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Language:
X-factor Chains
Description Given a positive integer X, an X-factor chain of length m is a sequence of integers, 1 = X0, X1, X2, …, Xm = X satisfying Xi < Xi+1 and Xi | Xi+1 where a | b means a perfectly divides into b. Now we are interested in the maximum length of X-factor chains and the number of chains of such length. Input The input consists of several test cases. Each contains a positive integer X (X ≤ 220). Output For each test case, output the maximum length and the number of such X-factors chains. Sample Input 2 3 4 10 100 Sample Output 1 1 1 1 2 1 2 2 4 6 Source
POJ Monthly--2007.10.06, ailyanlu@zsu
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代码：
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <vector>
#include <set>
#include <queue>
#pragma comment (linker,"/STACK:102400000,102400000")
#define maxn 1005
#define MAXN 2005
#define mod 1000000009
#define INF 0x3f3f3f3f
#define pi acos(-1.0)
#define eps 1e-6
#define lson rt<<1,l,mid
#define rson rt<<1|1,mid+1,r
#define FRE(i,a,b) for(i = a; i <= b; i++)
#define FREE(i,a,b) for(i = a; i >= b; i--)
#define FRL(i,a,b) for(i = a; i < b; i++)
#define FRLL(i,a,b) for(i = a; i > b; i--)
#define mem(t, v) memset ((t) , v, sizeof(t))
#define sf(n) scanf("%d", &n)
#define sff(a,b) scanf("%d %d", &a, &b)
#define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c)
#define pf printf
#define DBG pf("Hi\n")
typedef long long ll;
using namespace std;
//vector<int>
//只求解整数分解的因子的幂
vector<int> prime_factor_time(int n)
{
vector<int> res;
for (int i=2;i*i<=n;i++)
{
int time=0;
while (n%i==0)
{
++time;
n/=i;
}
res.push_back(time);
}
if (n!=1)
res.push_back(1);
return res;
}
//阶乘
ll factor(const int& n)
{
ll res=1;
for (int i=1;i<=n;i++)
res*=i;
return res;
}
int main()
{
int i,j,x;
while (~sf(x))
{
vector<int> num=prime_factor_time(x);
int all=0;
vector<int>::iterator it;
for (it=num.begin();it!=num.end();it++)
all+=*it;
ll ans=factor(all);
for (it=num.begin();it!=num.end();it++)
ans/=factor(*it);
pf("%d %lld\n",all,ans);
}
return 0;
}
X-factor Chains (poj 3421 数学排列组合)
原文：http://blog.csdn.net/u014422052/article/details/44628049