标签：acm algorithm poj 素数筛法 排列组合
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 5659 | Accepted: 1786 |
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
题意：给你一个数X，将X分解成1~X的因子数列，前一个数可以整数后一个数，求满足条件的最大链长以及有多少条这样长的链。
分析：很容易想到了素因数分解。不难推出，我们要求的最大链长就等于素因子的个数，最长链条数就是这些素因子的排列组合数。题目数据量较大，所以先打个素数表。
题目链接：http://poj.org/problem?id=3421
代码清单：
#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<stack>
#include<ctime>
#include<cctype>
#include<string>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int uint;
const int maxp = 10000 + 5;
const int maxn = 1100000 + 5;
int sum,X;
int prime[maxp];
bool vis[maxn];
int num[maxp],k; //存每个素因子的个数
void init(){ //素数筛法打表
sum=0;
memset(vis,true,sizeof(vis));
for(int i=2;i<=maxn;i++){
if(!vis[i]) continue;
prime[sum++]=i;
if(i>(int)sqrt(maxn)) continue;
for(int j=i*i;j<=maxn;j+=i)
vis[j]=false;
}
}
ll get_max(){ //得到最大链长，即素因子的个数
ll ans=0;
for(int i=0;i<k;i++)
ans+=(ll)num[i];
return ans;
}
ll get_sum(){ //得到链的种类数,即素因子的排列组合数
ll fenzi=1;
ll Max=get_max();
for(ll i=2;i<=Max;i++)
fenzi*=i;
for(int i=0;i<k;i++){
for(int j=2;j<=num[i];j++){
fenzi/=(ll)j;
}
}
return fenzi;
}
void solve(){
k=0;
memset(num,0,sizeof(num));
for(int i=0;i<sum;i++){
if(X%prime[i]==0){
while(X%prime[i]==0){
num[k]++;
X/=prime[i];
}
k++;
}
if(X==1){
break;
}
}
ll ans_max=get_max();
ll ans_sum=get_sum();
printf("%I64d %I64d\n",ans_max,ans_sum);
}
int main(){
init();
while(scanf("%d",&X)!=EOF){
solve();
}return 0;
}
POJ_3421_X-factor Chains(素数筛法)
标签：acm algorithm poj 素数筛法 排列组合
原文地址：http://blog.csdn.net/jhgkjhg_ugtdk77/article/details/46239889
