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Submission #558774

# Submission time Handle Problem Language Result Execution time Memory
558774 2022-05-08T10:04:20 Z kwongweng Travelling Merchant (APIO17_merchant) C++17
100 / 100
 67 ms 2128 KB 
/*
Solution for APIO 2016 - Merchant
Tags : binary search, shortest path (Floyd-Warshall)
Complexity O(n^3 * log (MOD))
*/
#include <bits/stdc++.h>
using namespace std;
 
#pragma GCC target ("avx2")
#pragma GCC optimization ("Ofast")
#pragma GCC optimization ("unroll-loops")
 
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef long double ld;
typedef pair<ll, ll> pll;
#define FOR(i, a, b) for(int i = a; i < b; i++)
#define ROF(i, a, b) for(int i = a; i >= b; i--)
#define ms memset
#define pb push_back
#define fi first
#define se second
 
ll MOD = 1000000007;
ll MOD1 = 998244353;
 
ll power(ll base, ll n){
	if (n == 0) return 1;
	if (n == 1) return base;
	ll halfn = power(base, n/2);
	if (n % 2 == 0) return (halfn * halfn) % MOD;
	return (((halfn * halfn) % MOD) * base) % MOD;
}
 
ll inverse(ll n){
	return power(n, MOD-2);
}
 
ll add(ll a, ll b){
	return (a+b) % MOD;
}
 
ll mul(ll a, ll b){
	a %= MOD;
	return (a*b) % MOD;
}
 
ll gcd(ll a, ll b){
    if (a == 1) return 1;
    if (a == 0) return b;
    return gcd(b%a, a);
}

ld pi = 3.141592653589793238;

void solve(){
    int n, m, k; cin >> n >> m >> k;
    ll b[n+1][k], s[n+1][k];
    FOR(i,1,n+1){
        FOR(j,0,k){
            cin >> b[i][j] >> s[i][j];
            //b[i][j] = buying price for jth item in ith market
            //s[i][j] = selling price
        }
    }
    ll mat[n+1][n+1];
    ms(mat,-1,sizeof(mat));
    FOR(i,0,m){
        int u, v, w; cin >> u >> v >> w;
        mat[u][v] = w;
    }
    FOR(i,1,n+1){
        FOR(j,1,n+1){
            if (mat[i][j]==-1) mat[i][j] = MOD;
        }
    }
    // O(n^3) Floyd-Warshall to find shortest distance between any 2 markets
    FOR(i,1,n+1){
        FOR(j,1,n+1){
            FOR(l,1,n+1){
                mat[j][l] = min(mat[j][l], mat[j][i]+mat[i][l]);
            }
        }
    }
    ll profit[n+1][n+1];
    FOR(i,1,n+1){
        FOR(j,1,n+1){
            ll mx = 0; // not buying/selling item
            FOR(l,0,k){
                if (b[i][l] != -1 && s[j][l] != -1) mx = max(mx, s[j][l] - b[i][l]);
            }
            profit[i][j] = mx;
            // max profit from buying an item in market i and selling it in market j
        }
    }
    ll L = 0, R = MOD;
    while (R-L>1){
        ll M = (L+R)/2;
        bool sol = false;
        // does there exist a nonnegative positive cycle?
        ll dist[n+1][n+1];
        FOR(i,1,n+1){
            FOR(j,1,n+1){
                if (mat[i][j] == MOD) dist[i][j] = -MOD;
                else dist[i][j] = profit[i][j] - M*mat[i][j];
            }
        }
        FOR(i,1,n+1){
            FOR(j,1,n+1){
                FOR(l,1,n+1){
                    dist[j][l] = max(dist[j][l], dist[j][i] + dist[i][l]);
                }
            }
        }
        FOR(i,1,n+1){
            if (dist[i][i] >= 0){
                sol = true; break;
            }
        }
        if (sol) L=M;
        else R=M;
    }
    cout << L << '\n';
    return;
}
 
int main() {
    cout << fixed << setprecision(8);
    ios::sync_with_stdio(false);
    if (fopen("input.txt", "r")) {
		freopen("input.txt", "r", stdin);
		freopen("output.txt", "w", stdout);
	}
    int TC = 1;
    //cin >> TC;
    FOR(i, 1, TC+1){
        //cout << "Case #" << i << ": ";
        solve();
    }
}

