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We often see the concept of function in Mathematics . But you know C Functions in language ？
Wikipedia definition of function ： Subroutines
In computer science , Subroutines （ English ：Subroutine, procedure, function, routine, method,
subprogram, callable unit）, It's a piece of code in a large program , A group of one or more statement blocks become . It's responsible for a particular task , And compared to other code , With relative independence .
Generally, there will be input parameters and return values , Provide encapsulation of the process and hiding of details . These codes are usually integrated into software Parts library .

2.c Classification of functions in language

1. Library function
2. Custom function

2.1. Library function

2.1.1. How to learn to find library functions

Why are there library functions ？
1. We know that in our study C In language programming , Always can't wait to know the result after a code is written , I want to print this result on our screen to see . At this time, we will frequently use a function ： Print the information to the screen in a certain format （printf）.
2. In the process of programming, we will frequently copy some strings （strcpy）.
3. In programming, we also calculate , Always calculate n Of k Such an operation to the power （pow）.
Like the basic functions we described above , They are not business code . In our development process, every programmer may use , In order to support portability and improve program efficiency , therefore C A series of similar library functions are provided in the basic library of the language , It is convenient for programmers to develop software .

Library function details we can see the website ：（ These websites are related to MSDN be similar ）

Reference - C++ Reference (cplusplus.com)

cppreference.com（ English version ）

cppreference.com（ Chinese translation ）

There are many header files in the first website , Click the start file to see the library functions contained in each header file , Open a library function , We can see from the detailed introduction of this function , Or we can search the function directly .

A brief summary ,C The library functions commonly used in the language are ：
IO function
String manipulation functions
Character manipulation functions
Memory manipulation function
Time / Date function
Mathematical functions
Other library functions

2.1.2. Some library function demonstrations （ Reference document , Learn several library functions ）

1.strlen function

The introduction on the website ：

Code example ：

notes ：

1.size_t It means unsigned integer （unsigned int type ）, The return value in the introduction is size_t type , So we use size_t Acceptance is the most standard way of writing .

2.%u Print unsigned integers .

2.strcpy function

MSDN Introduction on ：

Code example ：

3.memset function

MSDN Introduction on ：

Code example ：

notes ：memst Medium arr It's an array name , Address representing the first element of the array .

2.2. Custom function

2.2.1. Custom function introduction

If library functions can do everything , What do programmers do ？
So more importantly Custom function .
Custom functions are the same as library functions , Yes Function name , return type and Function parameter .
But the difference is that these are all designed by ourselves . This gives programmers a lot of room to play .

Basic composition ：

ret_type fun_name(para1, * )
{
statement;// Statement item
}
ret_type Return type
fun_name Function name
para1 Function parameter
notes ：
1. Functions can have no parameters and return values , If you don't need a return value , The return type is void Instead of .
2. Function design should pursue high cohesion and low coupling （ Do your own thing , Try not to have anything to do with other functions ）
3. It's not easy to have too many function parameters .
4. When designing functions , Try to release resources by those who apply （ Later on ）

2.2.2. Function application examples （※）

1. Write a function to find the maximum value of two integers .

Code ：

2. Write a function to exchange the contents of two shaping variables .

Error code ：

Debugging of error code ：

Correct code ：（ With the help of a pointer ）

notes ：

1. From here we can see that , When executing a function , The system will recreate the address for the formal parameter （ Instead of the actual parameter address when calling the function ）, The system just assigns the actual parameter value in the function call to the corresponding formal parameter . In the above error code, only x and y The values of the two formal parameters are exchanged , Because it's not the same address , So it doesn't matter a and b Value .

In a nutshell ： When the function is called , The actual parameter is passed to the formal parameter , A formal parameter is actually a temporary copy of an argument , Therefore, the modification of formal parameters will not affect the arguments .

3. The parameters of the function

3.1. The actual parameter （ Actual parameters ）

The parameters that are actually passed to the function , It's called the actual parameter .
The argument can be ： Constant 、 Variable 、 expression 、 function etc. .
Whatever the type of argument is , When you make a function call , They all have to have certain values , In order to pass these values to the parameter .

3.2. Formal parameters （ Shape parameter ）

Formal parameters refer to the variables in brackets after the function name , Because formal parameters are only instantiated when the function is called （ Allocate memory units ）, So it's called formal parameter .
Formal parameters are automatically destroyed when the function call is completed . So formal parameters are only valid in functions .

