一些模板

模板太多了，写啥更新啥，顺便当自己的存档

码风很乱，见谅

---

单点修改树状数组

#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
#define l() i&-i
using namespace std;

int n,m,a[500010],tree[500010],c,x,y;

inline int lowbit(int x)
{
    return x&(-x);
}

inline void updata(int x,int k)
{
    for(int i=x;i<=n;i+=lowbit(x))
        tree[i]+=k;
}

inline int query(int x)
{
    int ans=0;
    for(int i=x;i;i-=lowbit(x))
        ans+=tree[i];
    return ans;
}
inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

int main()
{
    n=read();
    m=read();
    for(int i=1;i<=n;i++)
    {
        a[i]=read();
        updata(i,a[i]);
    }
    for(int i=1;i<=m;i++)
    {
        c=read();
        if(c==1)
        {
            x=read();
            y=read();
            updata(x,y);
        }
        else
        {
            x=read();
            y=read();
            cout<<query(y)-query(x-1)<<endl;
        }
    }
}

区间修改树状数组

#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
#define l() i&-i
using namespace std;

int n,x,y,z,k,tree[500010],a,m,last=0;
inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

inline int lowbit(int x)
{
    return x&(-x);
}
inline void add(int x,int k)
{
    for(int i=x;i<=n;i+=lowbit(i))
        tree[i]+=k;
}

inline long long query(int x)
{
    long long ans=0;
    for(int i=x;i;i-=lowbit(i))
        ans+=tree[i];
    return ans;
}
int main()
{
    n=read(),m=read();
    for(int i=1;i<=n;i++)
    {
        a=read();
        add(i,a-last);
        last=a;
    }
    for(int i=1;i<=m;i++)
    {
        cin>>x;
        if(x==1)
        {
            cin>>y>>z>>k;
            add(y,k);
            add(z+1,-k);
        }
        if(x==2)
        {
            cin>>y;
            cout<<query(y)<<endl;
        }
    }
}

可持久化线段树（主席树）

#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
using namespace std;

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

int n,q,m,T[200001],tot,a[200001],b[200001];
struct cym{
    int l,r,val;
}tree[8000001];

inline int bulid(int l,int r)// 建树操作 
{
    int bj=++tot;
    tree[bj].val=0;
    int mid=(l+r)>>1;
    if(l>r)
    {
        tree[bj].l=bulid(l,mid);
        tree[bj].r=bulid(mid+1,r);
    }
    return bj;
}

inline int change(int pre,int l,int r,int zone)// 修改 
{
    int bj=++tot;
    tree[bj].l=tree[pre].l;
    tree[bj].r=tree[pre].r;
    tree[bj].val=tree[pre].val+1;
    int mid=(l+r)>>1;
    if(l<r)
    {
        if(zone<=mid)
            tree[bj].l=change(tree[pre].l,l,mid,zone);
        else
            tree[bj].r=change(tree[pre].r,mid+1,r,zone);
    }
    return bj;
}

inline int cx(int from,int to,int l,int r,int k)// 查询 
{
    if(l==r)
        return l;
    int x=tree[tree[to].l].val-tree[tree[from].l].val;
    int mid=(l+r)>>1;
    if(x>=k)
        return cx(tree[from].l,tree[to].l,l,mid,k);
    else
        return cx(tree[from].r,tree[to].r,mid+1,r,k-x);
}
int main()
{
    n=read(),q=read();
    for(rg int i=1;i<=n;i++)
    {
        a[i]=read();
        b[i]=a[i];
    }
    sort(b+1,b+n+1);// 排序 
    m=unique(b+1,b+n+1)-b-1;// 看一共有多少个不重复的元素 
    T[0]=bulid(1,m);// 把最后一个点建在 主席树数组T[0]的位置  
    for(rg int i=1;i<=n;i++)
    {
        int t=lower_bound(b+1,b+m+1,a[i])-b;// 第一个比a[i] 大的树的位置 
        T[i]=change(T[i-1],1,m,t);
    }
    for(rg int i=1;i<=q;i++)
    {
        int l=read(),r=read(),k=read();
        int anss=cx(T[l-1],T[r],1,m,k);
        printf("%d
",b[anss]);
    }
}

