POJ1811 Prime Test

Posted 2020-06-13

rabin_miller判断素数，pollard rho求质因式分解。别人的模板。

  1 /* 4344 */
  2 #include <iostream>
  3 #include <sstream>
  4 #include <string>
  5 #include <map>
  6 #include <queue>
  7 #include <set>
  8 #include <stack>
  9 #include <vector>
 10 #include <deque>
 11 #include <algorithm>
 12 #include <cstdio>
 13 #include <cmath>
 14 #include <ctime>
 15 #include <cstring>
 16 #include <climits>
 17 #include <cctype>
 18 #include <cassert>
 19 #include <functional>
 20 #include <iterator>
 21 #include <iomanip>
 22 using namespace std;
 23 //#pragma comment(linker,"/STACK:102400000,1024000")
 24 
 25 #define sti                set<int>
 26 #define stpii            set<pair<int, int> >
 27 #define mpii            map<int,int>
 28 #define vi                vector<int>
 29 #define pii                pair<int,int>
 30 #define vpii            vector<pair<int,int> >
 31 #define rep(i, a, n)     for (int i=a;i<n;++i)
 32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 33 #define clr                clear
 34 #define pb                 push_back
 35 #define mp                 make_pair
 36 #define fir                first
 37 #define sec                second
 38 #define all(x)             (x).begin(),(x).end()
 39 #define SZ(x)             ((int)(x).size())
 40 #define lson            l, mid, rt<<1
 41 #define rson            mid+1, r, rt<<1|1
 42 
 43 #define LL                __int64 
 44 #define Times            10
 45 
 46 LL n, mn;
 47 
 48 LL random(LL n) {
 49     return (double) rand() / RAND_MAX * n + 0.5;
 50 }
 51 
 52 LL multi(LL a, LL b, LL mod) {
 53     LL ret = 0;
 54     
 55     while (b) {
 56         if (b & 1)
 57             ret = (ret + a) % mod;
 58         b >>= 1;
 59         a = (a + a) % mod;
 60     }
 61     
 62     return ret;
 63 }
 64 
 65 LL pow(LL a, LL b, LL mod) {
 66     LL ret = 1;
 67     
 68     while (b) {
 69         if (b & 1)
 70             ret = multi(ret, a, mod);
 71         b >>= 1;
 72         a = multi(a, a, mod);
 73     }
 74     
 75     return ret;
 76 }
 77 
 78 bool witness(LL a, LL n) {
 79     LL d = n - 1;
 80     
 81     while (!(d & 1))
 82         d >>= 1;
 83     
 84     LL t = pow(a, d, n);
 85     while (d!=n-1 && t!=1 && t!=n-1) {
 86         t = multi(t, t, n);
 87         d <<= 1;
 88     }
 89     
 90     return t==n-1 || (d&1);
 91 }
 92 
 93 bool miller_rabin(LL n) {
 94     if (n == 2)
 95         return true;
 96     
 97     if (n<2 || (n&1)==0)
 98         return false;
 99     
100     rep(i, 0, Times) {
101         LL a = random(n-2) + 1;
102         if (!witness(a, n))
103             return false;
104     }
105     
106     return true;
107 }
108 
109 LL pollard_rho(LL n, int c) {
110     LL x, y, d, i = 1, k = 2;
111     x = random(n-2) + 1;
112     y = x;
113     
114     while (1) {
115         ++i;
116         x = (multi(x, x, n) + c) % n;
117         d = __gcd(y-x, n);
118         if (1<d && d<n)
119             return d;
120         
121         if (y == x)
122             return n;
123         
124         if (i == k) {
125             y = x;
126             k <<= 1;
127         }
128     }
129 }
130 
131 void find(LL n, int c) {
132     if (n == 1)
133         return ;
134     
135     if (miller_rabin(n)) {
136         mn = min(mn, n);
137         return ;
138     }
139     
140     LL p = n;
141     while (p >= n)
142         p = pollard_rho(p, c--);
143     find(p, c);
144     find(n/p, c);
145 }
146 
147 void solve() {
148     mn = n;
149     if (miller_rabin(n)) {
150         puts("Prime");
151         return ;
152     }
153     
154     find(n, 12312);
155     printf("%I64d\n", mn);
156 }
157 
158 int main() {
159     ios::sync_with_stdio(false);
160     #ifndef ONLINE_JUDGE
161         freopen("data.in", "r", stdin);
162         freopen("data.out", "w", stdout);
163     #endif
164     
165     int t;
166     
167     scanf("%d", &t);
168     while (t--) {
169         scanf("%I64d", &n);
170         solve();
171     }
172     
173     #ifndef ONLINE_JUDGE
174         printf("time = %d.\n", (int)clock());
175     #endif
176     
177     return 0;
178 }