DAY11 C Language Study: Recursion, Macros, Preprocessing, Hanoi Tower, Fibonacci, and More

C Language Study: Recursion, Macros, Preprocessing, Hanoi Tower, Fibonacci, and More

1. Function Recursion

What is Recursion?

Recursion refers to a function calling itself.

Essentially, recursion is another form of looping, but achieved through function calls instead of iteration.

✔ Advantages

• Clear and concise logic
• Ideal for solving backtracking, tree-structured, and mathematically inductive problems
  (e.g., Hanoi Tower, Fibonacci)

❗ Two rules must be satisfied

1. There must be a termination condition
   Otherwise it will recurse infinitely → stack overflow (Segmentation fault)

2. Avoid overly deep recursion levels
   Recursion consumes stack memory.

---

2. String Printing and strlen()

Before diving into recursion, let’s review string processing:

void show_str(char a[])
{
    int len = strlen(a); // Actual length (not counting '\0')
    for(int i = 0; i < len; i++)
    {
        putchar(a[i]);
    }
    printf("\nstrlen %lu\n", strlen(a));
}

Notes

• sizeof(str) returns the array capacity, e.g. char str[100] → 100 bytes
• strlen(str) returns the string length, e.g. "hello" → 5

This is a crucial distinction between:

✔ character arrays
✔ C-style strings

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3. Leap Year Determination Function

Leap year rules:

• Divisible by 4 but not by 100
• OR divisible by 400

int isLeapYear(int year)
{
    return ((year % 4 == 0 && year % 100 != 0) || year % 400 == 0);
}

Print leap years between 1900 and 2024:

for(int i = 1900; i < 2025; i++)
{
    if(isLeapYear(i))
        printf("year is %d\n", i);
}

---

4. Classic Recursion Applications

4.1 Factorial Calculation

int fun(int n)
{
    if(n == 1) return 1;
    return n * fun(n - 1);
}

Perfect example of a mathematically inductive recursive structure.

---

4.2 The Tower of Hanoi Problem

Problem description:
Given three rods A, B, C and n disks, move all disks from A to C following the rules:

• Only one disk can be moved at a time
• No disk may be placed on top of a smaller disk

void haonuota(int n, char src, char tmp, char dst)
{
    if (n == 1)
    {
        printf("%c -> %c\n", src, dst);
    }
    else
    {
        haonuota(n - 1, src, dst, tmp);
        printf("%c -> %c\n", src, dst);
        haonuota(n - 1, tmp, src, dst);
    }
}

Recursive logic:

1. Move n-1 disks from src → tmp
2. Move the largest disk from src → dst
3. Move n-1 disks from tmp → dst

---

4.3 Fibonacci Sequence

Recursive version:

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

⚠ Very inefficient (exponential complexity).

✔ Recommended: Loop-based Fibonacci (much faster)

int fib_loop(int n)
{
    if (n == 1 || n == 2)
        return 1;

    int a = 1, b = 1, c = 0;

    for(int i = 3; i <= n; i++)
    {
        c = a + b;
        a = b;
        b = c;
    }
    return c;
}

---

5. Macro Definitions (Macros)

Macros operate during the preprocessing stage, not runtime.

Characteristics:

• Simple text substitution
• No type checking
• No function call overhead

Examples:

#define PI 3.14
#define GETMAX(x,y) ((x) > (y) ? (x) : (y))
#define M 50
#define N (M + M)

Macro best practices

Wrap all parameters in parentheses to avoid precedence issues:

#define GETMAX(x,y) ((x) > (y) ? (x) : (y))

---

5.1 Multi-line Macros

#define PRINT(a,b,c) do{ \
    printf("%d\n", a);   \
    printf("%d\n", b);   \
    printf("%d\n", c);   \
}while(0)

---

6. C Language Preprocessing

Compilation stages:

1. Preprocessing
   Handle #include, #define, macro expansion
2. Compilation
   Convert to assembly
3. Assembly
   Produce .o object files
4. Linking
   Generate final executable (a.out or custom name)

---

7. Header Files

#include <...> → search system directories (e.g., /usr/include)
#include "..." → search current directory first, then system directories

Header files commonly contain:

• Macro definitions (#define)
• typedef alias definitions
• Function declarations
• extern variable declarations

Preventing multiple inclusion

#ifndef _FUNC_H_
#define _FUNC_H_

extern int add(int a, int b);

#endif

---

8. Conditional Compilation

Useful for platform-dependent code or debugging.

#if
#elif
#else
#endif

Check whether a macro exists:

#ifdef DEBUG
#endif

#ifndef DEBUG
#endif

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