Submission #249406

#	Time	Username	Problem	Language	Result	Execution time	Memory
249406		godwind	Travelling Merchant (APIO17_merchant)	C++14	33 / 100	710 ms	2300 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][N];

bool gr(double x, double y) {
	return x > y + eps;
}

bool check(double x) {
	for (int i = 1; i <= n; ++i) {
		for (int j = 1; j <= n; ++j) {
			d[i][j] = -INF;
		}
	}
	for (int a = 1; a <= n; ++a) {
		for (int b = 1; b <= n; ++b) {
			if (a == b) continue;
			if (dist[a][b] < INF) {
				double weight = (double)max_profit[a][b] - (double)dist[a][b] * x;
				d[a][b] = weight;
			}
		}
	}
	for (int k = 1; k <= n; ++k) {
		for (int i = 1; i <= n; ++i) {
			for (int j = 1; j <= n; ++j) {
				if (d[i][k] > -INF / 2 && d[k][j] > -INF / 2) {
					uax(d[i][j], d[i][k] + d[k][j]);
				}
			}
		}
	}
	for (int i = 1; i <= n; ++i) {
		if (gr(d[i][i], 0)) {
			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: 33 / 33
• Subtask 4: 0 / 34