模板库

缺省源

头文件

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
int main()
{
}

火车头

#pragma GCC optimize(3)
#pragma GCC target("avx,sse2,sse3,sse4,mmx")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")

#pragma GCC optimize("-fdelete-null-pointer-checks,inline-functions-called-once,-funsafe-loop-optimizations,-fexpensive-optimizations,-foptimize-sibling-calls,-ftree-switch-conversion,-finline-small-functions,inline-small-functions,-frerun-cse-after-loop,-fhoist-adjacent-loads,-findirect-inlining,-freorder-functions,no-stack-protector,-fpartial-inlining,-fsched-interblock,-fcse-follow-jumps,-fcse-skip-blocks,-falign-functions,-fstrict-overflow,-fstrict-aliasing,-fschedule-insns2,-ftree-tail-merge,inline-functions,-fschedule-insns,-freorder-blocks,-fwhole-program,-funroll-loops,-fthread-jumps,-fcrossjumping,-fcaller-saves,-fdevirtualize,-falign-labels,-falign-loops,-falign-jumps,unroll-loops,-fsched-spec,-ffast-math,Ofast,inline,-fgcse,-fgcse-lm,-fipa-sra,-ftree-pre,-ftree-vrp,-fpeephole2",3)

fread/fwrite

char buf[1<<23],*p1=buf,*p2=buf,obuf[1<<23],*O=obuf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(!isdigit(ch)){if(ch=='-') f=-1;ch=getchar();}
	while(isdigit(ch)) x=x*10+(ch^48),ch=getchar();
	return x*f;
}
void write(long long x)
{
    if(x>9)write(x/10);
    *O++=x%10+'0';
}//fwrite(obuf,O-obuf,1,stdout);

图论

最短路（Dijkstra）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e5+10,M=2e5+10;
int head[N],ver[M],nxt[M],tot=0,edge[M];
void add(int x,int y,int z)
{
	ver[++tot]=y;
	edge[tot]=z;
	nxt[tot]=head[x];
	head[x]=tot;
}
int dis[N];bool vis[N];
void dij(int s)
{
	priority_queue<pii> que;
	que.push(mp(0,s));
	memset(dis,0x3f,sizeof(dis));
	dis[s]=0;
	while(!que.empty())
	{
		int x=que.top().se;que.pop();
		if(vis[x])continue;
		vis[x]=1;
		for(int i=head[x];i;i=nxt[i])
		{
			int y=ver[i],z=edge[i];
			if(dis[x]+z<dis[y])
			{
				dis[y]=dis[x]+z;
				que.push(mp(-dis[y],y));
			}
		}
	}
}
int main()
{
	int n=read(),m=read(),s=read();
	for(int i=1;i<=m;i++){int u=read(),v=read(),w=read();add(u,v,w);}
	dij(s);
	for(int i=1;i<=n;i++)printf("%d ",dis[i]);
}

最短路（SPFA）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e4+10,M=5e5+10;
int head[N],ver[M],nxt[M],tot=0,edge[M];
void add(int x,int y,int z)
{
	ver[++tot]=y;
	nxt[tot]=head[x];
	head[x]=tot;
	edge[tot]=z;
}
int dis[N];bool vis[N];
void spfa(int s)
{
	queue<int> que;que.push(s);
	memset(dis,0x3f,sizeof(dis));dis[s]=0;
	while(!que.empty())
	{
		int x=que.front();que.pop();
		vis[x]=0;
		for(int i=head[x];i;i=nxt[i])
		{
			int y=ver[i],z=edge[i];
			if(dis[x]+z<dis[y])
			{
				dis[y]=dis[x]+z;
				if(!vis[y])vis[y]=1,que.push(y);
			}
		}
	}
}
int main()
{
	int n=read(),m=read(),s=read();
	for(int i=1;i<=m;i++){int u=read(),v=read(),w=read();add(u,v,w);}
	spfa(s);for(int i=1;i<=n;i++)printf("%d ",dis[i]==0x3f3f3f3f?0x7fffffff:dis[i]);
	return 0;
}

