POJ 3181 Dollar Dayz （有点像背包的dp -- JAVA大数）

题意：

给你k种硬币，价值分别为1，2，3，，k，要求问你凑出n 元钱的数量？

思路：

令dp[i][j] 表示利用前i 种硬币来凑出 j 元钱的数量。

那么边界 dp[1][i] 都是1

那么dp[i][j+o*i] += dp[i-1][j]

j表示用前i-1 种硬币凑出来的价值，o 是利用第i 种硬币的数量。

但是n 能到1000，种类能到100，那么这个数量会爆long long。 

得用大数。

吐槽：

一看只是加法的大数，就直接拿string 模拟了，可能大数写的太渣，超时了。

直接用JAVA写就好了。

import java.math.BigInteger;import java.util.*;public class Main {public static void main(String[] args){Scanner cin = new Scanner(System.in);int n = cin.nextInt();int k = cin.nextInt();BigInteger dp[][] = new BigInteger[107][1008];for (int i = 1; i < 107; ++i){for (int j = 0; j < 1007; ++j){if (i == 1)dp[i][j] = BigInteger.ONE;else dp[i][j] = BigInteger.ZERO;}}for (int i = 2; i <= k; ++i){        for (int j = 0; j <= n; ++j){            for (int o = 0; j+o*i <= n; ++o){                dp[i][j+o*i] = dp[i][j+o*i].add(dp[i-1][j]);            }        }    }System.out.println(dp[k][n]);cin.close();}}

Dollar Dayz

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 6965 Accepted: 2600

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

Source

USACO 2006 January Silver

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