NOIP 考前 数据结构复习

BZOJ 1455 左偏树即可

#include <cstdio>
#define LL long long
const LL Maxn=1000100;
struct Info{LL l,r,v,Dis;}Tree[Maxn];
LL Father[Maxn],n,m,Dead[Maxn],u,v;
inline void Swap(LL &x,LL &y){LL t=x;x=y;y=t;}
LL Get(LL x) {return x==Father[x]?x:Father[x]=Get(Father[x]);}
LL Merge(LL u,LL v)
{
    if (u==0 || v==0) return u+v;
    if (Tree[u].v>Tree[v].v) Swap(u,v);
    Tree[u].r=Merge(Tree[u].r,v);
    if (Tree[Tree[u].l].Dis<Tree[Tree[u].r].Dis) 
        Swap(Tree[u].l,Tree[u].r);
    Tree[u].Dis=Tree[Tree[u].l].Dis+1;
    return u;
}
int main()
{
    scanf("%lld",&n);
    for (LL i=1;i<=n;i++) scanf("%lld",&Tree[i].v),Tree[i].l=Tree[i].r=0;
    for (LL i=1;i<=n;i++) Father[i]=i;
    scanf("%lld",&m);
    for (LL i=1;i<=m;i++)
    {
        char ch=getchar();
        while (ch!='M' && ch!='K') ch=getchar();
        if (ch=='M')
        {
            scanf("%lld%lld",&u,&v);
            LL fu=Get(u);
            LL fv=Get(v);
            if (fu==fv || Dead[u] || Dead[v]) continue;
            LL Tmp=Merge(fu,fv);
            Father[fu]=Father[fv]=Tmp;
        } 
        if (ch=='K')
        {
            scanf("%lld",&u);
            if (Dead[u]) {puts("0"); continue;}
            LL fu=Get(u); Dead[fu]=true;
            printf("%lld\n",Tree[fu].v);
            LL Tmp=Merge(Tree[fu].l,Tree[fu].r);
            Father[fu]=Tmp;
            Father[Tmp]=Tmp;
        }
    }
    return 0;
}

 BZOJ 1803 用主席树维护Dfs序就可以了

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;
const int Maxn=200010;
const int Maxm=4010000;
inline void Get_Int(int &x)
{
    x=0; register char ch=getchar(); int f=1;
    while (ch<'0' || ch>'9') {if (ch=='-') f=-1; ch=getchar();}
    while (ch>='0' && ch<='9') {x=x*10+ch-'0'; ch=getchar();} x*=f;
}
inline void Put_Int(int x)
{
    char ch[20]; register int top=0;
    if (x<0) putchar('-'),x=-x;
    if (x==0) ch[++top]='0';
    while (x) ch[++top]=x%10+'0',x/=10;
    while (top) putchar(ch[top--]); putchar('\n');
}
struct Node {int Sum; Node * l,* r;};
Node Memory[Maxm],*port=Memory,* Root[Maxn],* null;
inline void Init() {null=port++;null->Sum=0;null->l=null->r=null;}
inline Node* NewNode(Node * last=NULL)
{
    Node * ret=port++;
    if (last==NULL) {ret->Sum=0; ret->l=ret->r=null;}
    else {ret->Sum=last->Sum+1; ret->l=last->l; ret->r=last->r;}
    return ret;
}
//======================================
int Begin[Maxn],End[Maxn],Dfn[Maxn],head[Maxn];
int cnt,Stamp,u,v,Rank[Maxn],n,C[Maxn],a[Maxn],num;
struct Info{int v,id;}Data[Maxn];
struct EDGE{int to,next;}edge[Maxn<<1];
inline bool Cmp(Info A,Info B) {return A.v<B.v;}
inline void Add(int u,int v) {edge[cnt].to=v;edge[cnt].next=head[u];head[u]=cnt++;}
void Dfs(int u,int fa)
{
    Dfn[Begin[u]=++Stamp]=u;
    for (int i=head[u];i!=-1;i=edge[i].next) 
        if (edge[i].to!=fa) Dfs(edge[i].to,u);
    Dfn[End[u]=++Stamp]=u;
}
Node * Update(int l,int r,Node *x,int v)
{
    Node * Ret=NewNode(x); 
    if (l==r) return Ret;
    int mid=(l+r)>>1;
    if (v<=mid)Ret->l=Update(l,mid,x->l,v); else
    Ret->r=Update(mid+1,r,x->r,v); 
    return Ret;
}
void Query(int L,int R,int K)
{
    Node * x=Root[L-1],*y=Root[R];
    int P=1,Q=num;
    while (P!=Q)
    {
        int mid=(P+Q)>>1;
        if (P==Q) 
        {
            printf("%d\n",C[P]);
            return;
        }
        if (y->l->Sum-x->l->Sum<K)
        {
            K-=(y->l->Sum-x->l->Sum);
            x=x->r,y=y->r;
            P=mid+1;
        } else
        {
            x=x->l,y=y->l;
            Q=mid;
        }
    }
    printf("%d\n",C[P]);
    return;
}
int main()
{
    // freopen("c.in","r",stdin);
    scanf("%d",&n); Init(); Root[0]=NewNode();
    for (int i=1;i<=n;i++) 
        scanf("%d",&a[i]),Data[i].v=a[i],Data[i].id=i;
    sort(Data+1,Data+n+1,Cmp);
    for (int i=1;i<=n;i++)
        C[++num]=Data[i].id,Rank[Data[i].id]=num;
    memset(head,-1,sizeof(head));
    for (int i=1;i<n;i++)
    {
        scanf("%d%d",&u,&v);
        Add(u,v),Add(v,u);
    }
    Dfs(1,0);
     
