Uva 1599 最佳路径

题目链接:https://uva.onlinejudge.org/external/15/1599.pdf

 

题意: 保证在最短路的时候,输出字典序最小的路径。

方法:

路径上有了权值,可以利用图论的数据结构来BFS,很方便。

逆序BFS,找到每个点距离终点的最短路长 d[x] ;

然后,从起点,沿着 d[u] = d[v] + 1; 的路径,分层BFS,选字典序最小的。找到那个最小字典序的节点之后,从新建队列。直到找完 d[0];

#include 
using namespace std;

const int maxn = 100000 + 5;
const int INF = 1000000000;

struct Edge
{
    int u,v,c;
    Edge(int u=0,int v = 0,int c = 0) : u(u),v(v),c(c) {}
};

int n,m;
vector edges;
vector<int> G[maxn];

void AddEdge(int from,int to,int c)
{
    edges.push_back(Edge(from,to,c));
    int idx = edges.size();
    G[from].push_back(idx-1);
}

int d[maxn];
bool vis[maxn];
vector<int> ans;

void rev_bfs()
{
    memset(vis, 0, sizeof(vis));
    d[n-1] = 0;
    vis[n-1] = true;

    queue<int> q;
    q.push(n-1);
    while(!q.empty())
    {
        int u = q.front();
        q.pop();
        for(int i = 0; i < G[u].size(); i++)
        {
            Edge _edge = edges[G[u][i]];
            int v = _edge.v;
            if(!vis[v])
            {
                vis[v] = true;
                d[v] = d[u] + 1;
                q.push(v);
            }
        }
    }
}


void bfs()
{
    memset(vis,0,sizeof(vis));
    vector<int> next;
    next.push_back(0);
    vector<int> ans;
    for(int i=0; i0]; i++)
    {
        int min_color = INF;

        for(int j=0; j///队列中一个级别的结点
        {
            int u = next[j];

            for(int k=0; k)
            {
                Edge _edge = edges[G[u][k]];
                int v = _edge.v;
                if(d[u]==d[v]+1)
                    min_color = min(min_color,_edge.c);
            }

        }
        ans.push_back(min_color);

        vector<int> next2;

        for(int j=0; j)
        {
            int u = next[j];
            for(int k=0; k)
            {
                Edge _edge = edges[G[u][k]];
                int v = _edge.v;
                if(d[u]==d[v]+1&&vis[v]==false&&_edge.c==min_color)
                {
                    vis[v] = 1;
                    next2.push_back(v);
                }
            }
        }
        next = next2;
    }

    printf("%d\n", ans.size());
    printf("%d", ans[0]);
    for(int i = 1; i < ans.size(); i++)
        printf(" %d", ans[i]);
    printf("\n");

}


int main()
{
    while(~scanf("%d%d",&n,&m))
    {
        memset(d,0,sizeof(d));
        edges.clear();
        for(int i=0;i)
            G[i].clear();
        for(int i=0; i)
        {
            int u,v,c;
            scanf("%d%d%d",&u,&v,&c);
            u--;
            v--;
            AddEdge(u,v,c);
            AddEdge(v,u,c);
        }
        rev_bfs();
        bfs();
    }

    return 0;
}
View Code

 

转载于:https://www.cnblogs.com/TreeDream/p/6052685.html

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