Submission #743961

#	Time	Username	Problem	Language	Result	Execution time	Memory
743961		becaido	Travelling Merchant (APIO17_merchant)	C++17	100 / 100	94 ms	3460 KiB

merchant

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,popcnt,sse4,abm")
#include <bits/stdc++.h>
using namespace std;

#ifdef WAIMAI
#define debug(HEHE...) cout << "[" << #HEHE << "] : ", dout(HEHE)
void dout() {cout << '\n';}
template<typename T, typename...U>
void dout(T t, U...u) {cout << t << (sizeof...(u) ? ", " : ""), dout(u...);}
#else
#define debug(...) 7122
#endif

#define ll long long
#define Waimai ios::sync_with_stdio(false), cin.tie(0)
#define FOR(x,a,b) for (int x = a, I = b; x <= I; x++)
#define pb emplace_back
#define F first
#define S second

const int INF = 2e9;
const int SIZE = 105;
const int KSIZ = 1005;

int n, m, k;
vector<pair<int, int>> adj[SIZE];
int a[SIZE][KSIZ], b[SIZE][KSIZ];
int dis[SIZE][SIZE], profit[SIZE][SIZE];
ll dp[SIZE][SIZE];

bool ok(int p) {
    if (p == 0) return 1;
    FOR (i, 1, n) FOR (j, 1, n) {
        if (i == j) dp[i][j] = -INF;
        else dp[i][j] = profit[i][j] - 1ll * dis[i][j] * p;
    }
    FOR (k, 1, n) FOR (i, 1, n) FOR (j, 1, n) dp[i][j] = max(dp[i][j], dp[i][k] + dp[k][j]);
    FOR (i, 1, n) if (dp[i][i] >= 0) return 1;
    return 0;
}

void solve() {
    cin >> n >> m >> k;
    FOR (i, 1, n) FOR (j, 1, k) cin >> a[i][j] >> b[i][j];
    while (m--) {
        int a, b, w;
        cin >> a >> b >> w;
        adj[a].pb(b, w);
    }
    FOR (i, 1, n) {
        fill(dis[i] + 1, dis[i] + n + 1, INF);
        priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
        pq.emplace(dis[i][i] = 0, i);
        while (pq.size()) {
            auto [d, pos] = pq.top();
            pq.pop();
            if (d > dis[i][pos]) continue;
            for (auto [np, w] : adj[pos]) if (d + w < dis[i][np]) pq.emplace(dis[i][np] = d + w, np);
        }
    }
    FOR (i, 1, n) FOR (j, 1, n) if (i != j) {
        int mx = 0;
        FOR (x, 1, k) if (a[i][x] != -1 && b[j][x] != -1 && a[i][x] < b[j][x]) mx = max(mx, b[j][x] - a[i][x]);
        profit[i][j] = mx;
    }
    int l = 0, r = 1e9;
    while (l < r) {
        int mid = (l + r) / 2 + 1;
        if (ok(mid)) l = mid;
        else r = mid - 1;
    }
    cout << l << '\n';
}

int main() {
    Waimai;
    solve();
}
/*
in1
4 5 2
10 9 5 2
6 4 20 15
9 7 10 9
-1 -1 16 11
1 2 3
2 3 3
1 4 1
4 3 1
3 1 1
out1
2
*/

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