There is an interesting and simple one person game. Suppose there is a number axis under your feet. You are at point A at first and your aim is point B. There are 6 kinds of operations you can perform in one step. That is to go left or right by a,b and c, here c always equals to a+b.
You must arrive B as soon as possible. Please calculate the minimum number of steps.
There are multiple test cases. The first line of input is an integer T(0 < T ≤ 1000) indicates the number of test cases. Then T test cases follow. Each test case is represented by a line containing four integers 4 integers A, B, a and b, separated by spaces. (-231 ≤ A, B < 231, 0 < a, b < 231)
For each test case, output the minimum number of steps. If it's impossible to reach point B, output "-1" instead.
2 0 1 1 2 0 1 2 4
1 -1根据题意,很容易知道要算 a*x+b*y = B-A中的x,y。但是解出来是一组特解,需要让x,y向0逼近
#include<iostream> #include<cstdio> #include<cmath> using namespace std; typedef long long LL; const LL INF = 0x3f3f3f3f; LL e_gcd(LL a, LL b, LL &x, LL &y) { if(b == 0) { x = 1; y = 0; return a; } LL r= e_gcd(b, a%b, x, y); LL temp = x; x = y; y = temp - a/b*y; return r; } int main() { LL T, A, B, a, b; scanf("%lld", &T); while(T--) { LL x, y, m; scanf("%lld %lld %lld %lld", &A, &B, &a, &b); LL GCD = e_gcd(a, b, x, y); if((B-A)%GCD != 0) cout << -1 << endl; else { a /= GCD; b /= GCD; x = (B-A)/GCD*x; y = (B-A)/GCD*y; LL ans = INF*INF; LL t = (y-x)/(a+b); for(LL i = t-1;i <= t+1; ++i) { if((abs(x + b*i) + abs(y - a*i)) == abs(x + b*i + y - a*i))//同号 { m = max(abs(x+b*i), abs(y-a*i)); } else m = abs(x+b*i) + abs(y-a*i);//异号 ans = min(ans, m); } cout << ans << endl; } } return 0; }