 ST表

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
const int MAXN=1e6+10;
inline int read()
{
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}
int Max[MAXN][21];
int Query(int l,int r)
{
    int k=log2(r-l+1); 
    return max(Max[l][k],Max[r-(1<<k)+1][k]);//把拆出来的区间分别取最值 
}
int main()
{

    int N=read(),M=read();
    for(int i=1;i<=N;i++) Max[i][0]=read();
    for(int j=1;j<=21;j++)
        for(int i=1;i+(1<<j)-1<=N;i++)//注意这里要控制边界 
            Max[i][j]=max(Max[i][j-1],Max[i+(1<<(j-1))][j-1]);//如果看不懂边界的话建议好好看看图 
    for(int i=1;i<=M;i++)
    {
        int l=read(),r=read();
        printf("%d
",Query(l,r));
    }
    return 0;
}

 Kruskal

/*
            Kruskal
            并查集
            结构体存边 
            luogu P3366 模板 
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
using namespace std;

int n,m,ans,now_e,now_v,cnt;

inline int read()// 读入优化 
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

struct Node{
    int start,end,power;
    // start为起始点
    // end 为终点 
    // power 为权值 
}edge[2000010];// 存边 
int fa[6666];//并查集 

int cmp(Node a,Node b)
{
    return a.power<b.power; 
}

inline int find(int x)// 并查集找祖先 
{
    if(x!=fa[x])
    {
        fa[x]=find(fa[x]);
    }
    return fa[x];
}

/*inline void merge(int x,int y,int n)// 并查集合并
// n用来记录最短路中应该加入哪个点 
{
    int fx=find(x);
    int fy=find(y);
    if(fx!=fy)
    {
        pre[fx]=fy;
        sum+=edge[n].power;
    }
}*/

inline void Kruskal()
{
    sort(edge+1,edge+1+m,cmp);// 排序
    for(rg int i=1;i<=m;i++)
    {
        now_e=find(edge[i].start);
        now_v=find(edge[i].end);
        if(now_e==now_v)
            continue;//若两点联通 就不需要了 
        ans+=edge[i].power;
        fa[now_v]=now_e;//合并
        if(++cnt==n-1)
            break;// 边数==点数-1 就结束循环 
    } 
}
int main()
{
    n=read(),m=read();
    for(rg int i=1;i<=n;i++)
    {
        fa[i]=i;// 并查集初始化 
    }
    for(rg int i=1;i<=m;i++)
    {
        edge[i].start=read();
        edge[i].end=read();
        edge[i].power=read();
    }
    Kruskal();
    printf("%d",ans);
}

 Prim

/*
            Prim
            链式前向星存图 
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
#define inf 0x7ffffff
using namespace std;

int head[5005],dis[5005],cnt,n,m,tot,now=1,ans;
bool vis[5005];

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

struct Node{
    int v,w,next;
}e[400010];

inline void add(int u,int v,int w)
{
    e[++cnt].v=v;
    e[cnt].w=w;
    e[cnt].next=head[u];
    head[u]=cnt;
}
inline int prim()
{
    for(rg int i=2;i<=n;i++)
        dis[i]=inf;
    for(rg int i=head[1];i;i=e[i].next)
    {
        dis[e[i].v]=min(dis[e[i].v],e[i].w);
    }
    while(++tot<n)//最小生成树边数==点数-1
    {
        rg int minn=inf;
        vis[now]=1;//标记点已经走过
        for(rg int i=1;i<=n;i++)
        {
            if(!vis[i]&&minn>dis[i])
            {
                minn=dis[i];
                now=i;
            }
         } 
         ans+=minn;
         //枚举now的连边，更新dis 
         for(rg int i=head[now];i;i=e[i].next)
         {
            rg int v=e[i].v;
            if(dis[v]>e[i].w&&!vis[v])
            {
                dis[v]=e[i].w;
                }    
         }         
     } 
     return ans;
}
int main()
{
    n=read(),m=read();
    for(rg int i=1,u,v,w;i<=m;i++)
    {
        u=read(),v=read(),w=read();
        add(u,v,w),add(v,u,w);//无向图 
    }
    printf("%d",prim());
}

稀疏图：Kruskal

稠密图：Prim

 Dijkstra

/*
            Dijkstra
            朴素：O(n^2)
            堆优化：O((n+m)log^2n)
            不可以处理负边权的图
            luogu P4799 模板 
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
#define ll long long
#define rg register
using namespace std;

