luogu 2152

SuperGcd

二进制算法

1. A = B, Gcd(A, B) = A;

2. A,B为偶数,  Gcd(A, B) = 2 * Gcd(A / 2, B / 2);

3. A 为偶数, B 为奇数，Gcd(A, B) = Gcd(A / 2, B);

4. A,B为奇数, Gcd(A, B) = Gcd(A - B, B)

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstring>
 
using namespace std;
const int N = 2e5 + ;
 
int C[N * ];
char s[N];
 
struct Node {
    inline void Init(int A[]) {
        scanf("%s", s); int Len = strlen(s); A[] = Len; for(int i = ; i <= Len; i ++) A[i] = s[i - ] - '';
    }
    inline int Cmp(int A[], int B[]) {
        if(A[] > B[]) return ; if(A[] < B[]) return -;
        for(int i = ; i <= A[]; i ++) if(A[i] > B[i]) return ; else if(A[i] < B[i]) return -;
        return ;
    }
    inline void Div(int A[]) {
        int tmp(), j = ;
        for(int i = ; i <= A[]; i ++) {tmp += A[i]; A[i] = tmp / ; tmp %= ; tmp *= ;}
        for(int i = ; i <= A[] && !A[i]; i ++, j = i); A[] = A[] - j + ;
        for(int i = ; i <= A[]; i ++) A[i] = A[i + j - ];
    }
    inline void Minus(int A[], int B[]) {
        for(int i = B[], j = A[]; i >= ; i --, j --) {
            if(A[j] < B[i]) {A[j] += ; A[j - ] --;} A[j] -= B[i];
        }
        int j = ;
        for(int i = ; i <= A[] && !A[i]; i ++, j = i); A[] = A[] - j + ;
        for(int i = ; i <= A[]; i ++) A[i] = A[i + j - ];
    }
    int a[N], b[N];
    inline void Mul(int A[], int B[]) {
        memset(C, , sizeof C);
        int j = ; for(int i = A[]; i >= ; i --) a[++ j] = A[i];
        j = ; for(int i = B[]; i >= ; i --) b[++ j] = B[i];
        for(int i = ; i <= A[]; i ++) {
            int x = ;
            for(int k = ; k <= B[]; k ++) {C[i + k - ] += a[i] * b[k] + x; x = C[i + k - ] / ; C[i + k - ] %= ;}
            C[i + B[]] = x;
        }
        j = A[] + B[]; while(!C[j] && j > ) j --; A[] = ;
        for(int i = j; i >= ; i --) A[++ A[]] = C[i];
    }
    inline void Out(int A[]) {for(int i = ; i <= A[]; i ++) printf("%d", A[i]);}
} Big_num_work;
 
void Gcd(int A[], int B[], int &tot) {
    int imp = Big_num_work.Cmp(A, B); if(imp == ) return ; if(imp < ) {Gcd(B, A, tot); return ;}
    int ta(), tb(); if(A[A[]] %  == ) Big_num_work.Div(A), ta = ; if(B[B[]] %  == ) Big_num_work.Div(B), tb = ;
    if(ta && tb) Gcd(A, B, ++ tot);
    else if(!ta && !tb) {Big_num_work.Minus(A, B); Gcd(A, B, tot);}
    else Gcd(A, B, tot);
}
 
int A[N], B[N], F[N];
 
int main() {
    Big_num_work.Init(A); Big_num_work.Init(B);
    int T = ; Gcd(A, B, T);
    if(T == ) Big_num_work.Out(A);
    else {
        int Tow[]; Tow[] = , Tow[] = ; F[] = F[] = ; for(int i = ; i <= T; i ++) Big_num_work.Mul(F, Tow);
        Big_num_work.Mul(A, F); Big_num_work.Out(A);
    }
    return ;
}