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Submission #767590

# Submission time Handle Problem Language Result Execution time Memory
767590 2023-06-26T21:23:03 Z canadavid1 Graph (BOI20_graph) C++17
100 / 100
 121 ms 22004 KB 
	#include <bits/stdc++.h>

using namespace std;
struct Node
{
    vector<pair<Node*,bool>> neigh;
    int x_parity = 0; // actual value = value + x*x_parity
    float value = NAN;
    bool seen = false; // collect_all_vi
    bool seen2 = false; // set_x
    variant<float,bool> assign(float val=0,int par=1) // float - unique solution for x
    {                                                 // bool - works for any/no x
        if(!isnan(value))
        {
            if(x_parity==par) return val == value;
            // solve linear equation x * x_parity + value == x*par + val
            // x * (x_parity - par) == val - value
            // x = val - value / (x_parity - par)
            float x = ((float) val - value) / ((float) x_parity - par);
            return x;
        }
        value = val;
        x_parity = par;
        float x = NAN;
        for(auto nt : neigh)
        {
            auto n = nt.first;
            auto t = nt.second;
            auto a = n->assign((1+t)-val,-par);
            if(a.index()==0)
            {
                // unique solution for x found
                if (!isnan(x) && x != get<float>(a)) return false;
                x = get<float>(a);
            }
            else if (!get<bool>(a)) return false;
        }
        if(isnan(x)) return true;
        return x;
    }
    void collect_v_i(vector<int>& v_i) // v_i in abs(x-v_i)
    {
        if(seen) return;
        seen = true;
        v_i.push_back(-value*x_parity);
        for(auto nt : neigh) nt.first->collect_v_i(v_i);
    }
    void set_x(float x)
    {
        if(seen2) return;
        seen2 = true;
        value += x*x_parity;
        for(auto nt : neigh) nt.first->set_x(x);
    }

    // need to decide for value of x (probably small, but uncertain)
    // the total weigth is a sum of elements of type abs(v_i+x)
        // collect all v_i (traversing) - x must be some -v_i. nlogn given sorting.
    // binary search over larger/smaller than these and these elements, gives linear relationship
            
                
};



signed main()
{
    cin.tie(nullptr)->sync_with_stdio(false);
    int N,M;
    cin >> N >> M;
    vector<Node> nodes(N);
    for(int i = 0; i < M; i++)
    {
        int a,b,c;
        cin >> a >> b >> c;
        nodes[a-1].neigh.push_back({&nodes[b-1],c>1});
        nodes[b-1].neigh.push_back({&nodes[a-1],c>1});
    }
    for(int t = 0; t < N; t++)
    {
        if(!isnan(nodes[t].value)) continue; // node already seen
        auto a = nodes[t].assign();
        if(a.index()==0) // a is a float => x is fixed
        {
            float x = get<float>(a);
            nodes[t].set_x(x); // recursive
        }
        else
        {
            // a is a bool.
            if (!get<bool>(a))
            {
                cout << "NO\n";
                exit(0);
            } // not possible.
            // need to figure out optimal value for x.
            vector<int> vi;
            nodes[t].collect_v_i(vi);
            sort(vi.begin(),vi.end());
            int x = vi[0];
            int cost = 0;
            for(auto i : vi) cost += (i-x);
            int min_cost = cost;
            int min_x = x;
            for(int i = 1; i < vi.size(); i++)
            {
                int next_x = vi[i];
                cost -= (next_x-x)*(vi.size()-i);
                cost += (next_x-x)*(i);
                x = next_x;
                if (min_cost > cost)
                {
                    min_cost = cost;
                    min_x = x;
                }
                
            }
            nodes[t].set_x(min_x);
        }
    }
    cout << "YES\n" << nodes[0].value;
    for(int i = 1; i < N; i++) cout << " " << nodes[i].value;
    cout << "\n";
    // assign "x" to some node
    // continue traversing, getting either x+int or int-x for some edges
    // if reencounter, might constrain x, set.
    // repeat for all connected components
    
