Submission #767590

#	Time	Username	Problem	Language	Result	Execution time	Memory
767590		canadavid1	Graph (BOI20_graph)	C++17	100 / 100	121 ms	22004 KiB

Graph

	#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 (stderr)

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 / 5
• Subtask 2: 12 / 12
• Subtask 3: 17 / 17
• Subtask 4: 24 / 24
• Subtask 5: 42 / 42