BZOJ1407 [Noi2002]Savage 【扩展欧几里得】

题目链接

BZOJ1407

题解

枚举\(m\)用扩欧判即可

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#define REP(i,n) for (int i = 1; i <= (n); i++)
using namespace std;
const int maxn = 20,maxm = 100005,INF = 1000000000;
inline int read(){
	int out = 0,flag = 1; char c = getchar();
	while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();}
	while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}
	return out * flag;
}
int C[maxn],P[maxn],L[maxn],n;
inline void exgcd(int a,int b,int& d,int& x,int& y){
	if (!b){d = a; x = 1; y = 0;}
	else exgcd(b,a % b,d,y,x),y -= (a / b) * x;
}
inline bool ok(int u,int v,int m){
	int a = P[u] - P[v],b = m,c = C[v] - C[u],d,x,y;
	exgcd(a,b,d,x,y);
	if (c % d) return true;
	b = abs(b / d);
	x = (x * c / d) % b;
	if (x <= 0) x += b;
	return x > min(L[u],L[v]);
}
inline bool check(int m){
	for (register int i = 1; i < n; i++)
		for (register int j = i + 1; j <= n; j++){
			if (!ok(i,j,m)) return false;
		}
	return true;
}
int main(){
	n = read(); int Max = 0;
	bool tag = true;
	REP(i,n){
		C[i] = read(),P[i] = read(),L[i] = read(),Max = max(Max,C[i]);
		C[i]--;
		if (P[i] != 1) tag = false;
	}
	if (tag){printf("%d",Max); return 0;}
	for (register int m = Max; ; m++){
		if (check(m)) {printf("%d\n",m); return 0;}
	}
	return 0;
}