Codeforces Round #276 (Div. 2) A. Factory (number theory)

This question can be performed in a brute force manner in the required way. If you do this for 1000000 times, you will not be able to perform the entire m operation, and you will never be able to perform the entire m operation (m cannot exceed 100000, the cycle is 1000000 times safer ). This method can be AC.

The following is an in-depth analysis of how many cycles can be used to determine the results: (a + B) % c = (a % c + B % c) % c, in this case, this question is actually 2 * a each time. Official answer:

Production will stops iff exists integerKLimit ≥ limit 0 suchA· 2KIs divisibleM. From this fact follows thatKMaximum will be aboutO(Log2 (M). So if we modeling some, for example, 20 days and production does not stop, then it will never stop and answer is "No". Otherwise answer is "Yes ".

# Include <iostream> # include <cstdio> # include <cstdlib> # include <cstring> # include <string> # include <cmath> # include <map> # include <set> # include <vector> # include <algorithm> # include <stack> # include <queue> # include <cctype> # include <sstream> using namespace std; # define pii pair <int, int> # define LL long intconst int eps = 1e-8; const int INF = 1000000000; const int maxn = 1000 + 5; int a, m; int main () {// freopen ("in8.txt", "r", stdin); // freopen ("out.txt", "w", stdout ); scanf ("% d", & a, & m); int w = 0; for (int I = 0; I <20; I ++) {if (a % m = 0) {w = 1; puts ("Yes"); break;} a % = m; a + = ;} if (w = 0) puts ("No"); // fclose (stdin); // fclose (stdout); return 0 ;}

If you do not want to do this, you can find the periodic rule. However, note that the cycle does not necessarily start with the first number. In fact, as long as the % m following has appeared before, so you don't have to calculate it any more. It must be the same in the future.

# Include <iostream> # include <cstdio> # include <cstdlib> # include <cstring> # include <string> # include <cmath> # include <map> # include <set> # include <vector> # include <algorithm> # include <stack> # include <queue> # include <cctype> # include <sstream> using namespace std; # define pii pair <int, int> # define LL long intconst int eps = 1e-8; const int INF = 1000000000; const int maxn = 1000 + 5; int a, m; set <int> s; int main () {cin> a> m; wh Ile (a % m! = 0) {if (s. find (a % m )! = S. end () {cout <"No" <endl; return 0;} s. insert (a % m); a + = (a % m);} cout <"Yes" <endl; return 0 ;}

 

Codeforces Round #276 (Div. 2) A. Factory (number theory)