CodeForces 48C D - The Race (Fraction,数学)
每个加油的站可以确定一个alpha的上下界,比如,第i次加油站a[i],前面加了i次油,a[i]*10≤ alpha*i <(a[i]+1)*10。
取最大的下界,取最小的上界,看看两者之间的满足条件的下一个加油站是否唯一。
因为可以用分数,所有就没用double了
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a; }
struct Fra
{
ll p,q;
Fra(ll x = ,ll y = ):p(x),q(y){ normal(p,q); }
void normal(ll &p,ll &q) { ll g = gcd(p,q); p/=g; q/=g; }
Fra operator = (int x) { p = x; q = ; return *this; }
Fra operator = (ll x) { p = x; q = ; return *this; }
Fra operator - () { return {-p,q}; }
Fra operator + (Fra &r) {
ll m,n;
m = p*r.q+r.p*q;
n = q*r.q;
normal(m,n);
return {m,n};
}
Fra operator += (Fra& r) { return *this = *this+r; }
Fra operator - (Fra &r) { return (-r) + *this; }
Fra operator -= (Fra &r) { return *this = *this-r; }
Fra operator * (Fra &r) {
ll m,n;
m = p*r.p;
n = q*r.q;
normal(m,n);
return {m,n};
}
Fra operator *= (Fra &r) { return (*this) = (*this)*r; }
Fra operator /(Fra &r) { return Fra(r.q,r.p) * (*this); }
Fra operator /=(Fra &r) { return (*this) = (*this)/r; }
bool operator == (const Fra& r) const { return p*r.q == r.p*q; }
bool operator < (const Fra& r) const { return p*r.q < r.p*q; }
void print() { normal(p,q); if(q<)q = -q,p = -p; printf("%lld/%lld\n",p,q); }
}; const int maxn = 1e3+; const ll INF = 1e16;
int main()
{
//freopen("in.txt","r",stdin);
int n; scanf("%d",&n);
Fra Low(),High(INF);
for(int i = ; i <= n; i++){
int t; scanf("%d",&t);
Low = max(Fra(t*,i),Low);
High = min(Fra(t*+,i),High);
}
Low = Fra(n+)*Low;
High = Fra(n+)*High;
int u = (High.p-)/High.q;
int d = (Low.p)/Low.q;
if(u/ != d/) {
puts("not unique");
}else {
printf("unique\n%d",d/);
}
return ;
}
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