Nan da algorithm design and Analysis course Review notes (3) l3-recursion

First, the recursive equation

According to the idea of divide and conquer, a recursive complexity can be written as a recursive equation.

First, the solution of the recursive equation--guess and then prove

This method is also referred to as the surrogate method, the steps are as follows:

1, the form of the Guess solution

2. Mathematical inductive method proves correct

Example:

We assume that there is a recursive formula like this:

We guess that the solution is T (n) =o (NLGN), and then the recursive substitution is

Special note: The result of our replacement must be strictly in line with conjecture, the above example if the last to arrive at T (N) <=cnlgn+1, we guessed wrong, we need to choose a new guessing formula.

Second, recursive regression equation--Recursive tree solution

The trouble with this method is that it is generally done using the surrogate method and the following master theorem

Example

For recursive equations:

Its recursive tree is as follows:

Third, Master theorem

If A>=1 and b>1, assume that there is a recursive function, the recursive type is as follows:

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Nan da algorithm design and Analysis course Review notes (3) l3-recursion