Bzoj 1101: [Poi2007]zap (Möbius inversion)

Answer =∑[GCD (x, y) = d] (1 <= x <= A, 1 <= y <= b).

Make a ' = A/d, b ' = b/d, simplify to get:

Answer =σ μ (t) * ⌊a '/t⌋*⌊b '/t⌋

⌊a '/t⌋ is equal to a continuous interval, ⌊b '/t⌋ the same, and the number is a square root level

so get out μ is prefixed and then chunked processed.

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#include <bits/stdc++.h>using namespace std;const int MAXN = 50009;bool CHECK[MAXN];int MU[MAXN], prime[maxn], N = 0; void init () {memset (check, false, sizeof check);mu[1] = 1;for (int i = 2; i < MAXN; i++) {if (!check[i]) {Mu[i] =-1;prime[n++] = i;}For (int j = 0; J < N && I * prime[j] < MAXN; J + +) {check[i * Prime[j]] = true;if (i% prime[j])mu[i * Prime[j]] =-mu[i];else {mu[i * Prime[j]] = 0;Break ;}}}for (int i = 1; i < MAXN; i++)Mu[i] + = mu[i-1];}void Work (int a, int b) {if (a > B) Swap (A, b);int ans = 0;for (int L = 1; L <= A; l++) {int R = min (A/(A/L), b/(B/L));ans + = (Mu[r]-mu[l-1]) * (a/l) * (B/L);L = R;}printf ("%d\n", ans);}int main () {init ();int T;cin >> T;While (t--) {int A, b, C;scanf ("%d%d%d", &a, &b, &c);Work (A/C, b/c);}return 0;}

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1101: [Poi2007]zap time limit: ten Sec Memory Limit: 162 MB
Submit: 1599 Solved: 554
[Submit] [Status] [Discuss] Description

FGD is cracking a cipher, and he needs to answer a number of similar questions: for a given integer, a, B, and D, how many positive integers are to X, Y, X<=a,y<=b, and gcd (x, y) =d. As a classmate of FGD, FGD hopes to get your help.

Input

The first line contains a positive integer n, which indicates that there are altogether n groups of queries. (1<=n<= 50000) next n rows, each line represents a query, three positive integers per line, respectively, A,b,d. (1<=d<=a,b<=50000)

Output

For each set of queries, output to the output file zap.out a positive integer that represents the integer logarithm that satisfies the condition.

Sample Input2
4 5 2
6 4 3Sample Output3
2HINT

For the first set of queries, an integer pair that satisfies the condition has (2,2), (2,4), (4,2). For the second set of queries, an integer pair that satisfies the condition has (6,3), (3,3).

Source

Bzoj 1101: [Poi2007]zap (Möbius inversion)