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 }

View Code