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7.4 Recursive call to function.mp4课程教案、知识点、字幕

大家好,我是云南大学信息学院丁海燕老师

欢迎走进C语言程序设计课堂

今天我们讲解函数的递归调用

C语言允许函数的递归调用

在调用一个函数的过程中又出现直接或间接地调用该函数本身

称为函数的递归调用

例如

z=f(y),表示在执行f函数的过程中又要调用f函数

这是直接调用本函数

如果在在执行f1函数的过程中要调用f2函数

而在调用f2函数过程中又要调用f1函数

则是间接调用本函数

如图所示

这两种都会调用都是无终止的自身调用

显然程序中不应出现这种无终止的自身调用

而只应出现有限次数的、有终止的递归调用

这可以用if语句来控制

只有在某一条件成立时才继续执行递归调用

否则就不再继续

下面用一个通俗的例子来理解递归的概念

因此可以用一个函数表示上述关系

下图表示求第5个学生年龄的过程

求解可分为两个阶段

第1阶段是“回溯”

即将第n个学生的年龄表示为第(n-1)个学生年龄的函数

而第(n-1)个学生的年龄仍然不知道

还要“回溯”到第(n-2)个学生的年龄……直到第1个学生的年龄

此时,age(1)已知,不必再向前推了

然后开始第2阶段,采用“递推”方法

从第1个学生的已知年龄推算出第2个学生的年龄(12岁)

从第2个学生的年龄推算出第3个学生的年龄(14岁)

一直到第5个学生的年龄(18岁)为止

也就是说,一个递归的问题可以分为“回溯”和“递推“两个阶段

要经历若干步才能求出最后的值

显然,如果要求递归过程不是无限制进行下去

必须具有一个结束递归过程的条件

例如,age(1)=10,就是使递归结束的条件

用一个主函数调用age函数,求得第5个学生的年龄

程序如下

声明函数age

输出第5个学生的年龄

c是用作存放函数的返回值的变量

如果n等于1,年龄为10

否则年龄是前一个学生的年龄加2

程序运行结果为18岁

main函数中实际上只有一个语句

整个问题的求解全靠一个age(5)函数调用来解决

函数调用过程如图所示

age函数共被调用5次,即age(5), age(4), age(3), age(2), age(1)

其中age(5)是main函数调用的,其余4次是在age函数中调用的

即递归调用4次

在某一次调用age函数时并不是立即得age(n)的值

而是一次又一次地进行递归调用,到age(1)时才有确定的值

然后再递推出age(2), age(3), age(4), age(5)

n=1时,执行c=10; 即不再递归调用age函数了,递归调用结束

下面来看例题7.7

主函数如下

56

00:09:55,800 --> 00:09:58,260

程序运行,输入10,输出10!=3628800

若编译系统为int型数据分配4个字节

能表示的最大数为2147483647

如果结果超出int型数据的最大值,会发生溢出

可将f,y和fac函数定义为float 或double型

调用递归函数fac(5)的过程如图所示

请注意每次调用fac函数后,其返回值f返回到哪里

应返回到调用fac函数处

例如当n=2时,执行f=fac(1)*2

再调用fac(1),返回值为1

这个1就取代f=fac(1)*2中的fac(1), 从而f=1*2=2

其余类似,递归终止条件为n=0或n=1

好了同学们,函数的递归调用我们就学到这,下节课再见

C Programming课程列表:

Chapter 1 Introduction

-1.1 The development and characteristics of C language

--1.The development and characteristics of C language .mp4

--1.1 Self test questions

-1.2 A simple C Language program

--1.2 A simple C Language program.mp4

--Discussion unit

--【Source program】 Example 1.1 output a line of text Hello, world! "

--【Source program】 Example 1.2 program composed of multiple functions, find the larger of two integers

--1.2 Self test questions

-1.3 Program, Programming Language and C Program Running Steps

--1.3 Program, Programming Language and C Program Running Steps.mp4

--Discussion unit

--Running steps of C source program in CodeBlocks

--1.3 Self test questions

-Course references

-chapter 1 Self-Test

Chapter 2 Algorithm

-2.1 The Concept and Description of Algorithms

--2.1 The Concept and Description of Algorithms.mp4

--Discussion unit

--2.1 Self test questions

-2.2 Examples of Simple Algorithms, Computational Thinking and Structured Programming

--2.2 Examples of Simple Algorithms, Computational Thinking and Structured Programming.mp4

--Discussion unit

--2.2 Self test questions

-Chapter 2 Self test questions

Chapter 3 Programming in C

-3.1 Simple Structure and Identifier of C Language Program

--3.1 Simple Structure and Identifier of C Language Program.mp4

--【Source program】 Example 3.1 input two integers and output the sum of two numbers.

--【Source program】 Example 3.2 input two integers and output the average value.

--【Source program】 Example 3.3 output the value of the character variable.

