Horner规则

霍纳（Horner）规则是采用最少的乘法运算策略，求多项式 A(x) = a[n]x^n + a[n-1]x^(n-1) + ... + a[1]x^1 + a[0]x^0 在x处的值。
该规则为 A(x) = (...((a[n]x + a[n-1])x + ... + a[1])x + a[0])。利用霍纳规则，编写C语言程序对多项式进行求值。
解：
分别用迭代和递归两种方法来实现，解题代码分别如下：
<1> 迭代：
#include <stdio.h>
int horner(int *array, int n, int x)
{
    int result = array[n];
    while(n)
    {
        result = result * x + array[--n];
    }
    return result;
}
 
int main(void)
{
    int result = 0, 
        i = 0, 
        x = 0, 
        amount = 0;
    do
    {
        printf("Input the amount of coefficients(include zero.):");
        scanf("%d", &amount);
    } while (amount <= 0);
 
    int a[amount];
    printf("Input the cofficients:");
    for (i = 0; i < amount; ++i)
    {
        scanf("%d", &a[i]);
    }
 
    printf("Input the x:");
    scanf("%d", &x);
 
    result = horner(a, amount - 1, x);
    printf("The result is :%d", result);
    return 0;
}
 
<2> 递归：
#include <stdio.h>

int horner(int *array, int n, int x)
{
    if ( !n )
    {
        return *array;
    }
    return horner(array + 1, n - 1, x) * x + *array;
}
 
int main(void)
{
    int result = 0, 
        i = 0, 
        x = 0, 
        amount = 0;
    do
    {
        printf("Input the amount of coefficients(include zero.):");
        scanf("%d", &amount);
    } while (amount <= 0);
 
    int a[amount];
    printf("Input the cofficients(Like:x,y,z  or  x y z):");
    for (i = 0; i < amount; ++i)
    {
        scanf("%d", &a[i]);
    }
 
    printf("Input the x:");
    scanf("%d", &x);
 
    result = horner(a, amount - 1, x);
    printf("The result is :%d", result);
    return 0;
}
  
      