oj.uz

Submission #767329

# Submission time Handle Problem Language Result Execution time Memory
767329 2023-06-26T15:48:53 Z GrindMachine Travelling Merchant (APIO17_merchant) C++17
100 / 100
 72 ms 2236 KB 
// Om Namah Shivaya

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a, b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a, b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

refs:
https://usaco.guide/problems/apio-2017traveling-merchant/solution
https://pastebin.com/raw/ZrNfjLpg (make sure to handle overflows!)
some submissions to identify the bug in my code (found bug in taking inputs)


profit = cost/length
lets say profit = cost (we ignore length for now)

how to solve for this case?

for every pair (u,v), create an edge if v is reachable from u
this graph says: if we are @u with an empty bag, we buy something @u, then sell it @v, what's the max profit?
the weights of the edges denote this profit
(we can also choose to buy nothing, weight = 0)

find the max cost cycle (inf possible)

come back to original problem

profit = cost/length
we also consider length

so when buying something from u and selling it @v, it's optimal to take the shortest path from u to v
so for every pair (u,v), we compute:
(max_add, shortest_path)

profit function is a ratio, annoying to deal with

think b.s in such cases

how to check if profit >= mid?
cost/length >= mid
cost >= mid*length
cost - mid*length >= 0

edge (max_add, shortest_path) becomes:
edge with weight (max_add - mid*shortest_path)

find if there is a cycle with sum of weights >= 0
=> floyd-warshalls

*/

const int MOD = 1e9 + 7;
const int N = 100 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
const int K = 1e3 + 5;

ll buy[N][K], sell[N][K];
ll sp[N][N], best_buy_sell[N][N];
ll weight[N][N], lp[N][N]; // lp = longest path

void solve(int test_case)
{
    ll n,m,k; cin >> n >> m >> k;
    rep1(i,n){
        rep1(j,k){
            cin >> buy[i][j] >> sell[i][j];
        }
    }

    memset(sp,0x10,sizeof sp);

    rep1(i,m){
        ll u,v,w; cin >> u >> v >> w;
        sp[u][v] = w;
    }

    rep1(p,n){
        rep1(i,n){
            rep1(j,n){
                amin(sp[i][j], sp[i][p] + sp[p][j]);
            }
        }
    }

    rep1(i,n){
        rep1(j,n){
            if(i == j) conts;
            if(sp[i][j] >= inf2) conts;

            rep1(p,k){
                if(buy[i][p] != -1 and sell[j][p] != -1){
                    ll val = sell[j][p] - buy[i][p];
                    amax(best_buy_sell[i][j], val);
                }
            }
        }
    }

    auto ok = [&](ll mid){
        memset(weight,-0x10,sizeof weight);
        memset(lp,-0x10,sizeof lp);

        rep1(i,n){
            rep1(j,n){
                if(i == j) conts;
                if(sp[i][j] >= inf2) conts;
                ll w = best_buy_sell[i][j] - mid*sp[i][j];
                if(w > -inf2){
                    weight[i][j] = lp[i][j] = w;                                
                }
            }
        }

        rep1(p,n){
            rep1(i,n){
                rep1(j,n){
                    amax(lp[i][j], lp[i][p] + lp[p][j]);
                    amin(lp[i][j], inf2);
                }
            }
        }

        rep1(i,n){
            rep1(j,n){
                if(i == j) conts;

                ll w = lp[i][j] + lp[j][i];
                if(w >= 0){
                    return true;
                }
            }
        }

        return false;
    };

    ll l = 0, r = inf1;
    ll ans = -inf2;

    while(l <= r){
        ll mid = (l+r) >> 1;
        if(ok(mid)){
            ans = mid;
            l = mid+1;
        }
        else{
            r = mid-1;
        }
    }

    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 56 ms 2152 KB Output is correct
2 Correct 38 ms 1364 KB Output is correct
3 Correct 41 ms 1456 KB Output is correct
4 Correct 5 ms 996 KB Output is correct
5 Correct 6 ms 980 KB Output is correct
6 Correct 6 ms 980 KB Output is correct
7 Correct 6 ms 980 KB Output is correct
8 Correct 1 ms 596 KB Output is correct
9 Correct 5 ms 980 KB Output is correct
10 Correct 5 ms 980 KB Output is correct
11 Correct 5 ms 980 KB Output is correct
12 Correct 1 ms 596 KB Output is correct
13 Correct 7 ms 980 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 980 KB Output is correct
2 Correct 6 ms 980 KB Output is correct
3 Correct 1 ms 596 KB Output is correct
4 Correct 5 ms 980 KB Output is correct
5 Correct 5 ms 980 KB Output is correct
6 Correct 5 ms 980 KB Output is correct
7 Correct 1 ms 596 KB Output is correct
8 Correct 7 ms 980 KB Output is correct
9 Correct 6 ms 1048 KB Output is correct
10 Correct 5 ms 980 KB Output is correct
11 Correct 6 ms 1080 KB Output is correct
12 Correct 5 ms 980 KB Output is correct
13 Correct 6 ms 980 KB Output is correct
14 Correct 1 ms 596 KB Output is correct
15 Correct 6 ms 980 KB Output is correct
16 Correct 6 ms 980 KB Output is correct
17 Correct 6 ms 1040 KB Output is correct
18 Correct 6 ms 1048 KB Output is correct
19 Correct 6 ms 980 KB Output is correct
20 Correct 6 ms 980 KB Output is correct
21 Correct 6 ms 980 KB Output is correct
22 Correct 7 ms 1052 KB Output is correct
23 Correct 6 ms 980 KB Output is correct
24 Correct 5 ms 1028 KB Output is correct
25 Correct 6 ms 980 KB Output is correct
26 Correct 1 ms 596 KB Output is correct
27 Correct 6 ms 980 KB Output is correct
28 Correct 6 ms 980 KB Output is correct
29 Correct 6 ms 1088 KB Output is correct
30 Correct 6 ms 1040 KB Output is correct
31 Correct 5 ms 980 KB Output is correct