--3.1 Self test questions

-3.2 Constants, Variables and Assignments

--3.2 Constants, Variables and Assignments.mp4

--Discussion unit

--3.2 Self test questions

-3.3 Arithmetic, assignment, increment and decrement operators

--3.3 Arithmetic, assignment, increment and decrement operators.mp4

--3.3 Self test questions

-3.4 Conditions, commas, addresses, byte operators, and mixed operations among various numerical data

--3.4 Conditions, commas, addresses, byte operators, and mixed operations among various numerical data

--【Source program】 example of sizeof

--3.4 Self test questions

-3.5 Input and Output Examples and Character Input and Output

--3.5 Input and Output Examples and Character Input and Output.mp4

--【Source program】 Example. Find the root of quadratic equation of one variable.

--【Source program】 Example 1. Successively output three characters of BOY.

--【Source program】Example 2. Input 3 characters of BOY from the keyboard and output them to the screen

--3.5 Self test questions

-3.6 Formatted output printf function

--3.6 Formatted output printf function.mp4

--【Source program】 Example 3.4 output of integer data.

--【Source program】 Example 3.5 real data output.

--【Source program】 Example 3.6 character data output.

--【Source program】 Example 3.7 uses %s to output a string.

--3.6 Self test questions

-3.7 Formatted input scanf function

--3.7 Formatted input scanf function.mp4

--Discussion unit

--【Source program】 Example 3.8 Input and output integer data

--【Source program】Example 3.9 Input and output single precision and double precision real data.

--【Source program】Example 3.10 input and output character data.

--【Source program】Example 3.11 input and output string.

--3.7 Self test questions

-3.8 Basic Data Types of C Language

--3.8 Basic Data Types of C Language.mp4

--3.8 Self test questions

-Chapter 3 Self test questions

-Operator and expression self test questions

Chapter 4 Selection Structure

-4.1 Relational operators, logical operators, and if statements

--4.1 Relational operators, logical operators, and if statements.mp4

--Discussion unit

--【source example】Example 4.1 Find the root of the quadratic equation of one variable.

--【Source program】Example 4.2 Input two real numbers and output them from small to large.

--4.1 Self test questions

-4.2 Switch Statement

--4.2 Switch Statement .mp4

--Discussion unit

--【Source program】Example 4.3 uses switch statement to implement simple menu program

--【Source program】Example 4.4 converts centesimal score into the corresponding grade system score.

--4.2 Self test questions

-4.3 Examples of Selection Structural Programs

--4.3 Examples of Selection Structural Programs.mp4

--【Source program】 Example 4.5 determines whether a year is a leap year.

--【Source program】 Example 4.6 find the solution of quadratic equation of one variable.

--【Source program】Example 4.7 calculate the transportation cost for the user.

--4.3 Self test questions

-Chapter 4 Self test questions

Chapter 5 Loop Structure

-5.1 While and Do-While Statement

--5.1 While and Do…while statement.mp4

--Discussion unit

--【Source program】example 5.1 Use while statement to find 1 + 2 + 3 + +100

--【Source program】example 5.2 using do while statement to find 1 + 2 + 3 + +100

--5.1 Self test questions

-5.2 For Statement

--5.2 for statement.mp4

--【Source program】example 5.3 Use for loop to find 1 + 2 + 3 +100

--5.2 Self test questions

-5.3 Change the State of Loop Execution and Nested Loop

--5.3 Change the state of loop execution and nested loop .mp4

--【Source program】example 5.4 collecting charity donations

--【Source program】example 5.5 output a number between 100 and 200 that cannot be divided by 3.

--【Source program】multiplication table

--【Source program】example 5.6 Output the following 4*5 matrix.

--5.3 Self test questions

-5.4 Loop Structure Program example 1

--5.4 Loop structure program example 1.mp4

--【Source program】example 1

--【Source program】example 2

--【Source program】example 3

--【Source program】 Example 4

--5.4 Self test questions

-5.5 Loop Structure Program example 2

--5.5 Loop structure program example 2.mp4

--【Source program】example 5. Output the following figure.

--【Source program】example6. The problem of 100 chickens and 100 coins

--【Source program】example 7. Find the approximate value of PI

--5.5 Self test questions

-Chapter 5 Self test questions

Chapter 6 Batch Data Processing with Array

-6.1 Definition, Reference and Initialization of One-Dimensional Arrays

--6.1 Definition, Reference of One-Dimensional Arrays.mp4

--Discussion unit

--6.1 Self test questions

-6.2 One-Dimensional Array Programming

--6.2 One-Dimensional Array Programming.mp4

--【Source program】example 1. Fibonacci sequence

--【Source program】example 2. Find the maximum value and the minimum value.

--【Source program】example 3 exchanging array elements in reverse order.

--【Source program】example 4. Bubble sorting.

--6.2 Self test questions

-6.3 Definition, Reference and Initialization of Two-Dimensional Arrays

--6.3 Definition, Reference of Two-Dimensional Arrays.mp4

--6.3 Self test questions

-6.4 Two-Dimensional Array Programming

--6.4 Two-Dimensional Array Programming.mp4

--【Source program】example 1. Get the average score of each subject.

--【Source program】Example 2. The elements of row and column of a 2D array are interchanged

--6.4 Self test questions

-6.5 Definition, initialization and input and output of character arrays

--6.5 Definition, initialization and input and output of character arrays .mp4

--Discussion unit

--【Source program】Example 6.6 Output a known string.

