洛谷P1072 Hankson 的趣味題(數學)
阿新 • • 發佈:2018-10-27
etc tps oid long long esp amp har con http
題意
題目鏈接
Sol
充滿套路的數學題。。
如果你學過莫比烏斯反演的話不難得到兩個等式
\[gcd(\frac{x}{a_1}, \frac{a_0}{a_1}) = 1\]
\[gcd(\frac{b_1}{b_0}, \frac{b_1}{x}) = 1\]
然後枚舉\(b_1\)的約數就做完了。。
// luogu-judger-enable-o2 // luogu-judger-enable-o2 #include<bits/stdc++.h> #define LL long long using namespace std; const int MAXN = 1e6; inline int read() { char c = getchar(); int x = 0, f = 1; while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();} while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar(); return x * f; } int T, a0, a1, b0, b1, ans; int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } void check(int x) { if(x % a1) return ; ans += (gcd(x / a1, a0 / a1) == 1 && gcd(b1 / b0, b1 / x) == 1); } int main() { T = read(); while(T--) { a0 = read(), a1 = read(), b0 = read(), b1 = read(); ans = 0; for(int x = 1; x * x <= b1; x++) { if(b1 % x == 0) { check(x); if(b1 != x) check(b1 / x); } } cout << ans << endl; } return 0; }
洛谷P1072 Hankson 的趣味題(數學)