K短路【模板】

A*+SPFA算法： 

(1)将有向图的所有边正向、反向分别存入两个不同的边集(Edges，Edges1)中。用反向边集，以所求终点t为源点，利用SPFA或Dijkstra求解出所有点到t的最短路径，用Dist[i]数组来表示点i到点t的最短距离。 

(2)建立一个优先队列，将源点s加入到队列中。 

(3)从优先队列中取出最小的点p，如果点p == t，则计算t出队的次数。如果当前路径长度就是s到t的第k短路长度，算法结束。否则遍历与p相连的所有的边，将扩展出的到p的邻接点信息加入到优先队列中取。 

注意： 

当s == t的时候，需要计算第k+1短路。因为s到t这条距离为0的路不能算是这k短路里边，当s == t的时候，只需要将k = k+1后再求第k短路就可以了。

<code class="hljs cpp has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<iostream></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<algorithm></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<cstdio></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<cstring></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<queue></span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">using</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">namespace</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">std</span>;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> MAXN = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1100</span>;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> MAXM = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">110000</span>;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> INF = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0xffffff0</span>;

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> EdgeNode
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> to;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> w;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> next;
}Edges[MAXM],Edges1[MAXM];

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Head[MAXN],Head1[MAXN];

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> Node
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> to;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> g,f;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">bool</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">operator</span> < (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span> Node &r) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span>
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(r.f == f)
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> r.g < g;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> r.f < f;
}
};
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> vis[MAXN],Dist[MAXN];

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> A_Star(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> start,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> end,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> N,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> k)
{
Node e,ne;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Cnt = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
priority_queue<Node> que;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(start == end)
k++;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(Dist[start] == INF)
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;
e.to = start;
e.g = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
e.f = e.g + Dist[e.to];
que.push(e);
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>( !que.empty() )
{
e = que.top();
que.pop();
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(e.to == end)
Cnt++;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(Cnt == k)
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> e.g;

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = Head[e.to]; i != -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i = Edges[i].next)
{
ne.to = Edges[i].to;
ne.g = e.g + Edges[i].w;
ne.f = ne.g + Dist[ne.to];
que.push(ne);
}
}
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;
}
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> SPFA(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> s,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> N)
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i <= N; ++i)
Dist[i] = INF;
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(vis,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(vis));
vis[s] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;
Dist[s] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
<span class="hljs-stl_container" style="box-sizing: border-box;"><span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">queue</span><<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>></span> Q;
Q.push(s);
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>( !Q.empty() )
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> u = Q.front();
Q.pop();
vis[u] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = Head1[u]; i != -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i = Edges1[i].next)
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> temp = Dist[u] + Edges1[i].w;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(temp < Dist[Edges1[i].to])
{
Dist[Edges1[i].to] = temp;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!vis[Edges1[i].to])
{
vis[Edges1[i].to] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;
Q.push(Edges1[i].to);
}
}
}
}
}

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> main()
{
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> N,M,u,v,w,s,t,k;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(~<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">scanf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d%d"</span>,&N,&M))
{
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Edges,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Edges));
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Edges1,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Edges1));
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Head,-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Head));
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Head1,-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Head1));
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i < M; ++i)
{
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">scanf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d%d%d"</span>,&u,&v,&w);
Edges[i].to = v;
Edges[i].w = w;
Edges[i].next = Head[u];
Head[u] = i;

Edges1[i].to = u;
Edges1[i].w = w;
Edges1[i].next = Head1[v];
Head1[v] = i;
}
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">scanf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d%d%d"</span>,&s,&t,&k);
SPFA(t,N);
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> kthlenth = A_Star(s,t,N,k);
<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d\n"</span>,kthlenth);
}

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
}</code>