霍纳规则解决多项式的求值问题

Posted 2020-10-26 legoxz

霍纳规则用来简化朴素多项式的求值。它将一元n次多项式的求值问题转化为n个一次式。

霍纳规则是采用最少的乘法运算策略，求多项式A(x) = a_nxⁿ+ a_n-1x^n-1+...+ a₁x + a₀在x0处的值，该规则是A(x₀)=(...((a_nx⁰+ a_n-1)x₀+...+ a₁)x₀+ a₀)

 1 #include<stdio.h>
 2 
 3 int horner(int a[], int x, int n);
 4  
 5 int main()
 6 {
 7     int n;
 8     scanf("%d", &n);
 9     
10     int a[n + 1];
11     int x;
12     for(int i = 0; i <= n; i++){
13         scanf("%d", &a[i]);
14     }
15     
16     scanf("%d", &x);
17     printf("%d", horner(a, x, n));
18     
19     return 0;
20 } 
21 
22 int horner(int a[], int x, int n)
23 {
24     int i = n;
25     int result = x;
26     while(i > 0){
27         result = a[i] + result * x;
28         i--;
29     }
30     
31     return result;
32 }