Submission #914596

#	Time	Username	Problem	Language	Result	Execution time	Memory
914596		dsyz	Travelling Merchant (APIO17_merchant)	C++17	100 / 100	66 ms	4340 KiB

merchant

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MAXN (1000005)
ll N,M,K;
ll buy[105][1005], sell[105][1005];
ll profit[105][105], graph1[105][105], graph2[105][105];
int main() {
	ios_base::sync_with_stdio(false);cin.tie(0);
	cin>>N>>M>>K;
	for(ll i = 0;i < N;i++){
		for(ll j = 0;j < N;j++){
			graph1[i][j] = 1e18;
		}
	}
	for(ll i = 0;i < N;i++){
		for(ll j = 0;j < K;j++){
			cin>>buy[i][j]>>sell[i][j]; //if buy[i][j] or sell[i][j] = -1 that means type j item cannot be bought/sold respectively at node i
		}
	}
	for(ll i = 0;i < M;i++){
		ll a,b,c;
		cin>>a>>b>>c;
		a--, b--;
		graph1[a][b] = c; //directed edge from a to b with weight c
	}
	for(ll k = 0;k < N;k++){
		for(ll i = 0;i < N;i++){
			for(ll j = 0;j < N;j++){
				graph1[i][j] = min(graph1[i][j],graph1[i][k] + graph1[k][j]);
			}
		}
	}
	for(ll i = 0;i < N;i++){
		for(ll j = 0;j < N;j++){
			for(ll k = 0;k < K;k++){ //note that this is not floyd warshall, just normal nested for loops to loop though buy[node i][item type k] and sell[node j][item type k]
				if(buy[i][k] != -1 && sell[j][k] != -1){
					profit[i][j] = max(profit[i][j],sell[j][k] - buy[i][k]); //if we buy at node i and then sell at node j, we can keep on buying the same type of most optimal item since there is infinite stock of the same type 
				}
			}
		}
	}
	ll high = 1e9 + 5;
	ll low = 0;
	while(high - low > 1){
		ll mid = (high + low) / 2;
		for(ll i = 0;i < N;i++){
			for(ll j = 0;j < N;j++){
				if(graph1[i][j] >= 1e18) graph2[i][j] = 1e18 - profit[i][j];
				else graph2[i][j] = (mid * graph1[i][j]) - profit[i][j];
			}
		}
		for(ll k = 0;k < N;k++){
			for(ll i = 0;i < N;i++){
				for(ll j = 0;j < N;j++){
					graph2[i][j] = min(graph2[i][j],graph2[i][k] + graph2[k][j]);
				}
			}
		}
		bool hasnegativecycle = false;
		for(ll i = 0;i < N;i++){
			if(graph2[i][i] <= 0){
				hasnegativecycle = true;
			}
		}
		if(hasnegativecycle){
			low = mid;
		}else{
			high = mid;
		}
	}
	cout<<low<<'\n';
}

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