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Submission #919154

# Submission time Handle Problem Language Result Execution time Memory
919154 2024-01-31T11:47:46 Z boris_mihov Travelling Merchant (APIO17_merchant) C++17
100 / 100
 54 ms 4184 KB 
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>

typedef long long llong;
const int MAXN = 100 + 10;
const int MAXK = 1000 + 10;
const llong INF = 1e18;
const int INTINF = 1e9;

int n, m, k;
int vis[MAXN];
bool cycleEdge[MAXN][MAXN];
llong dist[MAXN][MAXN];
llong cost[MAXN][MAXN];
llong edge[MAXN][MAXN];
llong buy[MAXN][MAXK];
llong sell[MAXN][MAXK];
llong vals[MAXN];
llong cpy[MAXN];

bool dfs(int node)
{
    vis[node] = 1;
    for (int i = 1 ; i <= n ; ++i)
    {
        if (!cycleEdge[node][i] || vis[i] == 2)
        {
            continue;
        }

        if (vis[i] == 1)
        {
            return true;
        }

        if (dfs(i))
        {
            return true;
        }
    }

    vis[node] = 2;
    return false;
}

bool check(llong c)
{
    for (int u = 1 ; u <= n ; ++u)
    {
        for (int v = 1 ; v <= n ; ++v)
        {
            if (dist[u][v] == INF)
            {
                edge[u][v] = INF;
            } else
            {
                edge[u][v] = c * dist[u][v] - cost[u][v];
            }
        }
    }

    std::fill(vals + 1, vals + 1 + n, INF);
    vals[1] = 0;

    for (int times = 1 ; times < n ; ++times)
    {
        for (int u = 1 ; u <= n ; ++u)
        {
            for (int v = 1 ; v <= n ; ++v)
            {
                if (vals[u] + edge[u][v] < vals[v])
                {
                    vals[v] = vals[u] + edge[u][v];
                }
            }
        }
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        cpy[i] = vals[i];
    }

    for (int u = 1 ; u <= n ; ++u)
    {
        for (int v = 1 ; v <= n ; ++v)
        {
            if (vals[u] + edge[u][v] < vals[v])
            {
                vals[v] = vals[u] + edge[u][v];
            }
        }
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        if (vals[i] != cpy[i])
        {
            return true;
        }
    }

    for (int u = 1 ; u <= n ; ++u)
    {
        for (int v = 1 ; v <= n ; ++v)
        {
            cycleEdge[u][v] = (v != u && vals[v] == vals[u] + edge[u][v]);
        }
    }

    std::fill(vis + 1, vis + 1 + n, 0);
    for (int i = 1 ; i <= n ; ++i)
    {
        if (!vis[i] && dfs(i))
        {
            return true;
        }
    }
    
    return false;
}

void solve()
{
    for (int mid = 1 ; mid <= n ; ++mid)
    {
        for (int from = 1 ; from <= n ; ++from)
        {
            if (from == mid) continue;
            for (int to = 1 ; to <= n ; ++to)
            {
                if (mid == to || from == to) continue;
                dist[from][to] = std::min(dist[from][to], dist[from][mid] + dist[mid][to]);
            }
        }
    }

    for (int u = 1 ; u <= n ; ++u)
    {
        for (int v = 1 ; v <= n ; ++v)
        {
            cost[u][v] = 0;
            for (int i = 1 ; i <= k ; ++i)
            {
                cost[u][v] = std::max(cost[u][v], sell[v][i] - buy[u][i]);
            }
        }
    }

    int l = 0, r = INTINF + 1, mid;
    while (l < r - 1)
    {
        mid = (l + r) / 2;
        if (check(mid)) l = mid;
        else r = mid;
    }

    std::cout << l << '\n';
}

void input()
{
    std::cin >> n >> m >> k;
    for (int i = 1 ; i <= n ; ++i)
    {
        for (int j = 1 ; j <= k ; ++j)
        {
            std::cin >> buy[i][j] >> sell[i][j];
            if (buy[i][j] == -1)
            {
                buy[i][j] = INF;
            }

            if (sell[i][j] == -1)
            {
                sell[i][j] = 0;
            }
        }
    }

    std::fill(&dist[0][0], &dist[MAXN - 1][MAXN - 1] + 1, INF);
    for (int i = 1 ; i <= m ; ++i)
    {
        llong u, v, d;
        std::cin >> u >> v >> d;
        dist[u][v] = std::min(dist[u][v], d);
    }
}

void fastIOI()
{
    std::ios_base :: sync_with_stdio(0);
    std::cout.tie(nullptr);
    std::cin.tie(nullptr);
}

int main()
{
    fastIOI();
    input();
    solve();

