HDOJ 1028 Ignatius and the Princess III （母函数）

最新推荐文章于 2025-09-12 18:08:49 发布

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最新推荐文章于 2025-09-12 18:08:49 发布

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原文链接：http://www.cnblogs.com/CKboss/p/3165204.html

本文介绍了一个编程问题“公主III”，该问题是计算给定正整数N的不同等式的数量。通过一个C++程序示例展示了如何使用动态规划解决这个问题，并提供了完整的代码实现。

Ignatius and the Princess III

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9532 Accepted Submission(s): 6722

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

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 
 5 using namespace std;
 6 
 7 const int maxn=200;
 8 
 9 int c1[maxn],c2[maxn];
10 
11 int main()
12 {
13     int n;
14 while(scanf("%d",&n)!=EOF)
15 {
16     for(int i=0;i<=n;i++)
17     {
18         c1[i]=1; c2[i]=0;
19     }
20 
21     for(int i=2;i<=n;i++)
22     {
23         for(int j=0;j<=n;j++)
24         {
25             for(int k=0;j+k<=n;k+=i)
26                 c2[k+j]+=c1[j];
27         }
28 
29         for(int j=0;j<=n;j++)
30         {
31             c1[j]=c2[j];  c2[j]=0;
32         }
33     }
34     printf("%d\n",c1[n]);
35 }
36 
37     return 0;
38 }

转载于:https://www.cnblogs.com/CKboss/p/3165204.html