[HDOJ5584] LCM Walk (number theory, regularity)

Title Link: http://acm.hdu.edu.cn/showproblem.php?pid=5584

Give a coordinate (ex, EY) and ask what points it came from. The rules for walking are X or y plus their least common multiple LCM (x, y).

Consider (ex, EY) is coming from other points, it is advisable to set when walking to (x, y), GCD, =K,X=K*M1, y=k*m2.

The next step may be (x, Y+X*Y/GCD (x, y)) or (X+X*Y/GCD (y), y).

denoted by K and m1,m2 (k*m1, k*m2+m1*m2*k) = (k*m1, k*m2* (m1+1)), or (K*m1+m1*m2*k, k*m2) = (k*m1* (m2+1), k*m2).

The following is only concerned (k*m1* (m2+1), k*m2). M1 and M2 coprime and (m2+1) with M2 also coprime.

Then GCD (k*m1* (m2+1), k*m2) =k, that is, the largest common factor of any change, is K. This also proves that the path is unique, and we are asking for the number of possible starting positions, so consider directly the case of X to add each time (i.e., y>x, swap x, y). We can push back from (ex, EY). X ' =k1*m1/(m2+1), when x is not an integer multiple of (y + K), that is, x/(k* (m2+1)) does not end with 0.

1#include <algorithm>2#include <iostream>3#include <iomanip>4#include <cstring>5#include <climits>6#include <complex>7#include <fstream>8#include <cassert>9#include <cstdio>Ten#include <bitset> One#include <vector> A#include <deque> -#include <queue> -#include <stack> the#include <ctime> -#include <Set> -#include <map> -#include <cmath> +  - using namespacestd; +  A intex, EY; at  - intMain () { -     //freopen ("in", "R", stdin); -     intT, _ =1; -scanf"%d", &T); -      while(t--) { inscanf"%d%d", &ex, &ey); -         intK =__GCD (ex, EY); to         if(Ex <ey) Swap (ex, EY); +         intAns =1; -          while(1) { the             if(ex% (ey + k)! =0) Break; *ans++; $ex = EX/(ey/k +1);Panax Notoginseng             if(Ex <ey) Swap (ex, EY); -K =__GCD (ex, EY); the         } +printf"Case #%d:%d\n", _++, ans); A     } the     return 0; +}

[HDOJ5584] LCM Walk (number theory, regularity)