4. Function call

4.1. Value transfer call

The formal and actual parameters of a function occupy different memory blocks , Modification of a parameter does not affect the argument .

4.2. Address call

Address call is a way to call a function by passing the memory address of the created variable outside the function to the function parameter .
This parameter transfer method can establish a real relationship between the function and the variables outside the function , That is, you can directly operate inside the function
As a variable outside the function .

notes ：

1. Because the address of the first element of the array is actually passed when transmitting the array , Therefore, when using an array to pass, it is equivalent to an address call .

2. The function of address transfer can be realized by using global variables , But not recommended .

4.3. practice （※）

1. Write a function to determine whether a number is a prime .
2. Write a function to determine whether a year is a leap year .
3. Write a function , To realize binary search of an ordered array .
4. Write a function , Every time you call this function , Will be num The value of the increase 1.
5. With the help of functions ： If certain conditions are met （n=5） Output hehe, Otherwise output haha.

Exercises 1：

Exercises 2：

Exercises 3：

Error code ：

Error code run result ：

Correct code ：

Correct code run results ：

notes ： Array arr Pass to binary_search When , In fact, the message is arr Address of the first element of the array , When passing parameters to an array like this , The number of such elements must be calculated outside and then passed in .

Exercises 4：

Correct code 1：

Correct code 2：

Correct code 3：

Error code ：

Exercises 5：

notes ： Function , If you want the function to end early , By means of return Realization , Code above , Functions with return values use return Add the return value to realize , Having no return value , Just one return And then .

5. Nested calls and chained access to functions

5.1. Nested calls

notes ：

1. The calling relationship is ：main Function call three_line,three_line It calls new_line. Functions can be called to each other , Nested call .

2. Functions can be called nested , But you can't nest definitions . Here's the picture Is an example of a nested definition , It's wrong. . All functions must be at the same level .

5.2 Chained access

Take the return value of one function as the parameter of another function .

Knowledge point 1：

As shown in the figure above , The third sentence is a combination of the first two sentences , the strlen The return value of the function is printf The parameters of the function , This is chain access .

Knowledge point 2：

Code ：

Running results ：

notes : Here's the picture MSDN Yes printf Function introduction ,printf The return value of the function is the number of characters that the function prints on the screen （ If an error occurs during printing , Return a negative number ）

6. Function declaration and definition

6.1. Function declaration and definition

Function declaration ：
1. Tell the compiler that there is a function called , What are the parameters , What is the return type . But does it exist , Function declarations do not determine .
2. The declaration of a function usually precedes the use of the function . To satisfy the requirement of declaration before use .
3. The declaration of the function is usually placed in the header file .
Function definition ：
The definition of a function refers to the concrete implementation of a function , Explain the function realization .

Functions are defined directly before the function is used ：

Functions are declared before they are used , Then define after the function is used ：

notes ：

1. If function definition comes later , It needs to be stated before .

2. If function definition comes later , But it is not stated above , The system will report that the function is undefined , Because compiler processing is from front to back , When he saw add After the function , The compiler will wonder if it has seen add function , If you haven't seen , The compiler will issue a warning （add Function undefined ）. Therefore, it is generally recommended to put the function in the front .

6.2. Function code written in actual project

Generally in the project , You won't write code like that , It's a split . So let's create one .h The header file , Create another .c The source file ,.h and .c Together, the files are called a module （ In this case, it is called the addition module ）, We put the declaration of the function in .h In the header file , Put the definition of the function in .c In the source file , There will be three files ：.h Function declaration file ,.c Function definition file ,.c Function call file where the main function of . At this time in .c The file containing the main function of contains its own .h The header file can be used in this file （ Include your own in double quotation marks , The in the library is enclosed in angle brackets ）, As shown in the figure below .

The process ： A company doesn't write add The code needs to be written by a programmer , So programmers need to write add.c Document and add.h File and then encrypt the static library of the project where the two files are located （ The binary ）, then add.h The header file （ The header file is equivalent to the specification , Let the company know what the function parameters are , Know how to use this function ） And static library encryption add.lib Documents are sold to the company （ Can't sell add.c file , If you sell add.c file , Companies know the function implementation code , Programmers can't sell to other companies ）, Company import add.h Documents and declarations add.lib File with its own main function code can be achieved .

