SPOJ HG - HUGE GCD

Posted 2020-10-03

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：

 1 const int maxn = 1e4 + 5;
 2 int n, m;
 3 ll a[maxn], b[maxn];
 4 
 5 int gcd(int x, int y){
 6     return y == 0? x: gcd(y, x % y);
 7 }
 8 void solve(){
 9     ll ans = 1;
10     bool flag = false;
11     for(int i = 0; i < n; i++){
12         for(int j = 0; j < m; j++){
13             int tmp = gcd(a[i], b[j]);
14             a[i] /= tmp; b[j] /= tmp;
15             ans *= tmp; 
16             if(ans >= mod){
17                 flag = true;
18                 ans %= mod;
19             }
20         }
21     }
22     if(flag) printf("%09lld\n", ans % mod);
23     else printf("%lld\n", ans);
24 }
25 
26 int main(){
27     scanf("%d", &n);
28     for(int i = 0; i < n; i++) scanf("%lld", &a[i]);
29     scanf("%d", &m);
30     for(int i = 0; i < m; i++) scanf("%lld", &b[i]);
31     solve();
32 }

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.