Cod sursa(job #2643591)

Utilizator Marius7122FMI Ciltea Marian Marius7122 Data 20 august 2020 15:36:26
Problema Arbore partial de cost minim Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.38 kb
// PRIM ALGORITHM

#include <iostream>
#include <fstream>
#include <vector>
#include <assert.h>

#define ll long long

using namespace std;

const int N = 200005;

ifstream fin("apm.in");
ofstream fout("apm.out");

vector<pair<int, int>> g[N];
int tata[N];
bool vis[N];
int n, m;

// <cost, nod>
class MinHeap
{
   vector<pair<int, int>> heap;
   vector<int> nodePosition;    // positia unui nod in heap
   int lastIndex;
 
public:
   MinHeap(int capacity)
   {
       lastIndex = 1;
       heap.resize(capacity + 1);
       nodePosition.resize(capacity + 1, -1);
   }
 
   void push(pair<int, int> x)
   {
       heap[lastIndex++] = x;
       nodePosition[x.second] = lastIndex - 1;
       bubbleUp(lastIndex-1);
   }
 
   void pop()
   {
        nodePosition[heap[1].second] = -1;
        heap[1] = heap[--lastIndex];
        nodePosition[heap[lastIndex].second] = 1;

        bubbleDown(1);
   }
 
   pair<int, int> top()
   {
       return heap[1];
   }
   
   int getNodeValue(int node)
   {
       int nodeIndex = nodePosition[node];
       return heap[nodeIndex].first;
   }

   void updateNodeValue(int node, int newValue)
   {
       int nodeIndex = nodePosition[node];
       heap[nodeIndex].first = newValue;
       bubbleUp(nodeIndex);
   }

   bool nodeExists(int node)
   {
       return nodePosition[node] != -1;
   }

   bool isEmpty()
   {
       return lastIndex == 1; 
   }
 
private:
   void bubbleUp(int i)
   {
       if(i == 1)
           return;
      
       if(heap[i/2] > heap[i])
       {
            swapNode(i/2, i);
            bubbleUp(i/2);
       }
   }
 
   void bubbleDown(int i)
   {
       int st = i*2;
       int dr = st+1;
 
       if(dr > lastIndex)
           return;
 
       if(heap[st] <= heap[dr] && heap[st] < heap[i])
       {
           swapNode(st, i);
           bubbleDown(st);
       }
       else if(heap[dr] <= heap[st] && heap[dr] < heap[i])
       {
           swapNode(dr, i);
           bubbleDown(dr);
       }
   }  

   void swapNode(int nodeIndex1, int nodeIndex2)
   {
        int node1 = heap[nodeIndex1].second;
        int node2 = heap[nodeIndex2].second;
        nodePosition[node1] = nodeIndex2;
        nodePosition[node2] = nodeIndex1;

        swap(heap[nodeIndex1], heap[nodeIndex2]);
   }
 
};


int main()
{
    fin >> n >> m;
    for(int i = 0; i < m; i++)
    {
        int x, y, c;
        fin >> x >> y >> c;
        g[x].push_back({y, c});
        g[y].push_back({x, c});
    }

    MinHeap heap(n);
    heap.push({0, 1});

    int costTotal = 0;
    while(!heap.isEmpty())
    {
        int nod = heap.top().second;
        costTotal += heap.top().first;
        vis[nod] = true;
        heap.pop();


        for(auto y : g[nod])
        {
            if(vis[y.first])
                continue;

            if(!heap.nodeExists(y.first))
            {
                heap.push({y.second, y.first});
                tata[y.first] = nod;
            }
            else if(y.second < heap.getNodeValue(y.first))
            {
                heap.updateNodeValue(y.first, y.second);
                tata[y.first] = nod;
            }
        }
    }

    fout << costTotal << '\n';
    fout << n - 1 << '\n';
    for(int i = 2; i <= n; i++)
        fout << i << ' ' << tata[i] << '\n';

    return 0;
}