hdu1028Ignatius and the Princess III(最基础的母函数模板)
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母函数也就是多项式乘积,某个数n,求能由1~n-1有多少种组成方法。
经典例题:
Ignatius and the Princess III
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12723 Accepted Submission(s): 8994
"The second problem is, given an positive integer N, we define an equation like this:
N=a[1]+a[2]+a[3]+...+a[m];
a[i]>0,1<=m<=N;
My question is how many different equations you can find for a given N.
For example, assume N is 4, we can find:
4 = 4;
4 = 3 + 1;
4 = 2 + 2;
4 = 2 + 1 + 1;
4 = 1 + 1 + 1 + 1;
so the result is 5 when N is 4. Note that "4 = 3 + 1" and "4 = 1 + 3" is the same in this problem. Now, you do it!"
41020
542627
以四为例可以看做多项式乘积即:(1+x+x^2+x^3+x^4)*(1+x^2+x^4)*(1+x^3)
只需按照数学方法来实现编程即可。
代码:
#include<stdio.h>
int main()
{
int n;
while(~scanf("%d",&n))
{
int i,j,k;
int c1[150],c2[150];
for(i=0;i<=n;i++)
{
c1[i]=1;//代表第j项的系数
c2[i]=0;
}//把全部的系数都初始化
for(i=2;i<=n;i++)//i代表的是第几个多项式
{
for(j=0;j<=n;j++)//j代表是第一个多项式的第几项
for(k=0;k+j<=n;k+=i)//j+k是后项与第一项相乘的指数和,用j+k<=n来限制指数不能大于题目要求的数值;
{
c2[j+k]+=c1[j];//j+k代表的是某项的指数
}
for(j=0;j<=n;j++)
{
c1[j]=c2[j];
c2[j]=0;
}
}
printf("%d\n",c1[n]);
}
return 0;
}
类似题目:
1398
Square Coins
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.
210300
1427
AC代码:
#include<stdio.h>
int main()
{
int n;
while(~scanf("%d",&n)&&n!=0)
{
int i,j,k;
int c1[310];
int c2[310];
for(i=0;i<=n;i++)
{
c1[i]=1;
c2[i]=0;
}
for(i=2;i*i<=n;i++)
{
for(j=0;j<=n;j++)
for(k=0;k+j<=n;k=k+i*i)//把i换成i*i即可
{
c2[j+k]+=c1[j];
}
for(j=0;j<=n;j++)
{
c1[j]=c2[j];
c2[j]=0;
}
}
printf("%d\n",c1[n]);
}
return 0;
}
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