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