2013
12-09

# Square Coins

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.

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.

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.

2
10
30
0

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;
}

1. Good task for the group. Hold it up for every yeara??s winner. This is a excellent oppotunity for a lot more enhancement. Indeed, obtaining far better and much better is constantly the crucial. Just like my pal suggests on the truth about ab muscles, he just keeps obtaining much better.

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