最大流

#include<bits/stdc++.h>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=210,M=1e4+10,inf=0x3f3f3f3f;
int head[N],ver[M],nxt[M],tot=1,edge[M];
void add(int x,int y,int z)
{
	ver[++tot]=y;
	edge[tot]=z;
	nxt[tot]=head[x];
	head[x]=tot;
}
int s,t,dis[N],cur[N];bool vis[N];
bool bfs()
{
	memcpy(cur,head,sizeof(head));
	memset(vis,0,sizeof(vis));
	memset(dis,0x3f,sizeof(dis));dis[s]=0;
	queue<int> que;que.push(s);
	while(!que.empty())
	{
		int x=que.front();que.pop();
		vis[x]=0;
		for(int i=head[x];i;i=nxt[i])
		{
			int y=ver[i],z=edge[i];
			if(dis[x]+1<dis[y]&&z)
			{
				dis[y]=dis[x]+1;
				if(!vis[y])
				{
					vis[y]=1;
					que.push(y);
				}
			}
		}
	}
	return dis[t]!=inf;
}
int dfs(int x,int limit)
{
	if(x==t||!limit)return limit;
	int flow=0,rlow=0;
	for(int &i=cur[x];i;i=nxt[i])
	{
		int y=ver[i],z=edge[i];
		if(dis[y]==dis[x]+1)
		{
			if(rlow=dfs(y,min(limit,z)))
			{
				flow+=rlow,limit-=rlow;
				edge[i]-=rlow,edge[i^1]+=rlow;
				if(!limit)break;
			}
		}
	}
	return flow;
}
signed main()
{
	int n=read(),m=read();s=read(),t=read();
	for(int i=1;i<=m;i++){int u=read(),v=read(),w=read();add(u,v,w),add(v,u,0);}
	ll ans=0;
	while(bfs())ans+=dfs(s,inf);
	printf("%lld",ans);
}
//zzt qwq

最小费用最大流

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=5e3+10,M=1e5+10,inf=0x3f3f3f3f;
int head[N],ver[M],nxt[M],tot=1,edge[M],cost[M];
bool vis[N];
void add(int x,int y,int z,int c)
{
	ver[++tot]=y,edge[tot]=z,cost[tot]=c;
	nxt[tot]=head[x],head[x]=tot;
}
int dis[N],cur[N];
bool spfa(int s,int t)
{
	memset(dis,0x3f,sizeof(dis));
	memcpy(cur,head,sizeof(head));
	queue<int> que;que.push(s),dis[s]=0;
	while(!que.empty())
	{
		int x=que.front();que.pop();
		vis[x]=0;
		for(int i=head[x];i;i=nxt[i])
		{
			int y=ver[i],z=edge[i],c=cost[i];
			if(z&&dis[x]+c<dis[y])
			{
				dis[y]=dis[x]+c;
				if(!vis[y])vis[y]=1,que.push(y);
			}
		}
	}
	return dis[t]!=inf;
}
int res=0;
int dfs(int x,int t,int limit)
{
//	printf("dfs(%d, %d, %d)\n",x,t,limit);
	if(x==t||!limit)return limit;
	int flow=0,rlow=0;vis[x]=1;
	for(int &i=cur[x];i;i=nxt[i])
	{
		int y=ver[i],z=edge[i],c=cost[i];
		if(z&&!vis[y]&&dis[x]+c==dis[y])
		{
			rlow=dfs(y,t,min(limit,z));
			if(rlow)flow+=rlow,limit-=rlow,edge[i]-=rlow,edge[i^1]+=rlow,res+=rlow*c;
			if(!limit)break;
		}
	}
	vis[x]=0;
	return flow;
}
int dinic(int s,int t)
{
	int ans=0;
	while(spfa(s,t))
	{
//		printf("hello!\n");
		int x=0;
		while(x=dfs(s,t,inf))ans+=x;
	}
	return ans;
}
int main()
{
	int n=read(),m=read(),s=1,t=n;
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read(),z=read(),c=read();
		add(x,y,z,c),add(y,x,0,-c);
	}
	int ans=dinic(s,t);
	printf("%d %d\n",ans,res);
	return 0;
}
//zzt qwq

