首页 > ACM题库 > HDU-杭电 > HDU 1398 Square Coins-背包问题-[解题报告] C++
2013
12-09

HDU 1398 Square Coins-背包问题-[解题报告] C++

Square Coins

问题描述 :

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.

输入:

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.

输出:

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.

样例输入:

2
10
30
0

样例输出:

1
4
27

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

const int N=320;

int money[]={0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289};
int c1[N],c2[N];

int main(){

    //freopen("input.txt","r",stdin);

    int n;
    while(~scanf("%d",&n) && n){
        for(int i=0;i<=n;i++){
            c1[i]=0;
            c2[i]=0;
        }
        c1[0]=1;
        for(int i=1;i<=17;i++){
            for(int j=0;j<=n;j++)
                for(int k=0;j+k*money[i]<=n;k++)
                    c2[j+k*money[i]]+=c1[j];
            for(int j=0;j<=n;j++){
                c1[j]=c2[j];
                c2[j]=0;
            }
        }
        printf("%d\n",c1[n]);
    }
    return 0;
}

解题报告转自:http://www.cnblogs.com/jackge/archive/2013/04/18/3028177.html


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  2. 约瑟夫也用说这么长……很成熟的一个问题了,分治的方法解起来o(n)就可以了,有兴趣可以看看具体数学的第一章,关于约瑟夫问题推导出了一系列的结论,很漂亮