1143 Lowest Common Ancestor (30 分)

好家伙，\(unordered\_map\)一直有一两个点超时，换成数组就过了，看来\(STL\)实现的哈希表还是没数组快啊。

向上标记法。

const int N=10010;
int fa[N];
unordered_map<int,int> pos;
int pre[N],in[N];
bool vis[N];
int n,m;

int build(int prel,int prer,int inl,int inr)
{
    if(prel > prer) return -1;

    int root=pre[prel];
    int k=pos[root];
    int leftLen=k-inl;
    int lchild=build(prel+1,prel+leftLen,inl,k-1);
    int rchild=build(prel+leftLen+1,prer,k+1,inr);

    if(~lchild) fa[lchild]=k;
    if(~rchild) fa[rchild]=k;
    return k;
}

int LCA(int u,int v)
{
    memset(vis,0,sizeof vis);
    while(u)
    {
        vis[u]=true;
        u=fa[u];
    }
    
    while(!vis[v]) v=fa[v];
    return v;
}

int main()
{
    cin>>m>>n;

    for(int i=1;i<=n;i++)
    {
        cin>>pre[i];
        in[i]=pre[i];
    }

    sort(in+1,in+n+1);
    for(int i=1;i<=n;i++)
        pos[in[i]]=i;

    build(1,n,1,n);

    while(m--)
    {
        int u,v;
        cin>>u>>v;
        if(pos.count(u) == 0 && pos.count(v) == 0)
            printf("ERROR: %d and %d are not found.",u,v);
        else if(pos.count(u) == 0)
            printf("ERROR: %d is not found.",u);
        else if(pos.count(v) == 0)
            printf("ERROR: %d is not found.",v);
        else
        {
            u=pos[u],v=pos[v];
            int lca=LCA(u,v);
            if(lca != u && lca != v)
                printf("LCA of %d and %d is %d.",in[u],in[v],in[lca]);
            else if(lca == u)
                printf("%d is an ancestor of %d.",in[u],in[v]);
            else
                printf("%d is an ancestor of %d.",in[v],in[u]);
        }
        puts("");
    }
    //system("pause");
    return 0;
}

同步前进法。

const int N=10010;
int fa[N];
unordered_map<int,int> pos;
int pre[N],in[N];
int dep[N];
int n,m;

int build(int prel,int prer,int inl,int inr,int d)
{
    if(prel > prer) return -1;

    int root=pre[prel];
    int k=pos[root];
    dep[k]=d;
    int leftLen=k-inl;
    int lchild=build(prel+1,prel+leftLen,inl,k-1,d+1);
    int rchild=build(prel+leftLen+1,prer,k+1,inr,d+1);

    if(~lchild) fa[lchild]=k;
    if(~rchild) fa[rchild]=k;
    return k;
}

int LCA(int u,int v)
{
    if(dep[u] < dep[v]) swap(u,v);
    
    while(dep[u] != dep[v]) u=fa[u];
    if(u == v) return v;
    while(fa[u] != fa[v])
    {
        u=fa[u];
        v=fa[v];
    }
    return fa[u];
}

int main()
{
    cin>>m>>n;

    for(int i=1;i<=n;i++)
    {
        cin>>pre[i];
        in[i]=pre[i];
    }

    sort(in+1,in+n+1);
    for(int i=1;i<=n;i++)
        pos[in[i]]=i;

    build(1,n,1,n,1);

    while(m--)
    {
        int u,v;
        cin>>u>>v;
        if(pos.count(u) == 0 && pos.count(v) == 0)
            printf("ERROR: %d and %d are not found.",u,v);
        else if(pos.count(u) == 0)
            printf("ERROR: %d is not found.",u);
        else if(pos.count(v) == 0)
            printf("ERROR: %d is not found.",v);
        else
        {
            u=pos[u],v=pos[v];
            int lca=LCA(u,v);
            if(lca != u && lca != v)
                printf("LCA of %d and %d is %d.",in[u],in[v],in[lca]);
            else if(lca == u)
                printf("%d is an ancestor of %d.",in[u],in[v]);
            else
                printf("%d is an ancestor of %d.",in[v],in[u]);
        }
        puts("");
    }
    //system("pause");
    return 0;
}