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HDUOJ----Ignatius and the Princess III

Ignatius and the Princess III

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 9893    Accepted Submission(s): 6996

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

Author

Ignatius.L

母函数.....对于任意一个数你   (1+x+x^2+x^3+x^4+x^5+x^6+x^7...+x^n)*(1+x^2+x^4+x^6+x^8+x^10+.....)*(1+x^3+.....);

 1 #include<iostream>
 2 #include<vector>
 3 using namespace std;
 4 int main()
 5 {
 6     int n,i,j,k;
 7     while(cin>>n)
 8     {
 9       vector<int>c1(n+1,1);
10       vector<int>c2(n+1,0);
11       for(i=2;i<=n;i++)
12       {
13          for(j=0;j<=n;j++)
14          {
15              for(k=0;k+j<=n;k+=i)
16              {
17                c2[j+k]+=c1[j];
18              }
19          }
20          for(j=1;j<=n;j++)
21          {
22              c1[j]=c2[j];
23              c2[j]=0;
24          }
25       }
26       cout<<c1[n]<<endl;
27     }
28     return 0;
29 }

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