     
    for (int i=1;i<=Stamp;i++) 
        Root[i]=Update(1,num,Root[i-1],Rank[Dfn[i]]);
    int m,x,k;
    scanf("%d",&m);
    for (int i=1;i<=m;i++)
    {
        scanf("%d%d",&x,&k); k=k*2;
        Query(Begin[x],End[x],k);
    }
    return 0;
}

BZOJ 3364 LCA

 
#include <cstdio>
#include <cstring>
const int Maxn=400100;
struct EDGE{int to,next,w;}edge[Maxn<<1];
int head[Maxn],Size[Maxn],Dep[Maxn],Top[Maxn],Dis[Maxn],Fa[Maxn],n,m,u,v,w,cnt,Q;
inline void Add(int u,int v,int w) {edge[cnt].to=v;edge[cnt].next=head[u];edge[cnt].w=w;head[u]=cnt++;}
void Dfs1(int u,int fa)
{
    Size[u]=1;
    for (int i=head[u];i!=-1;i=edge[i].next)
    {
        if (edge[i].to==fa) continue;
        Dep[edge[i].to]=Dep[u]+1; Fa[edge[i].to]=u; 
        Dis[edge[i].to]=Dis[u]+edge[i].w;
        Dfs1(edge[i].to,u);
        Size[u]+=Size[edge[i].to];
    }
}
void Dfs2(int u,int fa,int chain)
{
    int k=0; Top[u]=chain;
    for (int i=head[u];i!=-1;i=edge[i].next)
    {
        if (edge[i].to==fa) continue; 
        if (Size[edge[i].to]>Size[k] || k==0) k=edge[i].to;
    }
    if (k==0) return;
    Dfs2(k,u,chain);
    for (int i=head[u];i!=-1;i=edge[i].next)
        if (edge[i].to!=fa && edge[i].to!=k)
            Dfs2(edge[i].to,u,edge[i].to);
}
int Lca(int u,int v)
{
    while (true)
    {
        if (Top[u]==Top[v]) return Dep[u]>Dep[v]?v:u;
        if (Dep[Top[u]]>Dep[Top[v]]) u=Fa[Top[u]]; else v=Fa[Top[v]];
    }
}
int main()
{
    // freopen("c.in","r",stdin);
    while (scanf("%d%d",&n,&m)!=EOF)
    {
        memset(head,-1,sizeof(head));
        char Str[5];
        for (int i=1;i<=m;i++)
        {
            scanf("%d%d%d%s",&u,&v,&w,Str);
            Add(u,v,w),Add(v,u,w);
        }
        Dep[1]=1; Fa[1]=1; Dis[1]=0;
        Dfs1(1,0);
        Dfs2(1,0,1);
        scanf("%d",&Q);
        for (int i=1;i<=Q;i++) 
        {
            scanf("%d%d",&u,&v);
            printf("%d\n",Dis[u]+Dis[v]-2*Dis[Lca(u,v)]);
        }
    }
    return 0;
}

