Relationship between Recursion and stack

 

Recursion and stack
Recursion is an important concept and a heavy programming method. To put it simply, if a function, process, or data structure definition applies itself (as one of the definition items ), this function, process, or data structure is called recursion. For example, a factorial function can be recursively defined as follows:
It must be noted that the recursive definition cannot be a "loop definition ". Therefore, any recursive definition must meet the following two conditions:
① The application of the defined item in the definition (that is, the appearance of the definition item) has a smaller "scale ";
② The definition of the defined item on the minimum "scale" is not recursive.
For example, in the preceding factorial function definition, the defined item n! Application in definition (n-1 )! Has a "scale" (I .e. N-1) smaller than the original (I .e. N ). At the same time, n! The definition on the minimum "scale" (that is, 0) is not recursive (defined directly by the natural number 1 ). These two conditions actually constitute the basic principle of recursive programming. In addition, the part that reflects condition ② is usually written at the beginning of the recursion process.
There are many actual recursive definitions. It is easy to write Recursive Algorithms for solving these problems. The recursive algorithm for calculating factorial functions is as follows:
　　Public static int NN (int I) {<br/> if (I = 0) {<br/> return 1; <br/>} else <br/> return I * NN (I-1); <br/>}
Recursive call is triggered by running the recursive process. For example, the recursive call in the execution of F (3) -- the return process is 3-5 (.

F3 │ Bytes R Branch	① Success ┌ ┈ ┘ Zookeeper	F2 → Success Bytes T Branch	② Success ┌ ┈ ┘ Zookeeper	F1 → Success Bytes T Branch	③ Random ┌ ┈ ┘ Zookeeper	F0 → Success │ │
R1 Branch │ Bytes	Zookeeper └ ┈ ┐ 6 ⑥ └	T1 Branch Bytes Zookeeper	Zookeeper └ ┈ ┐ 2 ⑤ success	T1 Branch Bytes Zookeeper	← ┐ ┈ └ ┈ ┐ 1 ④ bytes	│ Bytes Limit limit 1

Figure 3-5 (a) f (3) execute recursive call-return order

Top →

3 R

Top →

2 R 3 R

Top →

1 R 2 R 3 R

Top →

2 R 3 R

Top →

3 R

Top →

Before calling F2

After F2 is called

After F1 is called

After f0 is called

After F1 is returned

After F2 is returned

Top →

Return After F3

Figure 3-5 (B) status changes of the corresponding Stack

Recursive call-return control is essentially different from non-recursive process control. It can also be implemented by a work stack. For the above process f, the return position R should be set to the internal and Outer Return statements. To distinguish the first level of recursion returned, you can save the called parameters together when the returned position is pushed to the stack. Figure 3-5 (B) shows the State Change Process of the stack corresponding to (.

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