三元环计数

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e5+10,M=2e5+10;
int head[N],ver[M],nxt[M],tot=0;
void add(int x,int y)
{
	ver[++tot]=y;
	nxt[tot]=head[x];
	head[x]=tot;
}
int u[M],v[M],deg[N],vis[N];
int main()
{
	int n=read(),m=read();
	for(int i=1;i<=m;i++)
	{
		u[i]=read(),v[i]=read();
		deg[u[i]]++,deg[v[i]]++;
	}
	for(int i=1;i<=m;i++)
	{
		if(deg[u[i]]>deg[v[i]])add(u[i],v[i]);
		else if(deg[u[i]]<deg[v[i]])add(v[i],u[i]);
		else add(max(u[i],v[i]),min(u[i],v[i]));
	}
	int ans=0;
	for(int x=1;x<=n;x++)
	{
		for(int i=head[x];i;i=nxt[i]){int y=ver[i];vis[y]=x;}
		for(int i=head[x];i;i=nxt[i])
		{
			int y=ver[i];
			for(int j=head[y];j;j=nxt[j])
			{
				int z=ver[j];
				if(vis[z]==x)ans++;
			}
		}
	}
	printf("%d\n",ans);
	return 0;
}
//zzt qwq

最小生成树（Borůvka）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=2e5+10;
struct dsu{
	int sz[N],fa[N];
	void init(int n){for(int i=1;i<=n;i++)fa[i]=i,sz[i]=1;}
	int getf(int x){return fa[x]==x?x:fa[x]=getf(fa[x]);}
	void mg(int x,int y)
	{
		if(getf(x)==getf(y))return;
		x=getf(x),y=getf(y);
		sz[y]+=sz[x];
		fa[x]=y;
	}
}B;

vector<pii> v[N];
//first:edge, second:ver
void add(int x,int y,int z){v[x].pb(mp(z,y));}
int now[N],pos[N],n,m,mn[N],p;
int boruvka()
{
	int ans=0;bool f=1; 
	while(f)
	{
		f=0;
		for(int i=1;i<=n;i++)pos[i]=-1,mn[i]=1e9;
		for(int x=1;x<=n;x++)
		{
			int fa=B.getf(x);
			for(int j=now[x];j<(int)v[x].size();j++)
			{
				now[x]=j;
				int y=v[x][j].se,z=v[x][j].fi;
				if(B.getf(y)==fa)continue;
				if(pos[fa]==-1||z<mn[fa])mn[fa]=z,pos[fa]=y;
				break;
			}
		}
		for(int i=1;i<=n;i++)
		{
			if(pos[i]==-1)continue;
			if(B.getf(i)==B.getf(pos[i]))continue;
			B.mg(i,pos[i]);
			ans+=mn[i];
			f=1;
		}
	}
	return B.sz[B.getf(1)]==n?ans:-1;
}
int main()
{
	n=read(),m=read();B.init(n);
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read(),z=read();
		add(x,y,z),add(y,x,z);
	}
	for(int i=1;i<=n;i++)sort(v[i].begin(),v[i].end());
	int ans=boruvka();
	if(~ans)printf("%d\n",ans);
	else puts("orz");
	return 0;
}

最小生成树（Kruskal）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=5010,M=2e5+10;
struct dsu{
	int fa[N];
	void init(int n){for(int i=1;i<=n;i++)fa[i]=i;}
	int getf(int x){return fa[x]==x?x:fa[x]=getf(fa[x]);}
	void mg(int x,int y){fa[getf(y)]=getf(x);} 
}B;
struct Edge{
	int u,v,w;
}e[M];
bool cmp(Edge x,Edge y){return x.w<y.w;}
int main()
{
	int n=read(),m=read(),cnt=0,ans=0;B.init(n);
	for(int i=1;i<=m;i++){int u=read(),v=read(),w=read();e[i]=Edge{u,v,w};}
	sort(e+1,e+m+1,cmp);
	for(int i=1;i<=m;i++)
	{
		int u=e[i].u,v=e[i].v,w=e[i].w;
		if(B.getf(u)==B.getf(v))continue;
		B.mg(u,v),ans+=w,cnt++;
	}
	if(cnt!=n-1)puts("orz");
	else printf("%d\n",ans);
	return 0;
}

