Poj 2191 various prime number Algorithms

From discuss. analysis: first, the prime [I... n], and then use the miller_rabin prime number test method to test whether 2 ^ prime [I]-1 is a prime number (can be typed into a table or not, which does not affect much ). If not, use Pollard to perform qualitative factorization on the number. Books on the miller_rabin prime number test method and Pollard integer prime factor factorization number theory are available, almost as templates. Code: 2191 accepted 172 K 16 Ms C ++ 3050b # include <iostream> # include <cstring> # include <ctime> # include <cstdlib> # include <cmath> # include <algorithm> // # define max (POW (2.0, 62) # Define c 240 # define time 6 using namespace STD ;__ int64 ans [65]; // store 2 ^ prime [I]-1 prime factor int prime [65], X [65], M, CNT ;__ int64 gcd (_ int64, __int64 B) {If (B = 0) return a; return gcd (B, A % B) ;}__ int64 mod_mult (_ int64 A, __int64 B, __int64 N) {_ Int64 S = 0; A = A % N; while (B) {If (B & 1) {S + = A; If (S> = N) s-= N;} A = A <1; if (a> = n) A-= N; B = B> 1;} return s ;} __int64 mod_exp (_ int64 A, _ int64 B ,__ int64 N) {_ int64 d = 1; A = A % N; while (B> = 1) {If (B & 1) d = mod_mult (D, A, n); A = mod_mult (a, a, n); B = B> 1 ;} return D;} bool wintess (_ int64 A ,__ int64 N) {_ int64 M, X, Y; int I, j = 0; M = n-1; while (M % 2 = 0) {M = m> 1; j ++;} X = mod_exp (a, m, n); for (I = 1; I <= J; I ++) {Y = mod_exp (x, 2, n); If (y = 1) & (X! = 1) & (X! = N-1) return true; X = y;} If (y! = 1) return true; return false;} bool miller_rabin (INT times ,__ int64 N) {_ int64 A; int I; If (n = 1) return false; if (n = 2) return true; If (N % 2 = 0) return false; srand (Time (null); for (I = 1; I <= times; I ++) {A = rand () % (n-1) + 1; if (wintess (A, n) return false;} return true ;} __int64 Pollard (_ int64 N, int c) {_ int64 I, K, X, Y, D; srand (Time (null); I = 1; k = 2; X = rand () % N; y = x; while (true) {I ++; X = (mod_mul T (x, x, n) + C) % N; D = gcd (Y-X, n); If (D> 1 & D <n) return D; if (y = x) return N; if (I = k) {Y = x; k = k <1 ;}} void get_prime (_ int64 N, int c) {// finds all prime factor _ int64 m in binary mode; If (n = 1) return; If (miller_rabin (time, n )) {ans [CNT ++] = N; return;} M = N; while (M> = N) M = Pollard (M, c --); get_prime (m, c); get_prime (N/m, c);} void Init () {int I, TMP; memset (x, 0, sizeof (x )); X [0] = x [1] = 1; M = 0; for (I = 2; I <= 63; I ++) {If (! X [I]) {Prime [++ m] = I; TMP = I * I; while (TMP <= 63) {x [TMP] = 1; TMP + = I ;}}} bool CMP (_ int64 N1 ,__ int64 N2) {return N1 <N2 ;} int main () {Init (); int P, i, J; scanf ("% d", & P); for (I = 1; I <= m; I ++) {If (prime [I] <= P) {__ int64 n = (_ int64) 1 <prime [I])-1; if (miller_rabin (time, n) // determine whether it is a prime number continue; memset (ANS, 0, sizeof (ANS); CNT = 0; get_prime (N, C ); // factorization factor sort (ANS, ANS + CNT, CMP); For (j = 0; j <cnt-1; j ++) printf ("% i64d *", ans [J]); printf ("% i64d = % i64d = (2 ^ % d)-1 \ n", ANS [J], n, prime [I]);} elsebreak;} return 0 ;}