初等數論解同余方程組，POJ 1006 同余方程組

以前的做法

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
typedef long long LL;
LL ai[4],ri[4],M;
void Exgcd(LL a,LL b,LL& d,LL& x,LL& y)
{if(b == 0) { d = a, x = 1, y = 0;}else {Exgcd(b,a%b,d,y,x); y -= x*(a / b);}
}
LL gcd(LL a,LL b)
{return b == 0 ? a : gcd(b,a%b);
}
LL solve(int n)
{LL a1,r1;LL a, b, c;LL x, y, d;a1 = ai[1], r1 = ri[1];for(int i = 2; i <= n; ++i){a = a1, b = ai[i], c = ri[i] - r1;Exgcd(a,b,d,x,y);if(c % d) return -1;LL t = b / d;x = (x * (c / d)% t + t) % t;r1 = a1 * x + r1;a1 = a1 *(ai[i] / d); }return r1;
}
int main()
{LL p,e,k,d;int Kase = 1;while(cin >> p >> e >>k >>d){ai[1] = 23, ai[2] = 28, ai[3] = 33;ri[1] = p , ri[2] = e, ri[3] = k;if(p == -1 && e == -1 && k == -1 && d == -1) break;LL ans = solve(3);M = 1;for(int i = 1; i <= 3; ++i) M = M * ai[i] / gcd(M,ai[i]);if(ans >= M) ans %= M; // 求最小的值. while(ans <= d) ans += M;printf("Case %d: the next triple peak occurs in %lld days.\n",Kase++,ans-d);}
}

中國剩余定理擼一發

初等數論解同余方程組，不過中國剩余定理 ai[i] 需要互質

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
typedef long long LL;
LL ai[4],ri[4],M;
void Exgcd(LL a,LL b,LL& d,LL& x,LL& y)
{if(b == 0) { d = a, x = 1, y = 0;}else {Exgcd(b,a%b,d,y,x); y -= x*(a / b);}
}
LL gcd(LL a,LL b)
{return b == 0 ? a : gcd(b,a%b);
}
LL China(int n)
{M = 1;LL Mi,x,y,d,ans = 0;for(int i = 1; i <= n; ++i) M *= ai[i];for(int i = 1; i <= n; ++i){Mi = M / ai[i];Exgcd(Mi,ai[i],d,x,y);ans = (ans + Mi * x * ri[i]) % M;}if(ans < 0) ans += M;return ans ;
}
int main()
{LL p,e,k,d;int Kase = 1;while(cin >> p >> e >>k >>d){ai[1] = 23, ai[2] = 28, ai[3] = 33;ri[1] = p , ri[2] = e, ri[3] = k;if(p == -1 && e == -1 && k == -1 && d == -1) break;LL ans = China(3);/*M = 1;for(int i = 1; i <= 3; ++i) M = M * ai[i] / gcd(M,ai[i]);*///if(ans >= M) ans %= M; // 求最小的值. while(ans <= d) ans += M;printf("Case %d: the next triple peak occurs in %lld days.\n",Kase++,ans-d);}
}