• LCA离线算法Tarjan的模板


    hdu 2586:题意:输入n个点的n-1条边的树,m组询问任意点 a b之间的最短距离

    思路:LCA中的Tarjan算法,RMQ还不会。。

    #include <stdio.h>
    #include <iostream>
    #include <string.h>
    using namespace std;
    const int N = 40010;
    const int M = 410;
    
    int head[N];            //树边邻接表的表头
    int __head[N];          //保存询问的邻接表的表头
    struct edge{            //保存边
        int u,v,w,next;
    }e[2*N];
    struct ask{            //保存询问
        int u,v,lca,next;
    }ea[M];
    int dir[N];              //保存点到树根的距离
    int fa[N];               //并查集,保存集合的代表元素
    int ance[N];             //保存集合的组合,注意对象是集合而不是元素
    bool vis[N];             //遍历时的标记数组
    
    inline void add_edge(int u,int v,int w,int &k) //保存边
    {
        e[k].u = u; e[k].v = v; e[k].w = w;
        e[k].next = head[u]; head[u] = k++;
        u = u^v; v = u^v; u = u^v;
        e[k].u = u; e[k].v = v; e[k].w = w;
        e[k].next = head[u]; head[u] = k++;
    }
    
    inline void add_ask(int u ,int v ,int &k) //保存询问
    {
        ea[k].u = u; ea[k].v = v; ea[k].lca = -1;
        ea[k].next = __head[u]; __head[u] = k++;
        u = u^v; v = u^v; u = u^v;   ///看上去深奥。。其实就是swap(u,v);
        ea[k].u = u; ea[k].v = v; ea[k].lca = -1;
        ea[k].next = __head[u]; __head[u] = k++;
    }
    
    int Find(int x)
    {
        return x == fa[x] ? x : fa[x] = Find(fa[x]);
    }
    void Union(int u ,int v)
    {
        fa[v] = fa[u];  //可写为  fa[Find(v)] = fa[u];
    }
    
    void Tarjan(int u)
    {
        vis[u] = true;
        ance[u] = fa[u] = u; //可写为 ance[Find(u)] = fa[u] = u;
        for(int k=head[u]; k!=-1; k=e[k].next)
            if( !vis[e[k].v] )
            {
                int v = e[k].v , w = e[k].w;
                dir[v] = dir[u] + w;
                Tarjan(v);
                Union(u,v);
                ance[Find(u)] = u;  
            }
        for(int k=__head[u]; k!=-1; k=ea[k].next)
            if( vis[ea[k].v] )
            {
                int v = ea[k].v;
                ea[k].lca = ea[k^1].lca = ance[Find(v)];
            }
    }
    
    int main()
    {
        int tcase;
        scanf("%d",&tcase);
        while(tcase--){
        int n,q;
        scanf("%d%d",&n,&q);
        memset(head,-1,sizeof(head));
        memset(__head,-1,sizeof(__head));
        int tot = 0;
        for(int i=1; i<n; i++)  //建树
        {
            int u,v,w;
            scanf("%d%d%d",&u,&v,&w);
            add_edge(u,v,w,tot);
        }
        tot = 0;
        for(int i=0; i<q; i++) //拆开保存询问
        {
            int u,v;
            scanf("%d%d",&u,&v);
            add_ask(u,v,tot);
        }
        memset(vis,0,sizeof(vis));
        dir[1] = 0;
        Tarjan(1);
        for(int i=0; i<q; i++)
        {
            int s = i * 2 , u = ea[s].u , v = ea[s].v , lca = ea[s].lca;
            printf("%d
    ",dir[u]+dir[v]-2*dir[lca]);
        }
        }
    
        return 0;
    }

    hdu 2874:和上题一样都是求两点之间的最短距离,但是有多棵树,所以存在不连通的情况(用father判断一下就OK),,然后华丽丽的 超内存,拿别人的代码也是MLE

    #include <stdio.h>
    #include <iostream>
    #include <string.h>
    using namespace std;
    const int N = 10001;
    const int M = 1000001;
    
    int head[N];
    int __head[N];
    struct edge{
        int u,v,w,next;
    }e[2*N];
    struct ask{
        int u,v,lca,next;
    }ea[2*M];
    int dir[N];
    int fa[N];
    int ance[N];
    bool vis[N];
    
    inline void add_edge(int u,int v,int w,int &k) //保存边
    {
        e[k].u = u; e[k].v = v; e[k].w = w;
        e[k].next = head[u]; head[u] = k++;
        u = u^v; v = u^v; u = u^v;
        e[k].u = u; e[k].v = v; e[k].w = w;
        e[k].next = head[u]; head[u] = k++;
    }
    
    inline void add_ask(int u ,int v ,int &k) //保存询问
    {
        ea[k].u = u; ea[k].v = v; ea[k].lca = -1;
        ea[k].next = __head[u]; __head[u] = k++;
        u = u^v; v = u^v; u = u^v;   ///看上去深奥。。其实就是swap(u,v);
        ea[k].u = u; ea[k].v = v; ea[k].lca = -1;
        ea[k].next = __head[u]; __head[u] = k++;
    }
    
    int Find(int x)
    {
        return x == fa[x] ? x : fa[x] = Find(fa[x]);
    }
    void Union(int u ,int v)
    {
        int x = Find(u);
        int y = Find(v);
        fa[x] = y;
    }
    
    void Tarjan(int u)
    {
        vis[u] = true;
        ance[u] = fa[u] = u; //可写为 ance[Find(u)] = fa[u] = u;
        for(int k=head[u]; k!=-1; k=e[k].next)
            if( !vis[e[k].v] )
            {
                int v = e[k].v , w = e[k].w;
                dir[v] = dir[u] + w;
                Tarjan(v);
                Union(u,v);
                ance[Find(u)] = u;  //可写为ance[u] = u;  //甚至不要这个语句都行
            }
        for(int k=__head[u]; k!=-1; k=ea[k].next)
            if( vis[ea[k].v] )
            {
                int v = ea[k].v;
                ea[k].lca = ea[k^1].lca = ance[Find(v)];
            }
    }
    
    int main()
    {
        int k,n,q;
        while(scanf("%d%d%d",&n,&k,&q)!=EOF){
    
        memset(head,-1,sizeof(head));
        memset(__head,-1,sizeof(__head));
        int tot = 0;
        for(int i=0; i<k; i++)  //建树
        {
            int u,v,w;
            scanf("%d%d%d",&u,&v,&w);
            add_edge(u,v,w,tot);
        }
        tot = 0;
        for(int i=0; i<q; i++) //拆开保存询问
        {
            int u,v;
            scanf("%d%d",&u,&v);
            add_ask(u,v,tot);
        }
        memset(vis,0,sizeof(vis));
        for(int i=1;i<=n;i++){  ///访问每个节点
            if(!vis[i]){
                dir[i]=0;
                Tarjan(i);
            }
        }
        for(int i=0; i<q; i++)
        {
            int s = i * 2 , u = ea[s].u , v = ea[s].v , lca = ea[s].lca;  ///s代表偶数边,奇偶只是方向不同罢了,所以取一个就行
            if(fa[u]!=fa[v]) printf("Not connected
    ");  ///父亲结点不同当然就不是同一棵子树了
            else printf("%d
    ",dir[u]+dir[v]-2*dir[lca]);
        }
        }
    
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/liyinggang/p/5343953.html
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