有关各种数据结构模板

FHQ-Treap

模板题-普通平衡树

#include <bits/stdc++.h>
using namespace std;
const int N = 1e5+10;
struct Node
{
    int l,r;
    int val,key;
    int size;
}tr[N];
int root,idx,n;
int add(int key)
{
    tr[++idx].val = rand(),tr[idx].key = key,tr[idx].size = 1;
    return idx;
}
void pushup(int u)
{
    tr[u].size = tr[tr[u].l].size + tr[tr[u].r].size + 1;
}
void split(int u,int key,int &x,int &y)
{
    if(!u) return x = y = 0,void();
    if(tr[u].key <= key) x = u,split(tr[u].r,key,tr[u].r,y);
    else y = u,split(tr[u].l,key,x,tr[u].l);
    pushup(u);
}
int merge(int x,int y)
{
    if(!x||!y) return x + y;
    if(tr[x].val > tr[y].val)
    {
        tr[x].r = merge(tr[x].r,y);
        pushup(x);
        return x;
    }
    tr[y].l = merge(x,tr[y].l);
    pushup(y);
    return y;
}
void insert(int key)
{
    int x,y;
    split(root,key,x,y);
    root = merge(x,merge(add(key),y));
}
void remove(int key)
{
    int x,y,z;
    split(root,key,x,z);
    split(x,key-1,x,y);
    y = merge(tr[y].l,tr[y].r);
    root = merge(merge(x,y),z);
}
int get_rank_by_key(int key)
{
    int x,y;
    split(root,key-1,x,y);
    int res = tr[x].size + 1;
    root = merge(x,y);
    return res;
}
int get_key_by_rank(int k)
{
    int u = root;
    while(u)
    {
        if(tr[tr[u].l].size + 1 == k) return tr[u].key;
        if(tr[tr[u].l].size >= k ) u = tr[u].l;
        else k-= tr[tr[u].l].size + 1,u = tr[u].r;
    }
    return -1;
}
int get_prev(int key)
{
    int x,y;
    split(root,key-1,x,y);
    int u = x;
    while(tr[u].r) u = tr[u].r;
    int res = tr[u].key;
    root = merge(x,y);
    return res;
}
int get_next(int key)
{
    int x,y;
    split(root,key,x,y);
    int u = y;
    while(tr[u].l) u = tr[u].l;
    int res = tr[u].key;
    root = merge(x,y);
    return res;
}
int main()
{
    scanf("%d",&n);
    while(n--)
    {
        int opt,x;
        scanf("%d%d",&opt,&x);
        if(opt==1) insert(x);
        else if(opt==2) remove(x);
        else if(opt==3) printf("%d\n",get_rank_by_key(x));
        else if(opt==4) printf("%d\n",get_key_by_rank(x));
        else if(opt==5) printf("%d\n",get_prev(x));
        else printf("%d\n",get_next(x));
    }
    return 0;
}

Splay

模板题-文艺平衡树

#include <bits/stdc++.h>
using namespace std;
const int N = 1e5+10;
struct Node
{
    int s[2],p,v;
    int size,flag;
    
    void init(int _p,int _v)
    {
        p = _p;
        v = _v;
        size = 1;
    }
}tr[N];

int root,idx;
int n,m;

void pushup(int x)
{
    tr[x].size = tr[tr[x].s[0]].size + tr[tr[x].s[1]].size + 1;
}

void pushdown(int x)
{
    if(tr[x].flag)
    {
        swap(tr[x].s[0],tr[x].s[1]);
        tr[tr[x].s[0]].flag ^= 1;
        tr[tr[x].s[1]].flag ^= 1;
        tr[x].flag = 0;
    }
}

void rotate(int x)
{
    int y = tr[x].p,z = tr[y].p;
    int k = tr[y].s[1] == x;
    tr[z].s[tr[z].s[1] == y] = x,tr[x].p = z;
    tr[y].s[k] = tr[x].s[k^1], tr[tr[x].s[k^1]].p = y;
    tr[x].s[k^1] = y,tr[y].p = x;
    pushup(y),pushup(x);
}

void splay(int x,int k)
{
    while(tr[x].p != k)
    {
        int y = tr[x].p,z = tr[y].p;
        if(z!=k)
        {
            if((tr[y].s[1] == x) ^ (tr[z].s[1] == y)) rotate(x);
            else rotate(y);
        }
        rotate(x);
    }
    if(!k) root = x;
}

void insert(int v)
{
    int u = root,p = 0;
    while(u) p = u,u = tr[u].s[v > tr[u].v];
    u = ++idx;
    if(p) tr[p].s[v > tr[p].v] = u;
    tr[u].init(p,v);
    splay(u,0);
}