1. The code the programmer has to write ：

2. The programmer will the project （add.c and add.h file ） Compile into a static library （add.lib）, At this point, in the project folder Debug There will be a... In the folder add.lib file , This is the static library .

3. take .h and .lib Documents are sold to the company

4. The company opens the file where its main function is located , Import purchased .h file , And enter the command #pragma comment(lib,"add.lib") To import static libraries , At this point, the function declaration header file #include"add.h" You can use this function .

7. Function recursion

7.1. What is recursion

The programming skill of program calling itself is called recursion （ recursion）, Function calling itself is function recursion .
Recursion as an algorithm is widely used in programming languages . A procedure or function has the function of directly or indirectly calling itself in its definition or description A method for the , It usually transforms a large and complex problem into a smaller problem similar to the original problem to solve .
The recursion strategy only needs a few programs to describe the repeated calculation needed in the process of solving problems , Greatly reduces the amount of code in the program .
The main way to think about recursion is ： Turn the big thing into a small one

Simple recursive code （ It's recursive code , But it will die ）：

Running results ： Dead cycle （ The program in the figure crashed , So stop ）

Error reporting of procedures ：

notes ：stack overflow Stack overflow means stack overflow , Very common errors in recursive code .

7.2. Two necessary conditions for recursion （ practice ）（※）

1. There are restrictions , When this constraint is met , Recursion doesn't continue .
2. After each recursive call, it gets closer and closer to this constraint .
notes ： If the condition is not met, it will recurse wirelessly , Stack overflow occurs .

Exercise one ：

Receive an integer value （ Unsigned ）, Print each bit of it in order .
for example ：
Input ：1234 Output ：1 2 3 4

Code ：

Graphic interpretation ：

notes ：

1.%u Stands for unsigned integer .

2. If there is no if Statement restrictions , It will be the same as the one in front main equally , Infinite recursion , Last appearance Stack overflow （stackoverflow） The phenomenon of , Cause the program to crash .（ There is a foreign website called stackoverflow Equivalent to the programmer's knowledge , If you don't know, you can ask questions on it ）Stack Overflow - Where Developers Learn, Share, & Build Careers

Stack overflow ： Each function call will request a space in the stack area of memory , If wireless recursion goes on , Stack space will be used up , No space can be opened up , There will be stack overflow .

Exercise 2 ：

Writing functions does not allow the creation of temporary variables , Find the length of the string .（ It means to write a function to realize the function strlen Function functions ）

Code 1：（ In fact, this code creates count Temporary variable , Does not meet the requirements of the topic ）

Code 2：（ The code that conforms to the meaning of the question ）

Code 2 Graphic interpretation ：

notes ：

1. The array name is the address of the first element of the array .

2. In this function ,char The defined character type takes up one byte , So it's a pointer s++; If it's an integer , You need a pointer s+=4; If it is double, You need a pointer s+=8.

7.3. Recursion and iteration （ practice ）（※）

Exercise one ：

seek n The factorial .（ Don't think about spillovers ）

Iterative implementation code ：

Recursively implemented code ：

Exercise 2 ：

Please n Fibonacci Numbers .（ Don't think about spillovers ）
Fibonacci number ：1 1 2 3 5 8 13 21 34 55......

Iterative implementation code ：

Recursively implemented code ：

notes ： Here the recursive system repeats many calculations , Efficiency is very low , For example, below , Computation first 40 individual Fibonacci number of hours , The third Fibonacci number is calculated 39088169 Time .

8. Several classic topics of function recursion （ Independent research ）（※）

1. The hanotta problem
2. The problem of frog jumping on the steps

8.1. The hanotta problem

subject ：
It's said that in the ancient temple of India , There is one called the Hanoi Tower (Hanoi) The game of . The game is on a copper device , There are three rods ( Number A、B、C), stay A From the bottom up 、 Place in order from large to small 64 A gold plate ( Pictured 1). The goal of the game ： hold A All the gold plates on the pole are moved to C On the pole , And still keep the original order . Operating rules ： Only one plate can be moved at a time , And keep the big plate down all the time during the moving process , Small in , The plate can be placed during the operation A、B、C On any pole .

