P3455 [POI2007]ZAP-Queries

題意：

求滿足$1\le x\le a,1\le y\le b$，且$gcd(x,y)=d$的二元組(x,y)的數量

題解：

莫比烏斯反演板子

代碼：

// Problem: P3455 [POI2007]ZAP-Queries // Contest: Luogu // URL: https://www.luogu.com.cn/problem/P3455 // Memory Limit: 125 MB // Time Limit: 2000 ms // Data:2021-08-20 13:18:12 // By Jozky#include <bits/stdc++.h> #include <unordered_map> #define debug(a, b) printf("%s = %d\n", a, b); using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair<int, int> PII; clock_t startTime, endTime; //Fe~Jozky const ll INF_ll= 1e18; const int INF_int= 0x3f3f3f3f; void read(){}; template <typename _Tp, typename... _Tps> void read(_Tp& x, _Tps&... Ar) {x= 0;char c= getchar();bool flag= 0;while (c < '0' || c > '9')flag|= (c == '-'), c= getchar();while (c >= '0' && c <= '9')x= (x << 3) + (x << 1) + (c ^ 48), c= getchar();if (flag)x= -x;read(Ar...); } template <typename T> inline void write(T x) {if (x < 0) {x= ~(x - 1);putchar('-');}if (x > 9)write(x / 10);putchar(x % 10 + '0'); } void rd_test() { #ifdef LOCALstartTime= clock();freopen("in.txt", "r", stdin); #endif } void Time_test() { #ifdef LOCALendTime= clock();printf("\nRun Time:%lfs\n", (double)(endTime - startTime) / CLOCKS_PER_SEC); #endif } const int maxn= 5e4; int cnt= 0; int prim[maxn], vis[maxn], mu[maxn]; ll sum[maxn]; void get_mu(int n) {mu[1]= 1;prim[1]= 1;for (int i= 2; i <= n; i++) {if (!vis[i]) {prim[++cnt]= i;mu[i]= -1;}for (int j= 1; j <= cnt && i * prim[j] <= n; j++) {vis[i * prim[j]]= 1;if (i % prim[j] == 0)break;mu[i * prim[j]]= -mu[i];}}for (int i= 1; i <= n; i++)sum[i]= sum[i - 1] + mu[i]; } ll solve(ll a, ll b, ll d) {ll ans= 0;for (ll l= 1, r= 0; l <= a; l= r + 1) {r= min(a / (a / l), b / (b / l));ans+= 1ll * (sum[r] - sum[l - 1]) * (a / l) * (b / l);}return ans; } int main() {//rd_test();get_mu(50000);int t;read(t);while (t--) {ll a, b, d;read(a, b, d);if (a > b)swap(a, b);a/= d;b/= d;printf("%lld\n", solve(a, b, d));}//Time_test(); }

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