HDU 1233: 还是畅通工程

Posted 2020-10-07

///@author Sycamore
///@date 9/16/2017
///@link http://acm.hdu.edu.cn/showproblem.php?pid=1233
#include <bits/stdc++.h>
//n:= # of vertices
//dist[i]:= distance between Vertex i and current MST
//inMST[i]:= weather Vertex i is in the MST
//parent[i]:= stores the edge (i,u) by which u is added to MST
using namespace std;
const int MAXN = 105, INF = INT_MAX/2;
int n;

//Adjacency list representation
struct Edge
{
   int to, weight;
   Edge()= default;
   Edge(int t, int w) :to(t), weight(w)
   {
   };
   //Notice that it‘s ‘>‘ in this occasion, serving as the predicate of pq
   friend bool operator<(const Edge &e, const Edge &f)
   {
      return e.weight > f.weight;
   }
};
vector<Edge>edge[MAXN];
int dist[MAXN], parent[MAXN];
bool inMST[MAXN];

void Init()
{
   for (int i = 0; i < n; i++)
   {
      edge[i].clear();
      inMST[i] = false;
      dist[i] = INF;//vital
      parent[i] = -1;
   }
}
void AddEdge(int i, int j, int w)
{
   edge[i].emplace_back(Edge(j, w));
}

//transforms the adjacency matrix into a adjacency list
void ReadInput()
{
   int i,j,w;
   for(int a=0;a<n*(n-1)/2;a++)
   {
      cin>>i>>j>>w;
      AddEdge(--i, --j, w);
      AddEdge(j,i,w);
   }
}
//a utility which counts the total weight of edges in MST
int Prim()
{
   int ret = 0;
   priority_queue<Edge>pq;
   
   //the source can be any vertex, here we start from Vertex 0
   pq.push(Edge(0, 0));
   dist[0] = 0;
   
   //totally n-1 edges in MST, because Edge(0,0) is virtual
   for (int i = 0; i<n && !pq.empty();)
   {
      //define variable u for convenience,
      //representing the vertex on which the current loop based
      int u = pq.top().to;
      if (inMST[u])//u is already put in MST
      {
         pq.pop();
         continue;
      }
      i++;
      ret += pq.top().weight;    //update ret
      inMST[u] = true;//mark it as used
      
      //for-loop to add adjacency edges of u
      for (const auto &adj : edge[u])
         if (!inMST[adj.to] && adj.weight < dist[adj.to])
         {
            pq.push(adj);
            parent[adj.to] = u;
         }
   }
   return ret;
}
int main()
{
   //speeds up cin/cout
   cin.tie(nullptr);
   ios::sync_with_stdio(false);
   while (cin >> n&&n)
   {
      Init();
      ReadInput();
      cout << Prim() << endl;
   }
   return 0;
}