Compilation message

merchant.cpp:10: warning: ignoring '#pragma GCC optimization' [-Wunknown-pragmas]
   10 | #pragma GCC optimization ("Ofast")
      | 
merchant.cpp:11: warning: ignoring '#pragma GCC optimization' [-Wunknown-pragmas]
   11 | #pragma GCC optimization ("unroll-loops")
      | 
merchant.cpp: In function 'int main()':
merchant.cpp:133:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  133 |   freopen("input.txt", "r", stdin);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
merchant.cpp:134:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  134 |   freopen("output.txt", "w", stdout);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 53 ms 2032 KB Output is correct
2 Correct 31 ms 468 KB Output is correct
3 Correct 33 ms 532 KB Output is correct
4 Correct 5 ms 376 KB Output is correct
5 Correct 5 ms 376 KB Output is correct
6 Correct 7 ms 340 KB Output is correct
7 Correct 5 ms 340 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 5 ms 340 KB Output is correct
10 Correct 5 ms 340 KB Output is correct
11 Correct 4 ms 340 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 6 ms 340 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 340 KB Output is correct
2 Correct 5 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 5 ms 340 KB Output is correct
5 Correct 5 ms 340 KB Output is correct
6 Correct 4 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 6 ms 340 KB Output is correct
9 Correct 6 ms 340 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 6 ms 416 KB Output is correct
12 Correct 5 ms 340 KB Output is correct
13 Correct 6 ms 340 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 340 KB Output is correct
17 Correct 5 ms 340 KB Output is correct
18 Correct 5 ms 340 KB Output is correct
19 Correct 6 ms 340 KB Output is correct
20 Correct 5 ms 340 KB Output is correct
21 Correct 5 ms 340 KB Output is correct
22 Correct 4 ms 340 KB Output is correct
23 Correct 5 ms 340 KB Output is correct
24 Correct 5 ms 384 KB Output is correct
25 Correct 6 ms 412 KB Output is correct
26 Correct 0 ms 212 KB Output is correct
27 Correct 6 ms 340 KB Output is correct
28 Correct 5 ms 340 KB Output is correct
29 Correct 6 ms 416 KB Output is correct
30 Correct 5 ms 340 KB Output is correct
31 Correct 5 ms 340 KB Output is correct

Subtask #3
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 412 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 6 ms 340 KB Output is correct
4 Correct 5 ms 340 KB Output is correct
5 Correct 6 ms 416 KB Output is correct
6 Correct 5 ms 340 KB Output is correct
7 Correct 5 ms 340 KB Output is correct
8 Correct 34 ms 688 KB Output is correct
9 Correct 61 ms 1876 KB Output is correct
10 Correct 44 ms 612 KB Output is correct
11 Correct 36 ms 596 KB Output is correct
12 Correct 38 ms 596 KB Output is correct
13 Correct 34 ms 596 KB Output is correct

Subtask #4
34.0 / 34.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 340 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 6 ms 416 KB Output is correct
4 Correct 5 ms 340 KB Output is correct
5 Correct 6 ms 340 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 340 KB Output is correct
9 Correct 5 ms 340 KB Output is correct
10 Correct 5 ms 340 KB Output is correct
11 Correct 6 ms 340 KB Output is correct
12 Correct 5 ms 340 KB Output is correct
13 Correct 5 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 5 ms 340 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 34 ms 688 KB Output is correct
18 Correct 61 ms 1876 KB Output is correct
19 Correct 44 ms 612 KB Output is correct
20 Correct 36 ms 596 KB Output is correct
21 Correct 38 ms 596 KB Output is correct
22 Correct 34 ms 596 KB Output is correct
23 Correct 6 ms 412 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 6 ms 340 KB Output is correct
26 Correct 5 ms 340 KB Output is correct
27 Correct 6 ms 416 KB Output is correct
28 Correct 5 ms 340 KB Output is correct
29 Correct 5 ms 340 KB Output is correct
30 Correct 53 ms 2032 KB Output is correct
31 Correct 31 ms 468 KB Output is correct
32 Correct 33 ms 532 KB Output is correct
33 Correct 5 ms 376 KB Output is correct
34 Correct 5 ms 376 KB Output is correct
35 Correct 7 ms 340 KB Output is correct
36 Correct 5 ms 340 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 5 ms 340 KB Output is correct
39 Correct 5 ms 340 KB Output is correct
40 Correct 4 ms 340 KB Output is correct
41 Correct 0 ms 212 KB Output is correct
42 Correct 6 ms 340 KB Output is correct
43 Correct 35 ms 568 KB Output is correct
44 Correct 37 ms 700 KB Output is correct
45 Correct 52 ms 1796 KB Output is correct
46 Correct 34 ms 596 KB Output is correct
47 Correct 45 ms 716 KB Output is correct
48 Correct 38 ms 596 KB Output is correct
49 Correct 67 ms 2116 KB Output is correct
50 Correct 0 ms 212 KB Output is correct
51 Correct 0 ms 212 KB Output is correct
52 Correct 31 ms 468 KB Output is correct
53 Correct 34 ms 548 KB Output is correct
54 Correct 32 ms 596 KB Output is correct
55 Correct 31 ms 596 KB Output is correct
56 Correct 36 ms 552 KB Output is correct
57 Correct 0 ms 212 KB Output is correct
58 Correct 9 ms 340 KB Output is correct
59 Correct 7 ms 340 KB Output is correct
60 Correct 6 ms 340 KB Output is correct
61 Correct 62 ms 2036 KB Output is correct
62 Correct 63 ms 2128 KB Output is correct
63 Correct 0 ms 212 KB Output is correct