Submission #249573

#	Time	Username	Problem	Language	Result	Execution time	Memory
249573		godwind	Travelling Merchant (APIO17_merchant)	C++14	0 / 100	1055 ms	2912 KiB

merchant

#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <set>
#include <map>
#include <queue>
#include <cstring>
#include <cmath>
#include <bitset>
#include <iomanip>
#include <functional>
//#include <unordered_map>
 
using namespace std;
 
template<typename T> void uin(T &a, T b) {if (b < a) a = b;}
template<typename T> void uax(T &a, T b) {if (b > a) a = b;}
 
#define int long long
#define double long double
#define left left228
#define right right228
#define mp make_pair
#define all(v) v.begin(), v.end()
 
const int N = 105, K = 1005;
const double eps = 1e-6;
const int INF = 1e18 + 228;
 
int n, m, k;
int buy[N][K], sell[N][K];
 
vector< pair<int, int> > g[N];
 
int dist[N][N];
int max_profit[N][N];
 
void pre() {
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= n; ++j) {
            dist[i][j] = INF;
        }
        dist[i][i] = 0;
    }
    for (int v = 1; v <= n; ++v) {
        for (pair<int, int> go : g[v]) {
            int to = go.first;
            int w = go.second;
            uin(dist[v][to], w);
        }
    }
    for (int k = 1; k <= n; ++k) {
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (dist[i][k] < INF && dist[k][j] < INF) {
                    uin(dist[i][j], dist[i][k] + dist[k][j]);
                }
            }
        }
    }
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= n; ++j) {
            for (int t = 1; t <= k; ++t) {
                if (buy[i][t] != -1 && sell[j][t] != -1) {
                    uax(max_profit[i][j], sell[j][t] - buy[i][t]);
                }
            }
        }
    }
}
 
double d[N], d2[N];
 
bool Gr(double x, double y) {
    return x > y + eps;
}
 
struct edge
{
    int from, to;
    double w;
    edge() {}
    edge(int _from, int _to, double _w) {
        from = _from;
        to = _to;
        w = _w;
    }
};
 
bool check(double x) {
    vector< edge > edges;
    for (int a = 1; a <= n; ++a) {
        for (int b = 1; b <= n; ++b) {
            if (dist[a][b] < INF) {
                double weight = (double)max_profit[a][b] - (double)dist[a][b] * x;
                edges.emplace_back( a, b, -weight );
            }
        }
    }
    for (int i = 1; i <= n; ++i) {
        d[i] = INF;
    }
    d[1] = 0;
 
    for (int it = 0; it < n; ++it) {
        for (auto e : edges) {
            if (d[e.from] < INF / 2 && d[e.from] + e.w < d[e.to]) {
                d[e.to] = d[e.from] + e.w;
            }
        }
    }
    for (int i = 1; i <= n; ++i) {
        d2[i] = d[i];
        if (d[i] < -INF / 2) return 1;
    }
    for (int it = 0; it < n; ++it) {
        for (auto e : edges) {
            if (d2[e.from] < INF / 2 && d2[e.from] + e.w < d2[e.to]) {
                d2[e.to] = d2[e.from] + e.w;
            }
        }
    }
    for (int i = 1; i <= n; ++i) {
        if (Gr(d[i], d2[i])) return 1;
    }
    return 0;
}
 
signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m >> k;
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= k; ++j) {
            cin >> buy[i][j] >> sell[i][j];
        }
    }
    for (int i = 0; i < m; ++i) {
        int u, v, w;
        cin >> u >> v >> w;
        g[u].emplace_back(v, w);
    }
    pre();
    double l = 0, r = 1e18;
    for (int i = 0; i < 100; ++i) {
        if (abs(r - l) <= eps) break;
        double M = (l + r) / 2.0;
        if (check(M)) {
            l = M;
        } else {
            r = M;
        }
    }
    cout << setprecision(15) << (int)r << '\n';
    return 0;
}
 
/*
 
 
*/

• Subtask 1: 0 / 12
• Subtask 2: 0 / 21
• Subtask 3: 0 / 33
• Subtask 4: 0 / 34