Algorithm complexity analysis method and algorithm overview

algorithm Definition : A description of the solution steps that solve a particular problem.

algorithm features : poor, deterministic, feasibility, input, output

design requirements for algorithms : correctness, readability, robustness, high efficiency and low storage requirements

algorithm Measurement Method : Post-mortem method (unscientific), pre-analysis and estimation method

The asymptotic growth of the function: given two functions f (n) and g (n), if there is an integer n, so that for all n>n,f (n) is always greater than g (n), then we say that f (n) is growing nearly faster than G (n).

So, can come to the conclusion: Determine an algorithm is not good, you can compare the algorithm's key execution times function of the asymptotic growth, the basic can be analyzed: an algorithm, with the increase of N, it will be better than the other algorithm, or more and more worse than an algorithm.

Steps to derive the large O-order:

• Replace all addition constants in run time with constant 1

• Only the highest order is kept in the modified run Count function

• If the highest order exists and is not 1, the constant multiplied by the item is removed

The result is the Big O-order

With this step, we can get the algorithm to run the number of expressions, and quickly get its time complexity, that is, the large O-order.

It is easy to deduce the large O-order, but the expression of how to get the number of runs is a mathematical foundation.

Common time complexity ordering:

O (1) <o (LOGN) <o (n) <o (NLONGN) <o (n^2) <o (n^3) <o (2^n) <o (n!) <o (N^n)

Algorithm complexity analysis method and algorithm overview