POJ 2891

中国剩余定理的扩展

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 1 #include<iostream>

 2 #include<cstdio>

 3 #include<vector>

 4 using namespace std;

 5 typedef long long int ll;

 6 ll exgcd(ll a, ll b, ll &x, ll &y)

 7 {

 8     if (b == 0) {

 9         x = 1;

10         y = 1;

11         return a;

12     }

13     ll d = exgcd(b,a%b,x,y);

14     ll t = x;

15     x = y;

16     y = t - a/b*y;

17     return d;

18 }

19 

20 ll get_res(vector<ll> &a, vector<ll> &r)

21 {

22     ll A(a[0]),R(r[0]),x,y,d;

23     for (int i(1); i<a.size(); ++i) {

24         d = exgcd(A,a[i],x,y);

25         ll c = r[i] - R;

26         if (c%d)return -1;

27         ll a1 = abs(a[i]/d);

28         x = x*c/d;

29         x = (x%a1 + a1)%a1;

30         R += A*x;

31         A *= a[i]/d;

32     }

33     return R;

34 }

35 

36 

37 int main()

38 {

39     int n;

40     while (scanf("%d",&n) != EOF) {

41         vector<ll> a;

42         vector<ll> r;

43         ll aa,rr;

44         for (int i(0); i<n; ++i) {

45             scanf("%I64d%I64d",&aa,&rr);

46             a.push_back(aa);

47             r.push_back(rr);

48         }

49         ll R = get_res(a,r);

50         cout<<R<<endl;

51     }

52 }