Complexity Data Structure Assignment Help
Complexity Data Structure
The complexity of an algorithm is the function which gives the running time and/or space in terms of the input size.
- An upper bound on the running time for any input of given size
- Assume all inputs of a given size are equally likely
- The lower bound on the running time
Algorithm Complexity is rough estimation of the number of steps performed by given computation depending on the size of the input data
- Measured through asymptotic notation
- O(g) where g is a function of the input data size
- Linear Complexity O(n) : All elements are processed once (or constant number of times)
- Quadratic Complexity O(n2) : Each of the elements is processed n times
Time And Memory Complexity
- Complexity can be expressed as formula on multiple variables, e.g.
- Algorithm filling a matrix of size n * m with natural numbers 1, 2, … will run in O(n*m)
- DFS traversal of graph with n vertices and m edges will run in O(n + m)
- Memory consumption should also be considered, for example:
- Running time O(n), memory requirement O(n2)
- n = 50 000 Ĺ• OutOfMemoryException
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