CSU 1446 Modified LCS 扩展欧几里得

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <cmath>
 6 #include <algorithm>
 7 #include <string>
 8 #include <queue>
 9 #include <stack>
10 #include <vector>
11 #include <map>
12 #include <set>
13 #include <functional>
14 #include <time.h>
15 
16 using namespace std;
17 
18 typedef long long ll;
19 
20 const int INF = 1<<30;
21 
22 ll N1, F1, D1, N2, F2, D2;
23 
24 ll exgcd(ll a, ll b, ll &x, ll &y) {
25     if (b==0) {
26         x = 1; y = 0;
27         return a;
28     }
29     ll res = exgcd(b, a%b, y, x);
30     y -= x*(a/b);
31     return res;
32 }
33 
34 ll myAbs(ll x) {
35     return x>0 ? x : -x;
36 }
37 
38 void input() {
39     scanf("%lld%lld%lld%lld%lld%lld", &N1, &F1, &D1, &N2, &F2, &D2);
40 }
41 
42 void solve() {
43     ll x, y;
44     ll d = exgcd(D1, D2, x, y);
45     if (0!=(myAbs(F1-F2)%d)) {
46         puts("0");
47         return ;
48     }
49     ll k = (F1-F2)/d;
50     ll k1 = -k*x, k2 = k*y;
51 
52     ll gg = max(F1, F2); //第一个交点必然大于等于两个起点
53     ll lcm = D1/d*D2;
54 
55     gg = ((F1+k1*D1-gg)%lcm + lcm)%lcm + gg; //求出第一个·交点
56 
57     ll f1 = (gg-F1)/D1 + 1; //计算出第一个交点分别在两个数列中的下标
58     ll f2 = (gg-F2)/D2 + 1;
59 
60     ll n1 = (N1-f1+(D2/d))/(D2/d);
61     ll n2 = (N2-f2+(D1/d))/(D1/d);
62     ll ans = min(n1, n2);
63     if (ans<0) ans = 0;
64     printf("%lld\n", ans);
65 }
66 
67 int main() {
68     #ifdef Phantom01
69         freopen("HNU12831.txt", "r", stdin);
70     #endif //Phantom01
71 
72     int Case;
73     scanf("%d", &Case);
74     while (Case--) {
75         input();
76         solve();
77     }
78 
79     return 0;
80 }