UVa 11137 Ingenuous Cubrency (DP)

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本文介绍了一种使用立方数值货币进行支付金额组合的算法。在Cubeland中，货币单位和实际硬币形状均为立方体，硬币面值从1到9261（21的三次方）。通过动态规划的方法计算不同面额组合支付特定金额的方式数量。

11137 - Ingenuous Cubrency

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2078

People in Cubeland use cubic coins. Not only the unit of currency is called acube but also the coins are shaped like cubes and their values are cubes. Coins with values of all cubic numbers up to 9261 (= 21³), i.e., coins with the denominations of 1, 8, 27, ..., up to 9261 cubes, are available in Cubeland.

Your task is to count the number of ways to pay a given amount using cubic coins of Cubeland. For example, there are 3 ways to pay 21 cubes: twenty one 1cube coins, or one 8 cube coin and thirteen 1 cube coins, or two 8 cube coin and five 1 cube coins.

Input consists of lines each containing an integer amount to be paid. You may assume that all the amounts are positive and less than 10000.

For each of the given amounts to be paid output one line containing a single integer representing the number of ways to pay the given amount using the coins available in Cubeland.

Sample input

Output for sample input

2
3
22
440022018293

可以化成一维来做：dp[i] += dp[i - a[j]];//不断往更大的数上叠加。

完整代码：

/*0.015s*/

#include <cstdio>
const int maxn = 10000;

long long dp[maxn];
int a[22];

int main()
{
	int i, j, n;
	for (i = 1; i <= 21; ++i)
		a[i] = i * i * i;
	for (i = 0; i <= maxn; ++i)
		dp[i] = 1;
	for (j = 2; j <= 21; ++j)
		for (i = a[j]; i <= maxn; ++i)
			dp[i] += dp[i - a[j]];
	while (~scanf("%d", &n))
		printf("%lld\n", dp[n]);
	return 0;
}