Ignatius and the Princess III
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 17692 Accepted Submission(s): 12403
"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!"
題目大意:給出一個整數n,將他拆分成1-n的整數,問有多少種組合數;
解題思路:母函數;指數爲 數值,用數組下標表示;係數爲方案數,用數組存的值表示;不過,也可以用完全揹包來做;
代碼如下:
#include"iostream"
#include"cstdio"
#include"cstring"
using namespace std;
const int maxn = 120;
int num[maxn + 1];
int c1[maxn + 1], c2[maxn + 1];
int main(){
int n;
while(scanf("%d", &n) != EOF){
for(int i = 1;i <= n;i ++)
num[i] = n / i;
memset(c1, 0, sizeof c1);
memset(c2, 0, sizeof c2);
for(int i = 0;i <= num[1];i ++)
c1[i] = 1;
for(int i = 2;i <= n;i ++){ //共有26個多項式
for(int j = 0;j <= maxn;j ++){ //共有maxn+1項
for(int k = 0;k <= num[i] && j + k*i <= maxn;k ++)
c2[j + k*i] += c1[j];
}
for(int j = 0;j <= maxn;j ++){
c1[j] = c2[j];
c2[j] = 0;
}
}
printf("%d\n",c1[n]);
}
return 0;
}