解决一元线性同余方程组问题
mod n1，n2 ，n3......间不要求互质
#include #include #include #include #include #include #include #include #include #define ms(a,b) memset(a,b,sizeof(a)) using namespace std; typedef long long ll; const int maxn = 100010; long long exgcd(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long ans = exgcd(b, a % b, x, y); long long temp = x; x = y; y = temp - (a / b) * y; return ans; } int crt(int t) ///解决一元线性同余方程组问题 { int flag = 1; long long n1, a1; if (t) { scanf("%lld%lld", &n1, &a1), t--; ///x ≡ a1(mod n1) } while (t--) { long long n2, a2, k1, k2; scanf("%lld%lld", &n2, &a2); ///x ≡ a2(mod n2) if (flag == 0) { continue; } long long d = exgcd(n1, n2, k1, k2); if ((a2 - a1) % d != 0) { flag = 0; } if (flag) { k1 = (k1 * (a2 - a1) / d % (n2 / d) + n2 / d) % (n2 / d); long long a = n1 * k1 + a1; long long n = n1 / d * n2; n1 = n; a1 = a; } } if (flag) { return a1; ///满足所有方程的最小解 } else { return -1; ///没有解返回-1 } } int main() { int t; while (cin >> t) { int ans = crt(t); cout << ans << endl; } return 0; }