--【Source program】Example 6.7 Output a diamond.

--【Source program】Example 6.10 Sorting of strings.

--6.5 Self test questions

-6.6 String Processing Function

--6.6 String Processing Function.mp4

--6.6 Self test questions

-6.7 Character Array Programming

--6.7 Character Array Programming.mp4

--6.7 Self test questions

-Chapter 6 Self test questions

Chapter 7 Modular Programming with Functions

-7.1 Function Concept and How to Define and Call Functions

--7.1 Function Concept and How to Define and Call Functions.mp4

--【Source program】Example 7.1

--7.1 Self test questions

-7.2 Data Transfer in Function Call, Call Procedure and Function Return Value

--7.2 Data Transfer in Function Call, Call Procedure and Function Return Value.mp4

--Discussion unit

--【Source program】Example 7.2

--7.2 Self test questions

-7.3 Declarations of called functions and nested calls to functions

--7.3 Declarations of called functions and nested calls to functions .mp4

--【Source program】Example 7.4 use a function to find the sum of t

--7.3 Self test questions

-7.4 Recursive call to function

--7.4 Recursive call to function.mp4

--【Source program】Example 7.6. How old is the fifth student?

--【Source program】Example 7.7 Use recursion method to find n!

--7.4 Self test questions

-7.5 Array as function parameter (1)

--7.5 Array as function parameter (1).mp4

--Discussion unit

--【Source program】Example 7.10

--7.5 Self test questions

-7.6 Array as function parameter (2)

--7.6 Array as function parameter (2).mp4

--【Source program】Selection sorting.

--【Source program】Example 7.13 find the maximum of a 3×4 matrix.

--7.6 Self test questions

-7.7 Local and global variables, internal and external functions

--7.7 Local and global variables, internal and external functions.mp4

--【Source program】Example 7.14

--7.7 Self test questions

-7.8 The Survival Period of Variables and the Storage Mode of Local Variables

--7.8 The Survival Period of Variables and the Storage Mode of Local Variables.mp4

--【Source program】Example 7.17

--7.8 Self test questions

-7.9 Storage Categories of Global Variables

--7.9 Storage Categories of Global Variables.mp4

--7.9 Self test questions

-Chapter 7 Self test questions

Chapter 8 Pointer

-8.1 Pointer Concept, Definition and Reference of Pointer Variables

--8.1 Pointer Concept, Definition and Reference of Pointer Variables.mp4

--【Source program】Example 8.1

--8.1 Self test questions

--Discussion unit

-8.2 Pointer variables as function parameters

--8.2 Pointer variables as function parameters.mp4

--Discussion unit

--【Source program】Example 8.3. Exchange two data with function call.

--8.2 Self test questions

-8.3 Pointer of array element, operation of pointer and reference of array element by pointer

--8.3 Pointer of array element, operation of pointer and reference of array element by pointer.mp4

--【Source program】Point to array elements with pointer variables.

--8.3 Self test questions

-8.4 Using Array Name as Function Parameter

--8.4 Using Array Name as Function Parameter.mp4

--【Source program】Store array elements in reverse order.

--8.4 Self test questions

-8.5 Reference to multidimensional arrays by pointers

--8.5 Reference to multidimensional arrays by pointers.mp4

--【Source program】Pointer variable pointing to one-dimensional array.

--8.5 Self test questions

-8.6 Referencing strings through pointers

--8.6 Referencing strings through pointers.mp4

--【Source program】Reference string by pointer.

--8.6 Self test questions

-8.7 Character pointer as function parameter

--8.7 Character pointer as function parameter.mp4

--【Source program】Character pointer as function parameter.

--8.7 Self test questions

-8.8 Pointer pointing to function

--8.8 Pointer pointing to function.mp4

--【Source program】Pointer variable pointing to the function.

--8.8 Self test questions

-8.9 Functions that return pointer values

--8.9 Functions that return pointer values.mp4

--【Source program】Intercept substring.

--8.9 Self test questions

-8.10 Pointer arrays and multiple pointers

--8.10 Pointer arrays and multiple pointers.mp4

--【Source program】Sorting of strings.

--8.10 Self test questions

-8.11 Dynamic memory allocation and pointer variables pointing to it

--8.11 Dynamic memory allocation and pointer variables pointing to it.mp4

--Discussion unit

--【Source program】Dynamic memory allocation.

--8.11 Self test questions

-Chapter 8 Self test questions

Chapter 9 Structure

-9.1 Define and use structural variables

--9.1 Define and use structural variables.mp4

--【Source program】Structure variable

--9.1 Self test questions

-9.2 Using structure arrays

--9.2 Using structure arrays.mp4

--Discussion unit

--【Source program】Structure array

--9.2 Self test questions

-9.3 Structure pointer

--9.3 Structure pointer.mp4

--【Source program】Structure pointer

--9.3 Self test questions

-Chapter 9 Self test questions

CodeBlocks Baidu online disk download

-CodeBlocks Baidu online disk download address

Final Exam

-Final Exam

--final exam

7.4 Recursive call to function.mp4笔记与讨论

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