    return 0;
}

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 47 ms 3664 KB Output is correct
2 Correct 23 ms 1368 KB Output is correct
3 Correct 27 ms 1368 KB Output is correct
4 Correct 4 ms 856 KB Output is correct
5 Correct 4 ms 856 KB Output is correct
6 Correct 4 ms 860 KB Output is correct
7 Correct 4 ms 1112 KB Output is correct
8 Correct 1 ms 460 KB Output is correct
9 Correct 4 ms 856 KB Output is correct
10 Correct 4 ms 856 KB Output is correct
11 Correct 4 ms 860 KB Output is correct
12 Correct 1 ms 600 KB Output is correct
13 Correct 4 ms 1116 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 860 KB Output is correct
2 Correct 4 ms 1112 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 4 ms 856 KB Output is correct
5 Correct 4 ms 856 KB Output is correct
6 Correct 4 ms 860 KB Output is correct
7 Correct 1 ms 600 KB Output is correct
8 Correct 4 ms 1116 KB Output is correct
9 Correct 4 ms 856 KB Output is correct
10 Correct 5 ms 860 KB Output is correct
11 Correct 5 ms 856 KB Output is correct
12 Correct 4 ms 860 KB Output is correct
13 Correct 5 ms 1112 KB Output is correct
14 Correct 1 ms 600 KB Output is correct
15 Correct 5 ms 1112 KB Output is correct
16 Correct 4 ms 1116 KB Output is correct
17 Correct 4 ms 856 KB Output is correct
18 Correct 5 ms 1112 KB Output is correct
19 Correct 5 ms 1112 KB Output is correct
20 Correct 5 ms 1116 KB Output is correct
21 Correct 5 ms 856 KB Output is correct
22 Correct 5 ms 860 KB Output is correct
23 Correct 5 ms 1116 KB Output is correct
24 Correct 4 ms 856 KB Output is correct
25 Correct 5 ms 1112 KB Output is correct
26 Correct 1 ms 600 KB Output is correct
27 Correct 5 ms 1112 KB Output is correct
28 Correct 5 ms 1112 KB Output is correct
29 Correct 5 ms 1112 KB Output is correct
30 Correct 5 ms 1096 KB Output is correct
31 Correct 4 ms 860 KB Output is correct

Subtask #3
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1112 KB Output is correct
2 Correct 1 ms 600 KB Output is correct
3 Correct 5 ms 1112 KB Output is correct
4 Correct 5 ms 1112 KB Output is correct
5 Correct 5 ms 1112 KB Output is correct
6 Correct 5 ms 1096 KB Output is correct
7 Correct 4 ms 860 KB Output is correct
8 Correct 29 ms 1624 KB Output is correct
9 Correct 48 ms 4040 KB Output is correct
10 Correct 28 ms 1624 KB Output is correct
11 Correct 28 ms 1880 KB Output is correct
12 Correct 30 ms 1624 KB Output is correct
13 Correct 31 ms 1872 KB Output is correct

Subtask #4
34.0 / 34.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 856 KB Output is correct
2 Correct 5 ms 860 KB Output is correct
3 Correct 5 ms 856 KB Output is correct
4 Correct 4 ms 860 KB Output is correct
5 Correct 5 ms 1112 KB Output is correct
6 Correct 1 ms 600 KB Output is correct
7 Correct 5 ms 1112 KB Output is correct
8 Correct 4 ms 1116 KB Output is correct
9 Correct 4 ms 856 KB Output is correct
10 Correct 5 ms 1112 KB Output is correct
11 Correct 5 ms 1112 KB Output is correct
12 Correct 5 ms 1116 KB Output is correct
13 Correct 5 ms 856 KB Output is correct
14 Correct 5 ms 860 KB Output is correct
15 Correct 5 ms 1116 KB Output is correct
16 Correct 4 ms 856 KB Output is correct
17 Correct 29 ms 1624 KB Output is correct
18 Correct 48 ms 4040 KB Output is correct
19 Correct 28 ms 1624 KB Output is correct
20 Correct 28 ms 1880 KB Output is correct
21 Correct 30 ms 1624 KB Output is correct
22 Correct 31 ms 1872 KB Output is correct
23 Correct 5 ms 1112 KB Output is correct
24 Correct 1 ms 600 KB Output is correct
25 Correct 5 ms 1112 KB Output is correct
26 Correct 5 ms 1112 KB Output is correct
27 Correct 5 ms 1112 KB Output is correct
28 Correct 5 ms 1096 KB Output is correct
29 Correct 4 ms 860 KB Output is correct
30 Correct 47 ms 3664 KB Output is correct
31 Correct 23 ms 1368 KB Output is correct
32 Correct 27 ms 1368 KB Output is correct
33 Correct 4 ms 856 KB Output is correct
34 Correct 4 ms 856 KB Output is correct
35 Correct 4 ms 860 KB Output is correct
36 Correct 4 ms 1112 KB Output is correct
37 Correct 1 ms 460 KB Output is correct
38 Correct 4 ms 856 KB Output is correct
39 Correct 4 ms 856 KB Output is correct
40 Correct 4 ms 860 KB Output is correct
41 Correct 1 ms 600 KB Output is correct
42 Correct 4 ms 1116 KB Output is correct
43 Correct 32 ms 1368 KB Output is correct
44 Correct 26 ms 1628 KB Output is correct
45 Correct 41 ms 2696 KB Output is correct
46 Correct 27 ms 1624 KB Output is correct
47 Correct 27 ms 1624 KB Output is correct
48 Correct 26 ms 1624 KB Output is correct
49 Correct 53 ms 4176 KB Output is correct
50 Correct 1 ms 600 KB Output is correct
51 Correct 0 ms 600 KB Output is correct
52 Correct 24 ms 1372 KB Output is correct
53 Correct 26 ms 1624 KB Output is correct
54 Correct 25 ms 1624 KB Output is correct
55 Correct 25 ms 1368 KB Output is correct
56 Correct 25 ms 1368 KB Output is correct
57 Correct 1 ms 600 KB Output is correct
58 Correct 5 ms 1112 KB Output is correct
59 Correct 9 ms 1112 KB Output is correct
60 Correct 5 ms 992 KB Output is correct
61 Correct 54 ms 4184 KB Output is correct
62 Correct 53 ms 4176 KB Output is correct
63 Correct 0 ms 604 KB Output is correct