NOJ1203 最多约数问题 [搜索 数论]

  1 #include<iostream>
  2 #include<cstring>
  3 #include<cstdlib>
  4 #include<cstdio>
  5 #include<algorithm>
  6 #include<cmath>
  7 #include<queue>
  8 #include<map>
  9 #include<set>
 10 #include<stack>
 11 #include<string>
 12 
 13 #define N 100005
 14 #define M 105
 15 #define mod 1000000007
 16 //#define p 10000007
 17 #define mod2 1000000000
 18 #define ll long long
 19 #define LL long long
 20 #define eps 1e-6
 21 #define inf 1000000
 22 #define maxi(a,b) (a)>(b)? (a) : (b)
 23 #define mini(a,b) (a)<(b)? (a) : (b)
 24 
 25 using namespace std;
 26 
 27 ll a,b;
 28 ll ma;
 29 int f[N];
 30 ll p[N];
 31 ll ccnt;
 32 
 33 void ini1()
 34 {
 35     memset(f,0,sizeof(f));
 36     ll i,j;
 37     ccnt=0;
 38     f[0]=f[1]=1;
 39     for(i=2;i<=N-5;i++){
 40         if(f[i]==1) continue;
 41         for(j=2*i;j<=N-5;j+=i){
 42             f[j]=1;
 43         }
 44     }
 45     for(i=2;i<=N-5;i++){
 46         if(f[i]==0){
 47             p[ccnt]=i;ccnt++;
 48         }
 49     }
 50    // printf(" cnt=%d\n",cnt);
 51 }
 52 
 53 ll quickpow(ll x,ll n)
 54 {
 55     ll re=1;
 56     while(n)
 57     {
 58         if( (n&1)!=0 ){
 59             re*=x;
 60         }
 61         n/=2;
 62         x*=x;
 63     }
 64     return re;
 65 }
 66 
 67 void dfs(ll st,ll now,ll cnt)
 68 {
 69     ll i;
 70     //printf(" st=%I64d p=%I64d now=%I64d cnt=%I64d ma=%I64d\n",st,p[st],now,cnt,ma);
 71     if(now>b) return;
 72     if(now>=a){
 73         ma=max(ma,cnt);
 74     }
 75     ll temp=log(b/now)/log(p[st]);
 76     ll re=quickpow(2,temp);
 77    // printf("  temp=%I64d re=%I64d ma=%I64d\n",temp,re,ma);
 78     if(re*cnt<=ma) return;
 79     if( now<a && (a-1)/now==b/now ) return;
 80     ll c=0;
 81     ll te=now;
 82    // printf("   te=%I64d now=%I64d\n",te,now);
 83     if(st>=ccnt) return;
 84     for(i=0;;i++){
 85         if(te>b) break;
 86        // printf("  nst=%I64d te=%I64d ncnt=%I64d\n",st+1,te,(c+1)*cnt);
 87         dfs(st+1,te,(c+1)*cnt);
 88         te*=p[st];
 89         c++;
 90     }
 91 }
 92 
 93 void ini()
 94 {
 95     ma=0;
 96 }
 97 
 98 void solve()
 99 {
100     if(a>b) swap(a,b);
101     if(b==1){
102         ma=1;return;
103     }
104     ma=2;
105     dfs(0,1,1);
106 }
107 
108 void out()
109 {
110     //printf("%I64d\n",ma);
111     cout<<ma<<endl;
112 }
113 
114 int main()
115 {
116     ini1();
117     //freopen("data.in","r",stdin);
118     //freopen("data.out","w",stdout);
119     //scanf("%d",&T);
120     //for(int ccnt=1;ccnt<=T;ccnt++)
121     //while(T--)
122   //  while(scanf("%I64d%I64d",&a,&b)!=EOF)
123     while(cin>>a>>b)
124     {
125         ini();
126         solve();
127         out();
128     }
129     return 0;
130 }