使用Java编写牛顿均差型插值多项式的构造，要求可以输入数表，可以输入使用几次插值计算，可以输入计算的自变量f的值。要完整代码

在Java中，我们可以创建一个牛顿插值多项式（也称为拉格朗日插值）的类，该类允许用户输入数表、插值次数以及计算的自变量值。下面是一个简单的示例代码，它实现了这个功能：

import java.util.Scanner;

public class NewtonInterpolator {
    private double[][] coefficients; // 存储多项式的系数

    public NewtonInterpolator(double[] xValues, double[] yValues) {
        if (xValues.length != yValues.length + 1) {
            throw new IllegalArgumentException("Number of x and y values must be the same or differ by one.");
        }
        coefficients = new double[yValues.length][];
        for (int i = 0; i < yValues.length; i++) {
            coefficients[i] = new double[i + 1];
            for (int j = 0; j <= i; j++) {
                coefficients[i][j] = yValues[i - j] / fact(i - j);
                for (int k = 0; k < j; k++) {
                    coefficients[i][j] *= xValues[i - k];
                }
            }
        }
    }

    private double fact(int n) {
        if (n == 0 || n == 1) return 1;
        else return n * fact(n - 1);
    }

    public double interpolate(double f) {
        int degree = coefficients[coefficients.length - 1].length - 1;
        double result = coefficients[0][degree];
        for (int i = 1; i <= degree; i++) {
            result += coefficients[i][degree] * Math.pow(f, degree - i);
        }
        return result;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.println("Enter number of data points (including end points): ");
        int numPoints = scanner.nextInt();
        double[] xValues = new double[numPoints];
        double[] yValues = new double[numPoints];

        System.out.println("Enter x values: ");
        for (int i = 0; i < numPoints; i++) {
            xValues[i] = scanner.nextDouble();
        }

        System.out.println("Enter y values: ");
        for (int i = 0; i < numPoints; i++) {
            yValues[i] = scanner.nextDouble();
        }

        System.out.println("Enter interpolation order: ");
        int interpolationOrder = scanner.nextInt();

        NewtonInterpolator interpolator = new NewtonInterpolator(xValues, yValues);
        System.out.print("Enter a value for f to interpolate: ");
        double f = scanner.nextDouble();
        double interpolatedValue = interpolator.interpolate(f);

        System.out.printf("Interpolated value at %f is %f\n", f, interpolatedValue);
        scanner.close();
    }
}

在这个例子中，`NewtonInterpolator`类接受两个数组作为输入，然后根据给定的插值次数计算并存储牛顿插值多项式的系数。`interpolate`方法用于实际的插值计算。

请注意，这只是一个基本实现，实际应用中可能会需要更多的错误处理和优化。运行此程序时，用户会被提示输入数据点的数量、坐标值以及插值的次数。然后用户可以输入一个自变量`f`，程序会返回对应的数据点处的插值结果。