#include <cstdio>
#include <cstring>
const int Maxn=400100;
struct EDGE{int to,next,w;}edge[Maxn<<1];
int head[Maxn],Dep[Maxn],Dis[Maxn],Fa[Maxn][20],n,m,u,v,w,cnt,Q;
inline void Add(int u,int v,int w) {edge[cnt].to=v;edge[cnt].next=head[u];edge[cnt].w=w;head[u]=cnt++;}
inline void Swap(int &x,int &y){int t=x;x=y;y=t;}
void Dfs(int u,int fa)
{
    for (int i=head[u];i!=-1;i=edge[i].next)
    {
        if (edge[i].to==fa) continue;
        Dep[edge[i].to]=Dep[u]+1; Fa[edge[i].to][0]=u; 
        Dis[edge[i].to]=Dis[u]+edge[i].w;
        Dfs(edge[i].to,u);
    }
}
inline void Init()
{
    for (int i=1;i<=18;i++)
        for (int j=1;j<=n;j++) Fa[j][i]=Fa[Fa[j][i-1]][i-1];
}
inline int Lca(int u,int v)
{
    if (Dep[u]>Dep[v]) Swap(u,v);    
    int Len=Dep[v]-Dep[u];
    for (int i=0;i<=18;i++)
        if (Len&(1<<i)) v=Fa[v][i];
    for (int i=18;i>=0;i--)
        if (Fa[u][i]!=Fa[v][i]) u=Fa[u][i],v=Fa[v][i];
    if (u!=v) return Fa[u][0];
    return u;
}
int main()
{
    // freopen("c.in","r",stdin);
    while (scanf("%d%d",&n,&m)!=EOF)
    {
        memset(head,-1,sizeof(head));
        char Str[5];
        for (int i=1;i<=m;i++)
        {
            scanf("%d%d%d%s",&u,&v,&w,Str);
            Add(u,v,w),Add(v,u,w);
        }
        Dep[1]=1; Fa[1][0]=1; Dis[1]=0;
        Dfs(1,0); Init();
        scanf("%d",&Q);
        for (int i=1;i<=Q;i++) 
        {
            scanf("%d%d",&u,&v);
            printf("%d\n",Dis[u]+Dis[v]-2*Dis[Lca(u,v)]);
        }
    }
    return 0;

BZOJ 1699 RMQ

#include <cstdio>
#include <cmath>
const int Maxn=50100;
int FMax[Maxn][20],FMin[Maxn][20],n,q,l,r,x;
inline int Min(int x,int y) {return x>y?y:x;}
inline int Max(int x,int y) {return x>y?x:y;}
inline void Init()
{
    for (int i=1;i<=18;i++)
        for (int j=1;j+(1<<(i-1))<=n;j++)
        {
            FMax[j][i]=Max(FMax[j+(1<<(i-1))][i-1],FMax[j][i-1]);
            FMin[j][i]=Min(FMin[j+(1<<(i-1))][i-1],FMin[j][i-1]);
        }
}
inline int Query(int l,int r)
{
    int Len=(int)log2(r-l+1);
     
    return Max(FMax[l][Len],FMax[r-(1<<Len)+1][Len])-Min(FMin[l][Len],FMin[r-(1<<Len)+1][Len]);
}
int main()
{
    // freopen("c.in","r",stdin);
    scanf("%d%d",&n,&q);
    for (int i=1;i<=n;i++) scanf("%d",&x),FMax[i][0]=x,FMin[i][0]=x;
    Init();
    for (int i=1;i<=q;i++)
    {
        scanf("%d%d",&l,&r);
        printf("%d\n",Query(l,r));
    }
    return 0;
}