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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.

Time Complexity

  1. Worst-Case
    • An upper bound on the running time for any input of given size
  2. Average-Case
    • Assume all inputs of a given size are equally likely
  3. Best-Case
    • 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
    • Examples:
  • 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
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Typical Complexities

Complexity Data Structure Assignment Help

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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