int get_k(int k)
{
    int u = root;
    while(true)
    {
        pushdown(u);
        if(tr[tr[u].s[0]].size >= k) u = tr[u].s[0];
        else if(tr[tr[u].s[0]].size + 1 == k) return u;
        else k -= tr[tr[u].s[0]].size + 1,u = tr[u].s[1];
        pushup(u);
    }
    return -1;
}

void output(int u)
{
    pushdown(u);
    if(tr[u].s[0]) output(tr[u].s[0]);
    if(tr[u].v >= 1 && tr[u].v <= n) printf("%d ",tr[u].v);
    if(tr[u].s[1]) output(tr[u].s[1]);
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 0;i<=n+1;i++) insert(i);
    while(m--)
    {
        int l,r;
        scanf("%d%d",&l,&r);
        l = get_k(l),r = get_k(r+2);
        splay(l,0),splay(r,l);
        tr[tr[r].s[0]].flag ^= 1;
    }
    output(root);
    return 0;
}

可持久化线段树（主席树）

模板题-求第K小数

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5+10;
struct Node
{
    int l,r;
    int cnt;
}tr[4*N + 17*N];
int root[N],idx,a[N];
int n,m;
vector<int> v;
int find(int x)
{
    return lower_bound(v.begin(),v.end(),x) - v.begin();
}
int build(int l,int r)
{
    int p = ++idx;
    if(l==r) return p;
    int mid = l + r >> 1;
    tr[p].l = build(l,mid),tr[p].r = build(mid+1,r);
    return p;
}

int insert(int p,int l,int r,int x)
{
    int q = ++idx;
    tr[q] = tr[p];
    if(l==r)
    {
        tr[q].cnt++;
        return q;
    }
    int mid = l + r >> 1;
    if(x<=mid) tr[q].l = insert(tr[p].l,l,mid,x);
    else tr[q].r = insert(tr[p].r,mid+1,r,x);
    tr[q].cnt= tr[tr[q].l].cnt + tr[tr[q].r].cnt;
    return q;
}

int query(int q,int p,int l,int r,int k)
{
    if(l==r) return r;
    int cnt = tr[tr[q].l].cnt - tr[tr[p].l].cnt;
    int mid = l + r >> 1;
    if(cnt>=k) return query(tr[q].l,tr[p].l,l,mid,k);
    else return query(tr[q].r,tr[p].r,mid+1,r,k-cnt);
}

int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 1;i<=n;i++)
    {
        scanf("%d",&a[i]);
        v.push_back(a[i]);
    }
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());

    root[0] = build(0,v.size()-1);
    for(int i = 1;i<=n;i++)
    {
        root[i] = insert(root[i-1],0,v.size()-1,find(a[i]));
    }

    while(m--)
    {
        int l,r,k;
        scanf("%d%d%d",&l,&r,&k);
        printf("%d\n",v[query(root[r],root[l-1],0,v.size()-1,k)]);
    }
    return 0;
}

AC自动机

模板题-AC自动机

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5+10,M = 2e6+10;
int tr[N][26],id[N],ne[N],tot,Size[N],cnt[N];
int q[N];
char str[M];
int h[N],e[N],Ne[N],n,idx;
void add(int a,int b)
{
    e[idx] = b,Ne[idx] = h[a],h[a] = idx++;
}
void insert(int x)
{
    int p = 0;
    for(int i = 0;str[i];i++)
    {
        int t = str[i] - 'a';
        if(!tr[p][t]) tr[p][t] = ++tot;
        p = tr[p][t];
    }
    id[x] = p;
}
void build()
{
    int tt = -1,hh = 0;
    for(int i = 0;i<26;i++) if(tr[0][i]) q[++tt] = tr[0][i];
    while(tt>=hh)
    {
        int t = q[hh++];
        for(int i = 0;i<26;i++)
        {
            int &p = tr[t][i];
            if(!p) p = tr[ne[t]][i];
            else
            {
                ne[p] = tr[ne[t]][i];
                q[++tt] = p;
            }
        }
    }
}
void dfs(int u)
{
    for(int i = h[u];~i;i=Ne[i])
    {
        int j = e[i];
        dfs(j);
        Size[u] += Size[j]; 
    }
}
int main()
{
    memset(h,-1,sizeof h);
    scanf("%d",&n);
    for(int i = 0;i<n;i++) scanf("%s",str),insert(i);
    build();
    scanf("%s",str);
    for(int i = 0,j = 0;str[i];i++)
    {
        int t = str[i] - 'a';
        j = tr[j][t];
        Size[j]++;
    }

    for(int i = 1;i<=tot;i++) add(ne[i],i);
    dfs(0);
    for(int i = 0;i<n;i++) printf("%d\n",Size[id[i]]);
    return 0;
}

线段树