Bzoj 2301-mo

For the given n queries, how many pairs (x, y) are asked each time , satisfy a≤x≤b, c≤y≤D, and gcd (x, y) = k, gcd (x,y) function x and the greatest common divisor of Y.

The topic here is very obvious.

for required f[n] = Sigma (A≤x≤b) Sigma (C≤y≤< Span lang= "en-us" >d) [gcd (x, y) =k] =  sigma (1≤x≤b)  sigma (1≤y≤d)  [gcd (x, y) =k] + sigma (1≤x≤ a-1)  sigma (1≤y≤c-1)  [gcd (x, y) =k]-  Sigma (1≤x≤a-1)  sigma (1≤y≤d) &NBSP;[GCD (x, y) =k]-  sigma (1≤x≤b)  sigma (1≤ y≤c-1)  [gcd (x, y) =k] 

For each g[n] = Sigma (1≤x≤a) sigma (1≤y≤c) [gcd (x, y) =k] = Sigma (1≤ x≤ a/k) Sigma (1≤y≤ c/k) [ GCD (x, y) =1] = Sigma (1≤x≤a/k) Sigma (1≤y≤c/k) Sigma (D|GCD (x, y)) mu[d] = Sigma (d) mu[d]*a/k/d*c/k/d

A/K/D*C/K/D This section of the interval can be added together to calculate the current value of the end is min (x/(x/i), y/(y/i))

Record the prefix of the Möbius function and update the entire interval so that the loop shrinks to the complexity of the sqrt (n)

1#include <bits/stdc++.h>2 using namespacestd;3 #definell Long Long4 #defineN 500005 intmu[n+Ten], prime[n+Ten], tot, sum[n+Ten];6 BOOLcheck[n+Ten];7 8 voidGet_mu ()9 {Tenmu[1] =1; One      for(intI=2; I<=n; i++){ A         if(!Check[i]) { -prime[tot++] =i; -Mu[i] =-1; the         } -          for(intj=0; J<tot; J + +){ -             if(LL) i*prime[j]>n) Break; -CHECK[I*PRIME[J]] =true; +             if(i%Prime[j]) { -MU[I*PRIME[J]] =-Mu[i]; +}Else  Break; A         } at     } -      for(intI=1; I<=n; i++) sum[i]=sum[i-1]+Mu[i]; - } -  - inta,b,c,d,k; -  in intSolveintXinty) - { toX/=k, y/=K; +     intmx = min (x, y), Len, ret=0; -      for(intI=1; I&LT;=MX; i=len+1) the     { *        //cout<<i<< "" <<ret<<endl; $len = min (x/(x/i), y/(y/i));Panax NotoginsengRET + = x/i* (y/i) * (sum[len]-sum[i-1]); -     } the     returnret; + } A  the intMain () + { -     //freopen ("In.txt", "R", stdin); $ Get_mu (); $     intT; -scanf"%d", &T); -      while(t--){ thescanf"%d%d%d%d%d", &a, &b, &c, &d, &k); -printf"%d\n", Solve (B,d) +solve (a1, C-1)-solve (A-1, d)-solve (b,c-1));Wuyi     } the     return 0; -}

Bzoj 2301-mo