38-佈線問題

題目地址

思路

最小生成樹問題，普里姆演算法

程式碼

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAXVEX = 505;
const int M = 0x3f3f3f3f;
int ans = 0; //記錄最小費用
int u, v;    //頂點數，邊數
int W[1000]; //每個點與外部裝置相連所需費用
typedef struct
 
 Map
{
    int arc[MAXVEX][MAXVEX]; //鄰接矩陣
    int numVertexes;         //頂點數
} MGraph;
int lowcost[MAXVEX]; //儲存相關頂點間邊的權值
void MiniSpanTree_Prim(MGraph *G)
{
    int minx;

    for (int i = 1; i <= G->numVertexes; i++)
    {
        lowcost[i] = G->arc[1][i]; //將與之有邊的權值存入陣列，記錄1和i之間的權值
    }
    lowcost[
 
1] = 0;
    for (int i = 1; i <G->numVertexes; i++)
    {
        minx = M; //初始化最小權值為無窮
        int j = 1, k;
        while (j <= G->numVertexes)
        {
            if (lowcost[j] != 0 && lowcost[j] < minx)
            {
                minx = lowcost[j];
                k = j;
 
 //將當前最小值的下表存入k
            }
            j++;
        }
        //cout<<adjvex[k]<<" "<<k<<endl;
        ans += minx;
        //cout<<ans<<endl;
        lowcost[k] = 0; //將當前定點的權值設定為0，表示此頂點已經完成任務
        for (j = 1; j <= G->numVertexes; j++)
        {
            if (lowcost[j] != 0 && G->arc[k][j] < lowcost[j])
            {
                lowcost[j] = G->arc[k][j]; //將較小權值存入lowcost
            }
        }
    }
}
int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        MGraph G;
        //memset(G.arc,M,sizeof(G.arc));
        memset(lowcost, 0, sizeof(lowcost));
        cin >> u >> v;
        int x, y, s; //x,y相連的點，s是x,y之間點路費
        G.numVertexes = u;
        for (int i = 0; i <= u; i++)
        {
            for (int j = 0; j <= u; j++)
                G.arc[i][j] = M;
        }
        for (int i = 0; i <= u; i++)
            G.arc[i][i] = 0;
        for (int i = 1; i <= v; i++)
        {
            cin >> x >> y >> s;
            G.arc[x][y] = G.arc[y][x] = s;
            // cout<<G.arc[x][y]<<" "<<G.arc[y][x]<<endl;
        }
        for (int i = 0; i < u; i++)
        {
            cin >> W[i];
        }
        sort(W, W + u);
        ans = 0;
        MiniSpanTree_Prim(&G);
        ans += W[0];
        cout << ans << endl;
    }
    return 0;
}