hdu-1028 Ignatius and the Princess III 【母函数】
2014-10-21 00:09
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Ignatius and the Princess III
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 14254 Accepted Submission(s): 10028
Problem Description
"Well, it seems the first problem is too easy. I will let you know how foolish you are later." feng5166 says.
"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!"
Input
The input contains several test cases. Each test case contains a positive integer N(1<=N<=120) which is mentioned above. The input is terminated by the end of file.
Output
For each test case, you have to output a line contains an integer P which indicate the different equations you have found.
Sample Input
4 10 20
Sample Output
5 42 627
#include<stdio.h> #include<iostream> #include<math.h> #include<stdlib.h> #include<ctype.h> #include<algorithm> #include<vector> #include<string.h> #include<queue> #include<stack> #include<set> #include<map> #include<sstream> #include<time.h> #include<utility> #include<malloc.h> #include<stdexcept> using namespace std; int n; int c1[10000]; int c2[10000]; int main () { int n; while (scanf ("%d",&n)!=EOF ) { for (int i=0;i<=n;i++) { c1[i]=1; c2[i]=0; } for (int i=2;i<=n;i++) { for (int j=0;j<=n;j++) { for (int k=0;k+j<=n;k+=i) { c2[j+k]+=c1[j]; } } for (int j=0;j<=n;j++) { c1[j]=c2[j]; c2[j]=0; } } printf("%d\n",c1 ); } return 0; }
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