首页 > 代码库 > 组合数学 - 母函数 + 模板题 ： 整数拆分问题
组合数学 - 母函数 + 模板题 ： 整数拆分问题
Ignatius and the Princess III
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 13129 Accepted Submission(s): 9285
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!"
"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
Mean:
给你一个n，问你n的拆分有多少种。
analyse:
经典的母函数运用题，不解释。
Time complexity：O(n^3)
Source code：
// Memory Time// 1347K 0MS// by : Snarl_jsb// 2014-09-18-15.21#include<algorithm>#include<cstdio>#include<cstring>#include<cstdlib>#include<iostream>#include<vector>#include<queue>#include<stack>#include<map>#include<string>#include<climits>#include<cmath>#define N 1000010#define LL long longusing namespace std;int c1[300],c2[300];int main(){ ios_base::sync_with_stdio(false); cin.tie(0);// freopen("C:\\Users\\ASUS\\Desktop\\cin.cpp","r",stdin);// freopen("C:\\Users\\ASUS\\Desktop\\cout.cpp","w",stdout); int n; while(cin>>n) { memset(c1,0,sizeof(c1)); memset(c2,0,sizeof(c2)); for(int i=0;i<=n;++i) { c1[i]=1; } for(int i=2;i<=n;i++) { for(int j=0;j<=n;++j) { for(int k=0;k<=n;k+=i) { c2[k+j]+=c1[j]; } } for(int j=0;j<=n;++j) { c1[j]=c2[j]; c2[j]=0; } } cout<<c1[n]<<endl; } return 0;}
组合数学 - 母函数 + 模板题 ： 整数拆分问题
声明：以上内容来自用户投稿及互联网公开渠道收集整理发布，本网站不拥有所有权，未作人工编辑处理，也不承担相关法律责任，若内容有误或涉及侵权可进行投诉： 投诉/举报 工作人员会在5个工作日内联系你，一经查实，本站将立刻删除涉嫌侵权内容。