import?java.util.Scanner;

public?class?Lagrange?{
	
	static?int?flag?=?0;
	
	public?static?float?lagrange（float?x0[]float?y0[]int?n?float?x）?{
		int?ij;
		float?p[]?=?new?float[100];
		float?y?=?0;
		for（i=0;i			p[i]?=?y0[i];
			for（j=0;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?ij;
		float?p[]?=?new?float[100];
		
		for（i=1;i			p[0]?=?y0[i];
			for（j=0;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（“-------------------請選擇插值方法---------------------“）;
	????????System.out.println（“--------------------1、拉格朗日-----------------------“）;
	????????System.out.println（“--------------------2、牛頓插值-----------------------“）;
	????????System.out.println（“--------------------退出請按0-------------------------“）;
	????????System.out.println（“-----------------------------------------------------“）;
	????????flag=as.nextInt（）;
	????????if（flag?==?0）?{
	????????	flag1=false;
	????????	System.out.println（“您已退出程序！歡迎下次使用?！埃?
	????????}
	????????if（flag?==?1）{
	????????	int?n?=?1;
	????????	float?x?=?0;
	????????	System.out.println（“請輸入n:“）;
	????????	n?=?as.nextInt（）;
	????????	System.out.println（“請輸入對應數組x0:“）;
	????????	//System.out.println（n）;
	????????	float?x0[]?=?new?float[n];
	????????	float?y0[]?=?new?float[n];
	????????	for（int?i=0;i	????????		x0[i]?=?as.nextFloat（）;
	????????	}
	????????	System.out.println（“請輸入對應數組y0:“）;
	????????	for（int?i=0;i	????????		y0[i]?=?as.nextFloat（）;
	????????	}
	????????	System.out.println（“請輸入值x:“）;
	????????	x?=?as.nextFloat（）;
	????????	System.out.println（“多項式解為：“+lagrange（x0y0nx））;
	????????}
	????????if（flag?==?2）{
	????????	int?i?n?=?0;
	????????	float?x?=?0b;
	????????	System.out.println（“請輸入n:“）;
	????????	n?=?as.nextInt（）;
	????????	System.out.println（“請輸入對應數組x0:“）;
	????????	//System.out.println（n）;
	????????	float?x0[]?=?new?float[n];
	????????	float?y0[]?=?new?float[n];
	????????	for（i=0;i	????????		x0[i]?=?as.nextFloat（）;
	????????	}
	????????	System.out.println（“請輸入對應數組y0:“）;
	????????	for（i=0;i	????????		y0[i]?=?as.nextFloat（）;
	????????	}
	????????	System.out.println（“請輸入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（“多項式解為：“+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
	????