图论 --- BFS + MST

#include<queue>
#include<cstdio>
#define INF 1<<30
#include<cstring>
#include<algorithm>
using namespace std;

int n,m,ans,cnt;
struct Node
{
    int x,y,step;
};
Node node[110];
int row,line;
int dist[60];
char Map[60][60];
bool vis[60][60],vist[60]; //邻接矩阵存储
int mark[60][60],dis[110][110];     //给每个字母一个编号
int dir[4][2]={-1,0, 0,1, 1,0, 0,-1};

void bfs(int index)
{
    queue<Node> que;
    memset(vis, false, sizeof(vis));
    Node now, next;
    node[index].step = 0;
    que.push(node[index]);
    vis[node[index].x][node[index].y] = true;
    while(!que.empty())
    {
        now = que.front();
        que.pop();
        int x = now.x, y = now.y;
        for(int i = 0; i < 4; ++i)
        {
            int tx = x + dir[i][0], ty = y +dir[i][1];
            if(vis[tx][ty] == false && Map[tx][ty] != ‘#‘) //如果这一步可以走
            {
                next.x = tx;
                next.y = ty;
                vis[tx][ty] = true;
                next.step = now.step + 1;
                que.push(next);
                if(Map[next.x][next.y] == ‘A‘ || Map[next.x][next.y] == ‘S‘)
                    dis[ mark[ node[index].x ][ node[index].y ] ][ mark[next.x][next.y] ] = next.step;
            }

        }
    }
}


int prim()
{
    for(int i = 0; i < cnt; ++i)
    {
        dist[i] = INF;
        vist[i] = false;
    }
    dist[0] = 0;
    while(1)
    {
        int min = INF, now = -1;
        for(int i = 0; i < cnt; ++i)
        {
            if(min > dist[i] && vist[i] == false)
            {
                min = dist[i];
                now = i;
            }
        }
        if(now == -1)
            return ans;
        ans += min;
        vist[now] = true;
        for(int i = 0; i < cnt; ++i)
            if(vist[i] == false && dist[i] > dis[now][i])
                dist[i] = dis[now][i];
    }
    return ans;
}

int main()
{
    int n_case;
    scanf("%d", &n_case);
    while(n_case--)
    {
        cnt = ans = 0;
        memset(mark, 0, sizeof(mark));
        scanf("%d%d", &row, &line);
        char ch;
        while(ch = getchar(), ch != ‘\n‘);
        for(int i = 0; i < line; ++i)
        {
            for(int j = 0; j < row; ++j)
            {
                Map[i][j] = getchar();
                if(Map[i][j] == ‘A‘ || Map[i][j] == ‘S‘)
                {
                    mark[i][j] = cnt;
                    node[cnt].x = i;
                    node[cnt++].y = j;
                }
            }
            while(ch = getchar(), ch != ‘\n‘);
        }
        for(int i = 0; i < cnt; ++i)
            bfs(i);  
        prim();
        printf("%d\n", ans);
    }
    return 0;
}