当前课程知识点:C Programming > Chapter 7 Modular Programming with Functions > 7.4 Recursive call to function > 7.4 Recursive call to function.mp4
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
-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
--【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
--Running steps of C source program in CodeBlocks
--1.3 Self test questions
-chapter 1 Self-Test
-2.1 The Concept and Description of Algorithms
--2.1 The Concept and Description of Algorithms.mp4
--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
--2.2 Self test questions
-Chapter 2 Self test questions
-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
--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
--【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
-4.1 Relational operators, logical operators, and if statements
--4.1 Relational operators, logical operators, and if statements.mp4
--【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
--【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
-5.1 While and Do-While Statement
--5.1 While and Do…while statement.mp4
--【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
--【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
--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
-6.1 Definition, Reference and Initialization of One-Dimensional Arrays
--6.1 Definition, Reference of One-Dimensional Arrays.mp4
--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
--【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
-7.1 Function Concept and How to Define and Call Functions
--7.1 Function Concept and How to Define and Call Functions.mp4
--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
--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
--【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
-8.1 Pointer Concept, Definition and Reference of Pointer Variables
--8.1 Pointer Concept, Definition and Reference of Pointer Variables.mp4
--8.1 Self test questions
-8.2 Pointer variables as function parameters
--8.2 Pointer variables as function parameters.mp4
--【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
--【Source program】Dynamic memory allocation.
--8.11 Self test questions
-Chapter 8 Self test questions
-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
--【Source program】Structure array
--9.2 Self test questions
-9.3 Structure pointer
--【Source program】Structure pointer
--9.3 Self test questions
-Chapter 9 Self test questions
-CodeBlocks Baidu online disk download address
-Final Exam
--final exam