ural 1013. K-based Numbers. Version 3（动态规划）

1013. K-based Numbers. Version 3

Let’s consider K-based numbers, containing exactly N digits. We define a number to be valid if its K-based notation doesn’t contain two successive zeros. For example:

• 1010230 is a valid 7-digit number;
• 1000198 is not a valid number;
• 0001235 is not a 7-digit number, it is a 4-digit number.

Given two numbers N and K, you are to calculate an amount of valid K based numbers, containing N digits.

You may assume that 2 ≤ K ≤ 10; N ≥ 2; N + K ≤ 1800.

Input

The numbers N and K in decimal notation separated by the line break.

Output

The result in decimal notation.

Sample

input	output
2 10	90

题意：

思路：和1009、1012一样；这三个题只是更改了数据范围；1012和本题用到了高精度运算；

import java.util.Scanner;
import java.util.regex.Pattern;
import java.lang.Math;
import java.math.BigInteger;



public class t1 {
    public static void main(String[] args) {
        Scanner ks=new Scanner(System.in);
        BigInteger a,b,c,d,e;
        a=new BigInteger("0");
        b=new BigInteger("0");
        c=new BigInteger("1");
        d=new BigInteger("0");
        e=new BigInteger("0");
        int n,k;
        n=ks.nextInt();
        k=ks.nextInt();
        int i;
        for(i=1;i<k;i++)
        {
            d=d.add(c);//调出进制数减1；
        }
        b=b.add(d);
        for(i=2;i<=n;i++)
        {
            e=b.multiply(c);//保存变量b的值；
            b=b.add(a);//更新b的值；
            b=b.multiply(d);//更新b的值
            a=e.multiply(c);//跟新a的值；
        }
        b=a.add(b);
        System.out.println(b.toString());
    }
}