51nod 1352: Collection Count

1352 set total base time limit: 1 seconds space limit: 131072 KB score: 20 Difficulty: 3-level algorithm topic collection attention

Give N fixed set {1,n},{2,n-1},{3,n-2},..., {n-1,2},{n,1}. Find out how many sets are satisfied: The first element is a multiple of a and the second element is a multiple of B.

Tips:

For the second set of test data, the collection is: {1,10},{2,9},{3,8},{4,7},{5,6},{6,5},{7,4},{8,3},{9,2},{10,1}. The conditions are met by 2nd and 8th.

Input

Line 1th: An integer T (1<=t<=50000) that indicates how many sets of test data. Line 2-t+1: three integers per line n,a,b (1<=n,a,b<=2147483647)

Output

For each set of test data output one number represents the number of sets that satisfy the condition, which is a row.

Input example

25 2 410) 2 3

Output example

12

Obviously, it is necessary to satisfy the equation a*xx+b*yy=1+n. My idea is to use the extension Euclid to find the minimum value greater than 0 xx, take its remain=n-(xx) *a, and then use remain divided by A, b least common multiple can be.

Feel 51nod on the topic for algorithm optimization requirements are very high, many times a careless out of the results of tle more than WA, so many places have to pay attention to the algorithm of time AH.

Code:

#include <iostream> #include <vector> #include <algorithm>using namespace Std;long long N,a,b,result, D,z,xx,yy;void EX_GCD (Long long A,long long B,long long &xx,long long &yy) {if (b==0) {xx=1;yy=0;d=a;} ELSE{EX_GCD (B,A%B,XX,YY); Long long t=xx;xx=yy;yy=t-(A/b) *yy;}} Long Long Cal2 () {RESULT=0;EX_GCD (A,B,XX,YY); Z=a*b/d;if ((1+n)%d) return 0;else{xx=xx* ((1+n)/d); long long r=b/d;xx = (xx %r+r)%r;if (xx==0) Xx+=r;long long remain=n-(xx) *a;if (remain<0) return 0;else{result++;result + = remain/z;} return result;} int main () {int count;scanf ("%d", &count), while (count--) {scanf ("%lld%lld%lld", &n,&a,&b);cout< <cal2 () <<endl;} return 0;}

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

51nod 1352: Collection Count