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;

}