SPOJ HG

题目链接：http://www.spoj.com/problems/HG/

题目大意：分别给N个和M个小于等于1e9的数，前N个数相乘为A，后M个数相乘为B，问你GCD(A, B)　　1<= N<= 1000，1 <=M <= 1000

解题思路：枚举a[i] 和b[i]，计算两者GCD，然后结果乘以GCD，两者都除以GCD。最后判断一下如何输出即可。

代码：

const int maxn = 1e4 + 5;
int n, m;
ll a[maxn], b[maxn];

int gcd(int x, int y){
    return y == 0? x: gcd(y, x % y);
}
void solve(){
    ll ans = 1;
    bool flag = false;
    for(int i = 0; i < n; i++){
        for(int j = 0; j < m; j++){
            int tmp = gcd(a[i], b[j]);
            a[i] /= tmp; b[j] /= tmp;
            ans *= tmp; 
            if(ans >= mod){
                flag = true;
                ans %= mod;
            }
        }
    }
    if(flag) printf("%09lld
", ans % mod);
    else printf("%lld
", ans);
}

int main(){
    scanf("%d", &n);
    for(int i = 0; i < n; i++) scanf("%lld", &a[i]);
    scanf("%d", &m);
    for(int i = 0; i < m; i++) scanf("%lld", &b[i]);
    solve();
}

题目：

HG - HUGE GCD

#math #number-theory

RK has received a homework assignment to compute the greatest common divisor of the two positive integers Aand B. Since the numbers are quite large, the professor provided him with N smaller integers whose product is A, and M integers with product B.

RK would like to verify his result, so he has asked you to write a program to solve his problem. If the result is more than 9 digits long, output only the last 9 digits.

INPUT

The first line of input contains the positive integer N (1<= N<= 1000).
The second line of input contains N space-separated positive integers less than 10^9, whose product is the number A.
The third line of input contains the positive integer M (1 <=M <= 1000).
The fourth line of input contains M space-separated positive integers less than 10^9, whose product is the number B.

OUTPUT

The first and only line of output must contain the greatest common divisor of numbers A and B. If the result is more than 9 digits long, output only the last (least significant) 9 digits.

SAMPLE

Input
3
2 3 5
2
4 5
Output
10

Input
3
358572 83391967 82
3
50229961 1091444 8863
Output
000012028

First sample description: The greatest common divisor of numbers A = 30 and B = 20 equals 10.