poj3181 Dollar Dayz (DP+大数)

Dollar Dayz

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Submit Status Practice POJ 3181

Appoint description: System Crawler (2016-05-27)

Description

Farmer John goes to Dollar Days at The Cow Store and discovers an unlimited number of tools on sale. During his first visit, the tools are selling variously for $1, $2, and $3. Farmer John has exactly $5 to spend. He can buy 5 tools at $1 each or 1 tool at $3 and an additional 1 tool at $2. Of course, there are other combinations for a total of 5 different ways FJ can spend all his money on tools. Here they are:

        1 @ US$3 + 1 @ US$2 
 1 @ US$3 + 2 @ US$1 
 1 @ US$2 + 3 @ US$1 
 2 @ US$2 + 1 @ US$1 
 5 @ US$1

Write a program than will compute the number of ways FJ can spend N dollars (1 <= N <= 1000) at The Cow Store for tools on sale with a cost of $1..$K (1 <= K <= 100).

Input

A single line with two space-separated integers: N and K.

Output

A single line with a single integer that is the number of unique ways FJ can spend his money.

Sample Input

5 3

Sample Output

5

一个DP题 不过由于数太大了。。。所以我选用的java...

其中dp数组存贮组成当前数的个数

import java.math.*;
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sca =new Scanner(System.in);
		int k,n;
		while(sca.hasNext())
		{
			n=sca.nextInt();
			k=sca.nextInt();
			BigInteger dp []=new BigInteger[1005];
			for(int i=0;i<1005;i++)
				dp[i]=BigInteger.ZERO;
			dp[0]=BigInteger.ONE;
			for(int i=1;i<=k;i++){
				for(int j=0;j<=n;j++){
					if(j>=i&&dp[j-i]!=BigInteger.ZERO){
						dp[j]=dp[j].add(dp[j-i]);
					}
				}
			}
			System.out.println(dp[n]);
		}
		
	}
}