hdu 1398Square Coins（dp或者母函数）

最新推荐文章于 2019-03-18 20:48:45 发布

原创最新推荐文章于 2019-03-18 20:48:45 发布 · 353 阅读

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本文介绍了一种算法，用于计算使用SquareCoins这种特殊货币的所有可能支付组合数量。SquareCoins的特点在于其价值为平方数，从1到289不等。通过动态规划的方法，文章给出了解决方案并附带了完整的C++实现代码。

Square Coins

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 10752 Accepted Submission(s): 7338

Problem Description

People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (=17^2), i.e., 1-credit coins, 4-credit coins, 9-credit coins, ..., and 289-credit coins, are available in Silverland.
There are four combinations of coins to pay ten credits:

ten 1-credit coins,
one 4-credit coin and six 1-credit coins,
two 4-credit coins and two 1-credit coins, and
one 9-credit coin and one 1-credit coin.

Your mission is to count the number of ways to pay a given amount using coins of Silverland.

Input

The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300.

Output

For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output.

Sample Input

Sample Output

Source

Asia 1999, Kyoto (Japan)

Recommend

Ignatius.L

i表示有几种可能性 dp数组是把每种可能性累加 j表示变化规律

#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
int dp[500];
int main() 
{
	int n,m,i,k,j;
	while(cin>>k&&k)
	{
		memset(dp,0,sizeof(dp));
		dp[0]=1;
		n=(int)sqrt(k*1.0);
		for(i=1;i<=n;i++)
		{
			for(j=i*i;j<=k;j++)
			{
				dp[j]+=dp[j-i*i];
			}
		}
		cout<<dp[k]<<endl;
	}
	return 0;
}