of the same word will trend to O(M^2) time therefor. You can avoid this quadratic behaviour by using str.join(): word = ”.join(list_of_words) which only takes … Read more
list The Average Case assumes parameters generated uniformly at random. Internally, a list is represented as an array; the largest costs come from growing beyond the current allocation size (because everything must move), or from inserting or deleting somewhere near the beginning (because everything after that must move). If you need to add/remove at both … Read more
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
Why the c++’s implemented string::substr() doesn’t use the KMP algorithm (and doesn’t run in O(N + M)) and runs in O(N * M)? I assume you mean find(), rather than substr() which doesn’t need to search and should run in linear time (and only because it has to copy the result into a new string). … Read more
::operator delete[] is documented on cplusplus.com (which is sometimes frowned upon) as: operator delete[] can be called explicitly as a regular function, but in C++, delete[] is an operator with a very specific behavior: An expression with the delete[] operator, first calls the appropriate destructors for each element in the array (if these are of … Read more
Algorithms with running time O(2^N) are often recursive algorithms that solve a problem of size N by recursively solving two smaller problems of size N-1. This program, for instance prints out all the moves necessary to solve the famous “Towers of Hanoi” problem for N disks in pseudo-code void solve_hanoi(int N, string from_peg, string to_peg, … Read more