# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|---|---|---|---|---|---|---|
1160546 | jus_teng | Travelling Merchant (APIO17_merchant) | C++20 | 0 ms | 0 KiB |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double ld;
const ll maxN = 100;
const ll maxK = 1000;
const ld inf = 1e18;
const ld eps = 1e-9;
ll n, m, k;
vector<vector<pair<ll, ll>>> adj;
vector<vector<ll>> b, s;
bool check(ld lambda) {
ll v = n * (k + 1);
vector<ld> dist(v, -inf);
// Initialize starting states (no item at each market)
for (ll u = 0; u < n; u++) {
dist[u * (k + 1)] = 0; // No item state
}
// Bellman-Ford: V-1 relaxations
for (ll iter = 0; iter < v - 1; iter++) {
bool updated = false;
for (ll u = 0; u < n; u++) {
ll uNoItem = u * (k + 1);
// Buy an item
for (ll j = 0; j < k; j++) {
if (b[u][j] != -1) {
ll uWithJ = u * (k + 1) + (j + 1);
ld weight = -b[u][j];
if (dist[uNoItem] > -inf && dist[uNoItem] + weight > dist[uWithJ] + eps) {
dist[uWithJ] = dist[uNoItem] + weight;
updated = true;
}
}
}
// Sell an item
for (ll j = 0; j < k; j++) {
ll uWithJ = u * (k + 1) + (j + 1);
if (s[u][j] != -1 && dist[uWithJ] > -inf) {
ld weight = s[u][j];
if (dist[uWithJ] + weight > dist[uNoItem] + eps) {
dist[uNoItem] = dist[uWithJ] + weight;
updated = true;
}
}
}
// Move with current item state
for (auto p : adj[u]) {
ll vMarket = p.first;
ll travelTime = p.second;
for (ll c = 0; c <= k; c++) {
ll uState = u * (k + 1) + c;
ll vState = vMarket * (k + 1) + c;
ld weight = -lambda * travelTime;
if (dist[uState] > -inf && dist[uState] + weight > dist[vState] + eps) {
dist[vState] = dist[uState] + weight;
updated = true;
}
}
}
}
if (!updated) break; // Early exit if no changes
}
// Check for positive cycles
for (ll u = 0; u < n; u++) {
ll uNoItem = u * (k + 1);
for (ll j = 0; j < k; j++) {
if (b[u][j] != -1) {
ll uWithJ = u * (k + 1) + (j + 1);
ld weight = -b[u][j];
if (dist[uNoItem] + weight > dist[uWithJ] + eps) {
return true;
}
}
ll uWithJ = u * (k + 1) + (j + 1);
if (s[u][j] != -1 && dist[uWithJ] > -inf) {
ld weight = s[u][j];
if (dist[uWithJ] + weight > dist[uNoItem] + eps) {
return true;
}
}
}
for (auto p : adj[u]) {
ll vMarket = p.first;
ll travelTime = p.second;
for (ll c = 0; c <= k; c++) {
ll uState = u * (k + 1) + c;
ll vState = vMarket * (k + 1) + c;
ld weight = -lambda * travelTime;
if (dist[uState] > -inf && dist[uState] + weight > dist[vState] + eps) {
return true;
}
}
}
}
return false;
}
ll solve() {
ld low = 0.0;
ld high = 1e12;
for (int iter = 0; iter < 50; iter++) { // Reduced to 50 for speed
ld mid = (low + high) / 2.0;
if (check(mid)) {
low = mid;
} else {
high = mid;
}
}
if (!check(low)) return 0;
return (ll)floor(low + eps); // Ensure rounding handles floating-point precision
}
int main() {
scanf("%lld %lld %lld", &n, &m, &k);
b.assign(n, vector<ll>(k));
s.assign(n,