input:slope.in output:slope.out

Time Limits: 1000 ms Memory Limits: 131072 KB

Description

Input

Output

Sample Input

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6 15698 17433
112412868 636515040
122123982 526131695
58758943 343718480
447544052 640491230
162809501 315494932
870543506 895723090

Sample Output

1
193409386/235911335

Data Constraint

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#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 200005
int n;
ll P, Q, p, q;
double k = 1000000000, lastk;
struct Point {
    ll x, y;
    int num;
}s[N],t[N];
ll gcd(ll a, ll b) {return !b ? a : gcd(b, a % b);}
bool cmp(Point a, Point b) {return a.y < b.y;}
double Abs(double x) {return x < 0 ? -x : x;}
double getk(Point a, Point b) {
    return (double)(b.y - a.y) / (double)(b.x - a.x);
}
int main() {
    freopen("slope.in", "r", stdin);
    freopen("slope.out", "w", stdout);
    scanf("%d%d%d", &n, &P, &Q);
    for (int i = 1; i <= n; i++) {
        scanf("%lld%lld", &s[i].x, &s[i].y);
        t[i].x = Q * s[i].x;
        t[i].y = Q * s[i].y - P * s[i].x;
        t[i].num = i;
    }
    sort(t + 1, t + n + 1, cmp);
    for (int i = 1; i < n; i++) {
        double nowk = Abs(getk(t[i], t[i + 1]));
        if (nowk < k) {
            k = nowk;
            p = s[t[i + 1].num].y - s[t[i].num].y;
            q = s[t[i + 1].num].x - s[t[i].num].x;
            lastk = getk(s[t[i].num], s[t[i + 1].num]);
        }
        else if (nowk == k) {
            nowk = getk(s[t[i].num], s[t[i + 1].num]);
            if (nowk < lastk) {
                lastk = nowk;
                p = s[t[i + 1].num].y - s[t[i].num].y;
                q = s[t[i + 1].num].x - s[t[i].num].x;
            }
        }
    }
    p = Abs(p); q = Abs(q);
    ll g = gcd(p, q);
    printf("%lld/%lld\n", p / g, q / g);
    return 0;
}