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

struct Node{
    int v,w,next;
}e[500010];

int head[100010],dis[100010],cnt;
bool vis[100010];
int n,m,s;

inline void add(int u,int v,int dis)
{
    e[++cnt].v=v;
    e[cnt].w=dis;
    e[cnt].next=head[u];
    head[u]=cnt;
}

struct node{
    int dis;// 值 
    int pos;// 位置 
    bool operator <( const node &x)const
    {
        return x.dis<dis;
    }
}; // 堆优化

priority_queue<node>q;

inline void dij()//名字太长了 容易打错 简写dij 
{
    dis[s]=0;
    q.push((node){0,s});
    while(!q.empty())
    {
        node tmp=q.top();
        q.pop();
        int x=tmp.pos,d=tmp.dis; 
        if(vis[x])
            continue;
        vis[x]=1;
        for(int i=head[x];i;i=e[i].next)
        {
            int y=e[i].v;
            if(dis[y]>dis[x]+e[i].w)
            {
                dis[y]=dis[x]+e[i].w;
            //    if(!vis[y])
                //{
                    q.push(node{dis[y],y});
            //    }
            }
        }
    }
} 

int main()
{
    n=read(),m=read(),s=read();
    for(rg int i=1;i<=n;i++)
        dis[i]=2147482647;// 尽量赋值大一点 防止答案超过这个数！！！
    for(rg int i=1,u,v,d;i<=m;i++)
    {
        u=read(),v=read(),d=read();
        add(u,v,d);
    }
    dij();
    for(int i=1;i<=n;i++)
        printf("%d ",dis[i]);
}

 倍增版LCA

/*
            LCA
            倍增 
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#define ll long long
#define rg register
using namespace std;

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

struct cym{
    int t,nex;
}e[1000001];

int depth[500001],fa[500001][22],lg[500001],head[500001],n,m,s;
int cnt;

inline void add(int x,int y)
{
    e[++cnt].t=y;
    e[cnt].nex=head[x];
    head[x]=cnt;
}

void dfs(int f,int fath)// f 表示当前的节点，fath 表示他的父亲节点 
{
    depth[f]=depth[fath]+1;
    fa[f][0]=fath;
    for(rg int i=1;(1<<i)<=depth[f];i++)
        fa[f][i]=fa[fa[f][i-1]][i-1];// 核心转移 
        // f的2^i祖先=f的2^(i-1)的祖先的2(i-1)祖先
        //2^i=2^(i-1)+2^(i-1)
    for(rg int i=head[f];i;i=e[i].nex)
        if(e[i].t!=fath)
            dfs(e[i].t,f); 
}

inline int lca(int x,int y)
{
    if(depth[x]<depth[y])// 我们不妨设x的深度>=y的深度
        swap(x,y);
    while(depth[x]>depth[y])
        x=fa[x][lg[depth[x]-depth[y]]-1];//先跳到同一深度
    if(x==y)
        return x;// 如果x是y的祖先，那他们的lca就是x
    for(rg int k=lg[depth[x]]-1;k>=0;k--)
    {
        if(fa[x][k]!=fa[y][k])
            x=fa[x][k],y=fa[y][k];
    } 
    return fa[x][0];//返回父节点 
}

int main()
{
    n=read(),m=read(),s=read();
    for(rg int i=1,x,y;i<=n-1;i++)
    {
        x=read(),y=read();
        add(x,y);
        add(y,x);
    }
    dfs(s,0);
    for(rg int i=1;i<=n;i++)
        lg[i]=lg[i-1]+(1<<lg[i-1]==i);
    // 预处理log2i +1的值 直接调用
     for(rg int i=1,x,y;i<=n;i++)
     {
         x=read(),y=read();
         printf("%d
",lca(x,y));
     }
}

 区间M的最小值（单调队列优化Dp）

#include <iostream>
#include <cstdio>
#include <algorithm>
//#include <windows.h>
#define ll long long
#define rg register
#define ull unsigned long long 

using namespace std;

int n,m;
int k,tot,head=1,tail=0;
int a[2000009],q[2000009];

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

int main()
{
    n=read(),m=read();
    for(rg int i=1;i<=n;i++)
        a[i]=read();
    for(rg int i=1;i<=n;i++)
    {
        printf("%d
",a[q[head]]);
        while(i-q[head]+1>m&&head<=tail)    
            head++;
        while(a[i]<a[q[tail]]&&head<=tail)
            tail--;
        q[++tail]=i;
    }
    //system("pause");
    return 0;
}