CEQU - Crucial Equation
Topic: Linear Diophantine Equation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| ///Linear Diophantine Equation | |
| #include <bits/stdc++.h> | |
| using namespace std; | |
| #define INF 1<<30 | |
| #define MAX 10005 | |
| #define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); | |
| typedef long long ll; | |
| int Extended_gcd(int a, int b, int &x, int &y) | |
| { | |
| if(a == 0) | |
| { | |
| x = 0; | |
| y = 1; | |
| return b; | |
| } | |
| int x1, y1; | |
| int d = Extended_gcd(b % a, a, x1, y1); | |
| x = y1 - (b / a) * x1; | |
| y = x1; | |
| return d; | |
| } | |
| //(note that this code does not consider the case a=b=0).We don't consider this case here. | |
| bool find_any_solution(int a, int b, int c, int &x0, int &y0, int &g) | |
| { | |
| g = Extended_gcd(abs(a),abs(b), x0, y0); | |
| if(c % g) return false; | |
| x0 *= c / g; | |
| y0 *= c / g; | |
| if(a < 0) x0 = -x0; | |
| if(b < 0) y0 = -y0; | |
| return true; | |
| } | |
| void shift_solution(int &x, int &y, int a, int b, int cnt) | |
| { | |
| x += cnt * b; | |
| y -= cnt * a; | |
| } | |
| //Note that if a or b is 0, then the problem only has one solution. We don't consider this case here. | |
| int find_all_solution(int a, int b, int c, int minx, int maxx, int miny, int maxy) | |
| { | |
| int x, y,g; | |
| if(!find_any_solution(a, b, c, x, y, g)) return 0; | |
| a /= g; | |
| b /= g; | |
| int sign_a = a > 0 ? +1 : -1; | |
| int sign_b = b > 0 ? +1 : -1; | |
| shift_solution(x, y, a, b, (minx - x)/b); | |
| if(x < minx) | |
| shift_solution(x, y, a, b, sign_b); | |
| if(x > maxx)return 0; | |
| int lx1 = x; | |
| shift_solution(x, y, a, b, (maxx - x)/b); | |
| if(maxx > x) | |
| shift_solution(x, y, a, b, -sign_b); | |
| int rx1 = x; | |
| shift_solution(x, y, a, b, -(miny - y)/a); | |
| if(y < miny)shift_solution(x, y, a, b, -sign_a); | |
| if(y > maxy) | |
| return 0; | |
| int lx2 = x; | |
| shift_solution(x, y, a, b, -(maxy - y)/a); | |
| if(y > maxy) | |
| shift_solution(x, y, a, b, sign_a); | |
| int rx2 = x; | |
| if(lx2 > rx2) swap(lx2, rx2); | |
| int lx = max(lx1, lx2); | |
| int rx = min(rx1, rx2); | |
| if(lx > rx) return 0; | |
| return (rx - lx)/ abs(b) + 1; | |
| } | |
| int main() | |
| { | |
| FASTIO | |
| ///* | |
| //double start_time = clock(); | |
| #ifndef ONLINE_JUDGE | |
| freopen("in.txt", "r", stdin); | |
| freopen("out.txt", "w", stdout); | |
| freopen("error.txt", "w", stderr); | |
| #endif | |
| //*/ | |
| int T; | |
| cin >> T; | |
| for(int cs = 1; cs <= T; cs++){ | |
| int a,b,c,x,y,g; | |
| cin >> a >> b >> c; | |
| if(find_any_solution(a,b,c,x,y,g)) cout << "Case "<<cs<<": Yes\n"; | |
| else cout << "Case "<<cs<<": No\n"; | |
| } | |
| //double end_time = clock(); | |
| //printf( "Time = %lf ms\n", ( (end_time - start_time) / CLOCKS_PER_SEC)*1000); | |
| return 0; | |
| } |
No comments:
Post a Comment