递归与迭代算法（一）

#include <stdio.h>

/************************************************************************/
/*                                                                      */
/* 自然数的阶乘 (factorial of natural number)                            */
/* fact(n) = 1                 if n = 0                                 */
/* fact(n) = n * fact(n - 1)   if n > 0                                 */
/*                                                                      */
/************************************************************************/

int factorial(int n) /* recursive */
{
    if (n == 0)
        return 1;
    else
        return n * factorial(n - 1);
}

int factorial_iter(int n) /* iterative */
{
    int total = 1;
    while (n > 0)
    {
        total *= n;
        n--;
    }
    return total;
}


/************************************************************************/
/*                                                                      */
/* 斐波那契数 (Fibonacci)                                                */
/* fib(n)  = 0                         if n = 0                         */
/* fib(n)  = 1                         if n = 1                         */
/* fib(n)  = fib(n - 1) + fib(n - 2)   if n >= 2                        */
/*                                                                      */
/************************************************************************/

int fib(int n) /* recursive */
{
    if (n == 0) return 0;
    else if (n == 1) return 1;
    else return fib(n - 1) + fib(n - 2);
}


/************************************************************************/
/*                                                                      */
/* 最大公约数 (Greatest common divisor)                                  */
/* gcd(x, y)  = x                         if y = 0                      */
/* gcd(x, y)  = gcd(y, remainder(x, y))   if x >= y and y > 0           */
/*                                                                      */
/* input: integer x, integer y such that x >= y and y >= 0              */
/*                                                                      */
/************************************************************************/

int gcd(int x, int y) /* recursive */
{
    if (y == 0) return x;
    else return gcd(y, x % y);
}

int gcd_iter(int x, int y)  /* iterative */
{
    int remainder = 0;
    while (y > 0)
    {
        remainder = x % y;
        x = y;
        y = remainder;
    }
    return x;
}


/************************************************************************/
/*                                                                      */
/* 汉诺塔 (Towers of Hanoi)                                              */
/*                                                                      */
/************************************************************************/
#define move(x, n, z) printf("%i. Move disk %i from %c to %c\n", ++c, n, x, z);
int c = 0;
void hanoi(int n, char x, char y, char z)
{
    if (n == 1) 
    {
        move(x, 1, z);
    }
    else
    {
        hanoi(n - 1, x, z, y);
        move(x, n, z);
        hanoi(n - 1, y, x, z);
    }
}


/************************************************************************/
/*                                                                      */
/* 二分查找 (Binary Search)                                              */
/*                                                                      */
/************************************************************************/

int bsearch_iter(int *data, int toFind, int start, int end)
{
    int mid = start + (end - start)/2;
    if (start > end)
        return -1;
    else if (data[mid] == toFind)
        return mid;
    else if (data[mid] > toFind)
        return bsearch_iter(data, toFind, start, mid-1);
    else
        return bsearch_iter(data, toFind, mid+1, end);
}


void main()
{
    printf("factorial(%d) = %d\n", 5, factorial(5));
    printf("factorial_iter(%d) = %d\n", 5, factorial_iter(5));
    printf("fibonacci(%d) = %d\n", 10, fib(10));
    printf("gcd(%d, %d) = %d\n", 35, 49, gcd(35, 49));
    printf("gcd_iter(%d, %d) = %d\n", 35, 49, gcd_iter(35, 49));

    hanoi(3, 'x', 'y', 'z');
    int x[] = { 3, 6, 7, 9, 12, 43, 225};
    printf("binary_search: %d's index is %d\n", 12, bsearch_iter(x, 12, 0, 6));
    printf("binary_search: %d's index is %d\n", 13, bsearch_iter(x, 13, 0, 6));
}