Subtask #3
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 980 KB Output is correct
2 Correct 1 ms 596 KB Output is correct
3 Correct 6 ms 980 KB Output is correct
4 Correct 6 ms 980 KB Output is correct
5 Correct 6 ms 1088 KB Output is correct
6 Correct 6 ms 1040 KB Output is correct
7 Correct 5 ms 980 KB Output is correct
8 Correct 41 ms 1648 KB Output is correct
9 Correct 72 ms 2208 KB Output is correct
10 Correct 39 ms 1524 KB Output is correct
11 Correct 41 ms 1620 KB Output is correct
12 Correct 41 ms 1528 KB Output is correct
13 Correct 39 ms 1492 KB Output is correct

Subtask #4
34.0 / 34.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 1048 KB Output is correct
2 Correct 5 ms 980 KB Output is correct
3 Correct 6 ms 1080 KB Output is correct
4 Correct 5 ms 980 KB Output is correct
5 Correct 6 ms 980 KB Output is correct
6 Correct 1 ms 596 KB Output is correct
7 Correct 6 ms 980 KB Output is correct
8 Correct 6 ms 980 KB Output is correct
9 Correct 6 ms 1040 KB Output is correct
10 Correct 6 ms 1048 KB Output is correct
11 Correct 6 ms 980 KB Output is correct
12 Correct 6 ms 980 KB Output is correct
13 Correct 6 ms 980 KB Output is correct
14 Correct 7 ms 1052 KB Output is correct
15 Correct 6 ms 980 KB Output is correct
16 Correct 5 ms 1028 KB Output is correct
17 Correct 41 ms 1648 KB Output is correct
18 Correct 72 ms 2208 KB Output is correct
19 Correct 39 ms 1524 KB Output is correct
20 Correct 41 ms 1620 KB Output is correct
21 Correct 41 ms 1528 KB Output is correct
22 Correct 39 ms 1492 KB Output is correct
23 Correct 6 ms 980 KB Output is correct
24 Correct 1 ms 596 KB Output is correct
25 Correct 6 ms 980 KB Output is correct
26 Correct 6 ms 980 KB Output is correct
27 Correct 6 ms 1088 KB Output is correct
28 Correct 6 ms 1040 KB Output is correct
29 Correct 5 ms 980 KB Output is correct
30 Correct 56 ms 2152 KB Output is correct
31 Correct 38 ms 1364 KB Output is correct
32 Correct 41 ms 1456 KB Output is correct
33 Correct 5 ms 996 KB Output is correct
34 Correct 6 ms 980 KB Output is correct
35 Correct 6 ms 980 KB Output is correct
36 Correct 6 ms 980 KB Output is correct
37 Correct 1 ms 596 KB Output is correct
38 Correct 5 ms 980 KB Output is correct
39 Correct 5 ms 980 KB Output is correct
40 Correct 5 ms 980 KB Output is correct
41 Correct 1 ms 596 KB Output is correct
42 Correct 7 ms 980 KB Output is correct
43 Correct 39 ms 1492 KB Output is correct
44 Correct 40 ms 1620 KB Output is correct
45 Correct 54 ms 2236 KB Output is correct
46 Correct 40 ms 1620 KB Output is correct
47 Correct 46 ms 1620 KB Output is correct
48 Correct 40 ms 1620 KB Output is correct
49 Correct 69 ms 2228 KB Output is correct
50 Correct 1 ms 596 KB Output is correct
51 Correct 1 ms 596 KB Output is correct
52 Correct 39 ms 1364 KB Output is correct
53 Correct 46 ms 1484 KB Output is correct
54 Correct 39 ms 1492 KB Output is correct
55 Correct 47 ms 1416 KB Output is correct
56 Correct 40 ms 1364 KB Output is correct
57 Correct 1 ms 596 KB Output is correct
58 Correct 6 ms 1108 KB Output is correct
59 Correct 6 ms 1132 KB Output is correct
60 Correct 6 ms 1108 KB Output is correct
61 Correct 65 ms 2128 KB Output is correct
62 Correct 72 ms 2220 KB Output is correct
63 Correct 1 ms 596 KB Output is correct