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[HDU 4344]Mark the Rope（Pollard_rho+Miller_Rabin）
Description
Eric has a long rope whose length is N, now he wants to mark on the rope with different colors. The way he marks the rope is:
1. He will choose a color that hasn’t been used
2. He will choose a length L (N>L>1) and he defines the mark’s value equals L
3. From the head of the rope, after every L length, he marks on the rope (you can assume the mark’s length is 0 )
4. When he chooses the length L in step 2, he has made sure that if he marks with this length, the last mark will be at the tail of the rope
Eric is a curious boy, he want to choose K kinds of marks. Every two of the marks’ value are coprime(gcd(l1,l2)=1). Now Eric wants to know the max K. After he chooses the max K kinds of marks, he wants to know the max sum of these K kinds of marks’ values.
You can assume that Eric always can find at least one kind of length to mark on the rope.
Solution
质因数分解一下就好了，应该是道模板题
然而我忘记还有质因数只有一个的情况，L不能等于N啊
QvQ拍了好久都没找到错在哪，后来随手输了个1024发现事情有蹊跷…
#include<iostream>#include<cstdio>#include<cstring>#include<cstdlib>#include<vector>#include<map>using namespace std;typedef long long LL;LL T,ans=0;vector<LL>v;map<LL,LL>num;LL gcd(LL a,LL b){ return b?gcd(b,a%b):a;}LL mul(LL a,LL b,LL p){ LL res=0; while(b) { if(b&1)res=(res+a)%p; a=(a+a)%p;b>>=1; } return res;}LL pow(LL a,LL n,LL p){ LL res=1; while(n) { if(n&1)res=mul(res,a,p); a=mul(a,a,p);n>>=1; } return res;}bool check(LL a,LL n,LL m,LL cnt){ LL x=pow(a,m,n),y=x; for(int i=1;i<=cnt;i++) { x=mul(x,x,n); if(x==1&&y!=1&&y!=x-1)return 1; y=x; } return x!=1;}bool Miller_Rabin(LL n){ if(n==2)return 1; if(n<=1||n&1==0)return 0; LL m=n-1,cnt=0; while(m&1==0)cnt++,m>>=1; for(int i=1;i<=7;i++) { if(check(rand()%(n-1)+1,n,m,cnt)) return 0; } return 1;}LL rho(LL n,LL c){ LL i=1,k=2,x=rand()%(n-1)+1,y=x,d; while(1) { x=(mul(x,x,n)+c)%n; d=x>y?gcd(x-y,n):gcd(y-x,n); if(d>1)return d; if(y==x)return n; if(i==k)y=x,k<<=1; i++; }}void solve(LL n){ if(n==1)return; if(Miller_Rabin(n)) { if(!num[n]) {v.push_back(n),ans++,num[n]=1;} num[n]*=n; return; } LL p=n; while(p==n)p=rho(n,rand()%(n-1)+1); solve(p);solve(n/p);}int main(){ scanf("%lld",&T); while(T--) { LL n; scanf("%lld",&n); v.clear(),num.clear(),ans=0; solve(n); if(v[0]==n)ans--; printf("%lld ",ans); LL sum=0; for(int i=0;i<ans;i++) sum+=num[v[i]]; if(ans==1)sum/=v[0]; printf("%lld\n",sum); } return 0;}
[HDU 4344]Mark the Rope（Pollard_rho+Miller_Rabin）