Code ：

#define _CRT_SECURE_NO_WARNINGS 1
#include<stdio.h>

void move(char pos1, char pos2)
{
	printf("%c->%c  ", pos1, pos2);
}

void Hanoi(int n, char pos1, char pos2, char pos3)
{
	if (n == 1)
	{
		move(pos1, pos3);
	}
	else
	{
		Hanoi(n - 1, pos1, pos3, pos2);
		move(pos1, pos3);
		Hanoi(n - 1, pos2, pos1, pos3);
	}

}

int main()
{
	int n = 0;
	printf(" Please enter the number of plates ：");
	scanf("%d", & n);
	Hanoi(n, 'A', 'B', 'C');
	return 0;
}

Running results ：

analysis ：

From this question we can see , In the case of the tower of Hanoi ：A The rod is the starting rod ,B The rod is a transfer rod ,C The pole is the target pole .

When A On 1 null ：A->C

When A On 2 null ：A->B A->C B->C

When A On 3 null ：A->C A->B C->B A->C B->A B->C A->C

It can be seen that all mobile ideas are ： When there is n(n $\geqslant$ 2) null , There are three steps , as follows ：

First step ： take n-1 A plate from the pole A Through bar C（ here C It's a transfer lever ） Move to lever B

The second step ： take A A plate on the moves to the pole C

The third step ： take n-1 A plate from the pole B（ here B Is the starting rod ） Through bar A（ here A For the transfer rod ） Move to lever C

8.2. The problem of frog jumping on the steps

subject ：
A frog can jump up at a time 1 Stepped steps , You can jump on it 2 level . Ask the frog to jump on one n How many jumps are there in the steps ？（ Different results are calculated according to different order ）.

Code ：

#define _CRT_SECURE_NO_WARNINGS 1
#include<stdio.h>

int fib(int n)
{
	if (n == 1)
		return 1;
	else if (n == 2)
		return 2;
	else
		return fib(n - 1) + fib(n - 2);

}

int main()
{
	int n = 0;
	printf(" Please enter the order ：");
	scanf("%d", &n);
	int s = fib(n);
	printf(" All in all %d Jump \n", s);
	return 0;
}

Running results ：

analysis ：

To put it another way , It's a number n, Let go 1 and 2 Formed by different arrangements . Due to the influence of arrangement order , For slightly larger n Come on , There are many kinds .

n=1, Only One Jump ,[1].
n=2, So there are two Jump ,[2],[1,1].
n=3, So there are 3、 ... and Jump ,[1,1,1],[1,2],[2,1].
n=4, So there are 5、 ... and Jump ,[1,1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,2].
n=5, So there are 8、 ... and Jump ,[1,1,1,1,1],[1,1,1,2],[1,1,2,1],[1,2,1,1],[2,1,1,1],[2,2,1],[2,1,2],[1,2,2].

We found that , When n Add... In turn 1 when , Its combinatorial number just constitutes a Fibonacci sequence （ That is, the size of a certain number , Equal to the sum of the two preceding numbers ）.

Depth analysis ：

hypothesis n A stair , Yes f(n) Seed walking method . Frogs can jump for the first time 1 A step or 2 A stair , If you jump one step, you'll be left with n-1 There are steps f(n-1) Seed walking method , jump 2 One step left n-2 There are steps f(n-2) Seed walking method .

Introduction ： go n There are... Steps in total f(n-1)+f(n-2) Seed walking method .

Add ：

For similar problems ： A frog can jump up at a time 1 Stepped steps , You can jump on it 2 level , You can jump on it 3 level . Ask the frog to jump on one n How many jumps are there in the steps ？

analysis ：

n=1, One Jump

n=2, two Jump

n=3, Four Jump

n=4, 7、 ... and Jump

We found that , Start with the fourth number , The latter number is the sum of the first three numbers

Code ：

#define _CRT_SECURE_NO_WARNINGS 1
#include<stdio.h>

int fib(int n)
{
	if (n == 1)
		return 1;
	else if (n == 2)
		return 2;
	else if (n == 3)
		return 4;
	else
		return fib(n - 1) + fib(n - 2) + fib(n - 3);

}

int main()
{
	int n = 0;
	printf(" Please enter the order ：");
	scanf("%d", &n);
	int s = fib(n);
	printf(" All in all %d Jump \n", s);
	return 0;
}

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