UVA10198 Counting大数+递推

Posted 2021-05-19 海岛Blog

Gustavo knows how to count, but he is now learning how write numbers. As he is a very good student, he already learned 1, 2, 3 and 4. But he didn’t realize yet that 4 is different than 1, so he thinks that 4 is another way to write 1. Besides that, he is having fun with a little game he created himself: he make numbers (with those four digits) and sum their values. For instance:
132 = 1 + 3 + 2 = 6
112314 = 1 + 1 + 2 + 3 + 1 + 1 = 9 (remember that Gustavo thinks that 4 = 1)
    After making a lot of numbers in this way, Gustavo now wants to know how much numbers he can create such that their sum is a number n. For instance, for n = 2 he noticed that he can make 5 numbers: 11, 14, 41, 44 and 2 (he knows how to count them up, but he doesn’t know how to write five). However, he can’t figure it out for n greater than 2. So, he asked you to help him.
Input
Input will consist on an arbitrary number of sets. Each set will consist on an integer n such that 1 ≤ n ≤ 1000. You must read until you reach the end of file.
Output
For each number read, you must output another number (on a line alone) stating how much numbers Gustavo can make such that the sum of their digits is equal to the given number.
Sample Input
2
3
Sample Output
5
13

问题链接：UVA10198 Counting
问题简述：（略）
问题分析：大数递推问题，用Java语言来解决。
程序说明：（略）
参考链接：（略）
题记：（略）

AC的Java语言程序如下：

/* UVA10198 Counting */

import java.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String args[]){
		Scanner input = new Scanner(System.in);

		int N = 1000;
		BigInteger f[] = new BigInteger[N + 1];
		Arrays.fill(f, BigInteger.ZERO);

		f[0] = BigInteger.valueOf(1);
		f[1] = BigInteger.valueOf(2);
		f[2] = BigInteger.valueOf(5);
		f[3] = BigInteger.valueOf(13);

		for(int i = 4; i <= N; i++)
	        	f[i] = f[i].add(f[i-1]).add(f[i-1]).add(f[i-2]).add(f[i-3]);
	    
	    	int n;
	    	while(input.hasNextInt()){
	    		n = input.nextInt();
	    		System.out.println(f[n]);
		}
	}
}