Imagine you were looking up the details of buses as they arrived at a bus stop, based on their bus number (or whatever identifier you use). It’s somewhat reasonable to think that if you’ve just seen a number 36 bus, you’re less likely to see another one imminently than to see one of the other buses that stops there. … Read more
Check this out. Exponential is worse than polynomial. O(n^2) falls into the quadratic category, which is a type of polynomial (the special case of the exponent being equal to 2) and better than exponential. Exponential is much worse than polynomial. Look at how the functions grow k^1000 is exceptionally huge unless k is smaller than something like 1.1. Like, … Read more
See Quicksort on wikipedia: Typically, quicksort is significantly faster in practice than other Θ(nlogn) algorithms, because its inner loop can be efficiently implemented on most architectures, and in most real-world data, it is possible to make design choices which minimize the probability of requiring quadratic time. Note that the very low memory requirement is a big … Read more
Kruskal is O(E log E); your derivation is right. You could also say O(E log V) because E <= V * V, so log(E) <= 2 log(V) (I don’t know why I remember that, other than that I think a prof put that on an exam at one point…)
For each node u in an undirected graph, let twodegree[u] be the sum of the degrees of u’s neighbors. Show how to compute the entire array of twodegree[.] values in linear time, given a graph in adjacency list format. This is the solution can someone explain what degree[u] does in this case and how twodegree[u] … Read more
I hope this is helpful to anybody having trouble understanding computational time complexity for Breadth First Search a.k.a BFS. Time complexity is as follows: I have tried to simplify the code and complexity computation but still if you have any questions let me know.
A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input array to be sorted. Some sorting algorithms are stable by nature like Insertion sort, Merge Sort, Bubble Sort, etc. And some sorting algorithms are not, like Heap Sort, Quick … Read more
If you have an array of size n and you want to build a heap from all items at once, Floyd’s algorithm can do it with O(n) complexity. See Building a heap. This corresponds to the std::priority_queue constructors that accept a container parameter. If you have an empty priority queue to which you want to add n items, one at a time, … Read more
Your sum can be rewritten as and the first group is O(N) while the other is O(E).
Dijkstra’s shortest path algorithm is O(ElogV) where: V is the number of vertices E is the total number of edges Your analysis is correct, but your symbols have different meanings! You say the algorithm is O(VElogV) where: V is the number of vertices E is the maximum number of edges attached to a single node. Let’s rename your E to N. So one analysis says O(ElogV) and another … Read more