import java.util.Scanner;
public class Lagrange {
static int flag = 0;
public static float lagrange(float x0[],float y0[],int n, float x) {
int i,j;
float p[] = new float[100];
float y = 0;
for(i=0;i<n;i++){
p[i] = y0[i];
for(j=0;j<n;j++) {
if(i!=j) p[i] *= (x-x0[j])/(x0[i]-x0[j]);
}
y += p[i];
}
return y;
}
public static void newton(float x0[],float y0[],int n) {
int i,j;
float p[] = new float[100];
for(i=1;i<n;i++){
p[0] = y0[i];
for(j=0;j<n;j++) {
p[j+1] = (p[j] - y0[j])/(x0[i] - x0[j]);
y0[i] = p[i];
}
}
}
public static void main(String args[]){
boolean flag1 = true;
while(flag1){
Scanner as = new Scanner(System.in);
System.out.println("-----------------------------------------------------");
System.out.println("-------------------插值法求解近似值-------------------");
System.out.println("-------------------请选择插值方法---------------------");
System.out.println("--------------------1、拉格朗日-----------------------");
System.out.println("--------------------2、牛顿插值-----------------------");
System.out.println("--------------------退出请按0-------------------------");
System.out.println("-----------------------------------------------------");
flag=as.nextInt();
if(flag == 0) {
flag1=false;
System.out.println("您已退出程序！欢迎下次使用。");
}
if(flag == 1){
int n = 1;
float x = 0;
System.out.println("请输入n:");
n = as.nextInt();
System.out.println("请输入对应数组x0:");
//System.out.println(n);
float x0[] = new float[n];
float y0[] = new float[n];
for(int i=0;i<n;i++){
x0[i] = as.nextFloat();
}
System.out.println("请输入对应数组y0:");
for(int i=0;i<n;i++){
y0[i] = as.nextFloat();
}
System.out.println("请输入值x:");
x = as.nextFloat();
System.out.println("多项式解为："+lagrange(x0,y0,n,x));
}
if(flag == 2){
int i, n = 0;
float x = 0,b;
System.out.println("请输入n:");
n = as.nextInt();
System.out.println("请输入对应数组x0:");
//System.out.println(n);
float x0[] = new float[n];
float y0[] = new float[n];
for(i=0;i<n;i++){
x0[i] = as.nextFloat();
}
System.out.println("请输入对应数组y0:");
for(i=0;i<n;i++){
y0[i] = as.nextFloat();
}
System.out.println("请输入x的值");
x = as.nextFloat();
newton(x0, y0, n);
b = y0[n-1];
for(i=n-2;i>=0;i--){
b = b*(x - x0[i]) + y0[i];
}
System.out.println("多项式解为："+b);
//5
//x0=0.4 0.55 0.65 0.8 0.9
//y0=0.41075 0.5781 0.69675 0.88811 1.02652
//x=0.596 x=0.895
}
}
}
}
//n=4
//x0={0.5616 0.5628 0.5640 0.5652}
//y0={0.8274 0.8265 0.8257 0.8249}
//x=0.5635
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