}

Compilation message

Graph.cpp: In function 'int main()':
Graph.cpp:105:30: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  105 |             for(int i = 1; i < vi.size(); i++)
      |                            ~~^~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 0 ms 212 KB answer = YES
3 Correct 1 ms 324 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 0 ms 212 KB answer = YES
6 Correct 0 ms 212 KB answer = YES
7 Correct 0 ms 320 KB answer = YES
8 Correct 0 ms 212 KB answer = YES
9 Correct 1 ms 316 KB answer = NO
10 Correct 0 ms 320 KB answer = YES
11 Correct 1 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 324 KB answer = YES
14 Correct 1 ms 320 KB answer = YES
15 Correct 0 ms 212 KB answer = YES
16 Correct 1 ms 320 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 320 KB answer = YES
19 Correct 1 ms 316 KB answer = YES
20 Correct 0 ms 316 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 0 ms 212 KB answer = YES
3 Correct 1 ms 324 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 0 ms 212 KB answer = YES
6 Correct 0 ms 212 KB answer = YES
7 Correct 0 ms 320 KB answer = YES
8 Correct 0 ms 212 KB answer = YES
9 Correct 1 ms 316 KB answer = NO
10 Correct 0 ms 320 KB answer = YES
11 Correct 1 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 324 KB answer = YES
14 Correct 1 ms 320 KB answer = YES
15 Correct 0 ms 212 KB answer = YES
16 Correct 1 ms 320 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 320 KB answer = YES
19 Correct 1 ms 316 KB answer = YES
20 Correct 0 ms 316 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 320 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 316 KB answer = YES
30 Correct 1 ms 212 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 316 KB answer = YES
36 Correct 1 ms 212 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 0 ms 212 KB answer = YES
3 Correct 1 ms 324 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 0 ms 212 KB answer = YES
6 Correct 0 ms 212 KB answer = YES
7 Correct 0 ms 320 KB answer = YES
8 Correct 0 ms 212 KB answer = YES
9 Correct 1 ms 316 KB answer = NO
10 Correct 0 ms 320 KB answer = YES
11 Correct 1 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 324 KB answer = YES
14 Correct 1 ms 320 KB answer = YES
15 Correct 0 ms 212 KB answer = YES
16 Correct 1 ms 320 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 320 KB answer = YES
19 Correct 1 ms 316 KB answer = YES
20 Correct 0 ms 316 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 320 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 316 KB answer = YES
30 Correct 1 ms 212 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 316 KB answer = YES
36 Correct 1 ms 212 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 1 ms 340 KB answer = YES
43 Correct 1 ms 340 KB answer = YES
44 Correct 1 ms 340 KB answer = YES
45 Correct 1 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 1 ms 340 KB answer = YES
48 Correct 1 ms 340 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 0 ms 212 KB answer = YES
3 Correct 1 ms 324 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 0 ms 212 KB answer = YES
6 Correct 0 ms 212 KB answer = YES
7 Correct 0 ms 320 KB answer = YES
8 Correct 0 ms 212 KB answer = YES
9 Correct 1 ms 316 KB answer = NO
10 Correct 0 ms 320 KB answer = YES
11 Correct 1 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 324 KB answer = YES
14 Correct 1 ms 320 KB answer = YES
15 Correct 0 ms 212 KB answer = YES
16 Correct 1 ms 320 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 320 KB answer = YES
19 Correct 1 ms 316 KB answer = YES
20 Correct 0 ms 316 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 320 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 316 KB answer = YES
30 Correct 1 ms 212 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 316 KB answer = YES
36 Correct 1 ms 212 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 1 ms 340 KB answer = YES
