Submission #406365

#	Time	Username	Problem	Language	Result	Execution time	Memory
406365		aryan12	Travelling Merchant (APIO17_merchant)	C++17	100 / 100	98 ms	4296 KiB

merchant

#include <bits/stdc++.h>
using namespace std;
#define int long long

mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());

const int N = 110, K = 1010;
 
int nodes, edges, items;
int buy[N][K], sell[N][K];
int value[N][N], dist[N][N];
 
bool Check(long long x) {
    long long efficiency[N][N];
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            efficiency[i][j] = -1e16;
        }
    }
    for(int i = 1; i <= nodes; i++) {
        for(int j = 1; j <= nodes; j++) {
            if(dist[i][j] != 1e16) {
                efficiency[i][j] = max(efficiency[i][j], value[i][j] - dist[i][j] * x);
            }
        }
    }
    for(int k = 1; k <= nodes; k++) {
        for(int i = 1; i <= nodes; i++) {
            for(int j = 1; j <= nodes; j++) {
                efficiency[i][j] = max(efficiency[i][j], efficiency[i][k] + efficiency[k][j]);
            }
        }
    }
    /*cout << "Outputing the efficiency\n";
    for(int i = 1; i <= nodes; i++) {
        for(int j = 1; j <= nodes; j++) {
            cout << efficiency[i][j] << " ";
        }
        cout << "\n";
    }*/
    for(int i = 1; i <= nodes; i++) {
        if(efficiency[i][i] >= 0)
            return true;
    }
    return false;
}

void Solve() {
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            dist[i][j] = 1e16;
            value[i][j] = 0;
        }
    }
    cin >> nodes >> edges >> items;
    for(int i = 1; i <= nodes; i++) {
        for(int j = 1; j <= items; j++) {
            cin >> buy[i][j] >> sell[i][j];
        }
    }
    for(int i = 1; i <= edges; i++) {
        int v, u, w;
        cin >> v >> u >> w;
        dist[v][u] = w;
    }
    for(int k = 1; k <= nodes; k++) {
        for(int i = 1; i <= nodes; i++) {
            for(int j = 1; j <= nodes; j++) {
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
    for(int item_number = 1; item_number <= items; item_number++) {
        for(int buy_node = 1; buy_node <= nodes; buy_node++) {
            for(int sell_node = 1; sell_node <= nodes; sell_node++) {
                if(buy[buy_node][item_number] != -1 && sell[sell_node][item_number] != -1 && dist[buy_node][sell_node] != 1e15) {
                    value[buy_node][sell_node] = max(value[buy_node][sell_node], sell[sell_node][item_number] - buy[buy_node][item_number]);
                }
            }
        }
    }
    /*cout << "Minimum distance to travel from a pair of indices (i, j) are as follows: \n";
    for(int i = 1; i <= nodes; i++) {
        for(int j = 1; j <= nodes; j++) {
            cout << dist[i][j] << " ";
        }
        cout << "\n";
    }

    cout << "Maximum value which can be gained when travelling from i to j is as follows: \n";
    for(int i = 1; i <= nodes; i++) {
        for(int j = 1; j <= nodes; j++) {
            cout << value[i][j] << " ";
        }
        cout << "\n";
    }*/

    int ans = 0;
    int left = 0, right = 1e10;
    while(left <= right) {
        int mid = (left + right) >> 1;
        if(Check(mid)) {
            ans = mid;
            left = mid + 1;
        }
        else {
            right = mid - 1;
        }
    }
    cout << ans << "\n";
}

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    Solve();
    return 0;
}

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