UVA 11137 Ingenuous Cubrency(dp + 完全背包)

Problem I: Ingenuous Cubrency

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

10 21779999

Output for sample input

2322440022018293

题意：有1 ^ 3, 2 ^ 3, 3 ^ 3.....21 ^3 这几种块。求去组合和给定n块有多少种方式

思路：类似组硬币问题， 完全背包，状态转移方程d[j] += d[j - coin[i]]。

代码：

#include <stdio.h>#include <string.h>int coin[21], n, i, j;long long d[10005];int main() {for (i = 0; i < 21; i ++)coin[i] = (i + 1) * (i + 1) * (i + 1);d[0] = 1;for (i = 0; i < 21; i ++)for (j = coin[i]; j < 10000; j ++)d[j] += d[j - coin[i]];while (~scanf("%d", &n)) {printf("%lld\n", d[n]);}return 0;}