43 Correct 1 ms 340 KB answer = YES
44 Correct 1 ms 340 KB answer = YES
45 Correct 1 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 1 ms 340 KB answer = YES
48 Correct 1 ms 340 KB answer = YES
49 Correct 7 ms 1356 KB answer = YES
50 Correct 7 ms 1492 KB answer = YES
51 Correct 7 ms 1588 KB answer = YES
52 Correct 3 ms 1236 KB answer = NO
53 Correct 1 ms 340 KB answer = YES
54 Correct 2 ms 596 KB answer = YES
55 Correct 4 ms 852 KB answer = YES
56 Correct 7 ms 1364 KB answer = YES
57 Correct 7 ms 1236 KB answer = YES
58 Correct 6 ms 1312 KB answer = YES
59 Correct 6 ms 1236 KB answer = YES
60 Correct 7 ms 1364 KB answer = YES
61 Correct 3 ms 852 KB answer = YES
62 Correct 40 ms 12084 KB answer = NO
63 Correct 51 ms 12384 KB answer = YES
64 Correct 41 ms 12336 KB answer = NO
65 Correct 65 ms 12376 KB answer = YES
66 Correct 2 ms 468 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 0 ms 212 KB answer = YES
3 Correct 1 ms 324 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 0 ms 212 KB answer = YES
6 Correct 0 ms 212 KB answer = YES
7 Correct 0 ms 320 KB answer = YES
8 Correct 0 ms 212 KB answer = YES
9 Correct 1 ms 316 KB answer = NO
10 Correct 0 ms 320 KB answer = YES
11 Correct 1 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 324 KB answer = YES
14 Correct 1 ms 320 KB answer = YES
15 Correct 0 ms 212 KB answer = YES
16 Correct 1 ms 320 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 320 KB answer = YES
19 Correct 1 ms 316 KB answer = YES
20 Correct 0 ms 316 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 320 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 316 KB answer = YES
30 Correct 1 ms 212 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 316 KB answer = YES
36 Correct 1 ms 212 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 1 ms 340 KB answer = YES
43 Correct 1 ms 340 KB answer = YES
44 Correct 1 ms 340 KB answer = YES
45 Correct 1 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 1 ms 340 KB answer = YES
48 Correct 1 ms 340 KB answer = YES
49 Correct 7 ms 1356 KB answer = YES
50 Correct 7 ms 1492 KB answer = YES
51 Correct 7 ms 1588 KB answer = YES
52 Correct 3 ms 1236 KB answer = NO
53 Correct 1 ms 340 KB answer = YES
54 Correct 2 ms 596 KB answer = YES
55 Correct 4 ms 852 KB answer = YES
56 Correct 7 ms 1364 KB answer = YES
57 Correct 7 ms 1236 KB answer = YES
58 Correct 6 ms 1312 KB answer = YES
59 Correct 6 ms 1236 KB answer = YES
60 Correct 7 ms 1364 KB answer = YES
61 Correct 3 ms 852 KB answer = YES
62 Correct 40 ms 12084 KB answer = NO
63 Correct 51 ms 12384 KB answer = YES
64 Correct 41 ms 12336 KB answer = NO
65 Correct 65 ms 12376 KB answer = YES
66 Correct 2 ms 468 KB answer = YES
67 Correct 66 ms 14788 KB answer = YES
68 Correct 69 ms 14780 KB answer = YES
69 Correct 60 ms 14336 KB answer = YES
70 Correct 90 ms 22004 KB answer = YES
71 Correct 69 ms 14572 KB answer = YES
72 Correct 70 ms 11340 KB answer = YES
73 Correct 68 ms 10836 KB answer = YES
74 Correct 43 ms 8980 KB answer = YES
75 Correct 17 ms 7764 KB answer = NO
76 Correct 9 ms 1620 KB answer = YES
77 Correct 17 ms 3028 KB answer = YES
78 Correct 28 ms 5076 KB answer = YES
79 Correct 62 ms 9820 KB answer = YES
80 Correct 46 ms 9128 KB answer = YES
81 Correct 29 ms 12212 KB answer = NO
82 Correct 89 ms 14372 KB answer = YES
83 Correct 88 ms 15084 KB answer = YES
84 Correct 86 ms 15304 KB answer = YES
85 Correct 81 ms 14716 KB answer = YES
86 Correct 62 ms 14460 KB answer = YES
87 Correct 32 ms 11872 KB answer = NO
88 Correct 108 ms 13028 KB answer = YES
89 Correct 68 ms 10500 KB answer = YES
90 Correct 68 ms 10572 KB answer = YES
91 Correct 67 ms 11080 KB answer = YES
92 Correct 33 ms 5672 KB answer = YES
93 Correct 32 ms 5520 KB answer = YES
94 Correct 52 ms 14668 KB answer = NO
95 Correct 28 ms 10828 KB answer = NO
96 Correct 121 ms 19996 KB answer = YES
97 Correct 27 ms 14156 KB answer = NO