数据结构

线段树合并

//P3224 永无乡
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e5+10;
int rt[N],pos[N];
struct sgt{
	struct seg{
		int ls,rs,sum;
		seg(){ls=rs=sum=0;}
	}t[N<<5];
	int tot;
	sgt(){tot=0;}
	int modify(int l,int r,int x,int d)
	{
		int p=++tot;
		if(l==r){t[p].sum+=d;return p;}
		int mid=(l+r)>>1;
		if(x<=mid)t[p].ls=modify(l,mid,x,d);
		else t[p].rs=modify(mid+1,r,x,d);
		t[p].sum=t[t[p].ls].sum+t[t[p].rs].sum;
		return p;
	}
	int mg(int p,int q,int l,int r)
	{
		if(!p||!q)return p|q;
		if(l==r){t[p].sum+=t[q].sum;return p;}
		int mid=(l+r)>>1;
		t[p].ls=mg(t[p].ls,t[q].ls,l,mid);
		t[p].rs=mg(t[p].rs,t[q].rs,mid+1,r);
		t[p].sum=t[t[p].ls].sum+t[t[p].rs].sum;
		return p;
	}
	int query(int p,int l,int r,int k)
	{
		if(t[p].sum<k)return -1;
		if(l==r)return l;int mid=(l+r)>>1;
		if(t[t[p].ls].sum>=k)return query(t[p].ls,l,mid,k);
		else return query(t[p].rs,mid+1,r,k-t[t[p].ls].sum);
	}
}T;
int p[N];
struct dsu{
	int fa[N];
	void init(int n){for(int i=1;i<=n;i++)fa[i]=i;}
	int getf(int x){return fa[x]==x?x:fa[x]=getf(fa[x]);}
	void mg(int x,int y){fa[getf(y)]=getf(x);}
}B;
int main()
{
//	freopen("1.out","w",stdout);
	int n=read(),m=read();
	for(int i=1;i<=n;i++)p[i]=read(),pos[p[i]]=i;
	for(int i=1;i<=n;i++)rt[i]=T.modify(1,n,p[i],1);
	B.init(n);
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read();
		x=B.getf(x),y=B.getf(y);
		if(B.getf(x)==B.getf(y))continue;
		rt[x]=T.mg(rt[x],rt[y],1,n); 
		B.mg(x,y);
	}
	int Q=read();
	while(Q--)
	{
		char s[3];scanf("%s",s);
		if(s[0]=='Q')
		{
			int x=read(),k=read();
			x=B.getf(x);
			int tmp=T.query(rt[x],1,n,k);
			if(~tmp)printf("%d\n",pos[tmp]);
			else puts("-1");
		}
		else
		{
			int x=read(),y=read();
			x=B.getf(x),y=B.getf(y);
			if(B.getf(x)==B.getf(y))continue;
			rt[x]=T.mg(rt[x],rt[y],1,n);
			B.mg(x,y);
		}
	}
	return 0;
}

莫队

//P4462
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
using namespace std;
const int N=1e5+10;
int a[N],k,cnt[N],ans,Ans[N],sum[N];
void del(int x){ans-=cnt[x^k];cnt[x]--;}
void add(int x){ans+=cnt[x^k];cnt[x]++;}
struct query
{
	int l,r,bl,pos;
	query(){}
	query(int ll,int rr,int bb,int pp){l=ll;r=rr;bl=bb;pos=pp;}
}q[N];
bool cmp(query x,query y){return x.bl!=y.bl?x.l<y.l:(x.bl&1)?x.r<y.r:x.r>y.r;}
int main()
{
	int n,m;scanf("%d%d%d",&n,&m,&k);
	int t=sqrt(n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]),sum[i]=sum[i-1]^a[i];
	for(int i=1;i<=m;i++)
	{
		int l,r;scanf("%d%d",&l,&r);
		q[i]=query(l-1,r,(l-1)/t+1,i);
	}
	sort(q+1,q+m+1,cmp);
	int l=0,r=-1;
	for(int i=1;i<=m;i++)
	{
		int ll=q[i].l,rr=q[i].r;

		while(l<ll)del(sum[l++]);
		while(l>ll)add(sum[--l]);
		while(r<rr)add(sum[++r]);
		while(r>rr)del(sum[r--]);
		Ans[q[i].pos]=ans;
	}
	for(int i=1;i<=m;i++) printf("%d\n",Ans[i]);
	return 0;
}

主席树

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=2e5+10;
int a[N],t[N],rt[N];
int tot=0;
struct president
{
	struct node
	{
		int ls,rs,sum;
		node(){ls=rs=sum=0;}
	}t[N<<5];
	int build(int l,int r)
	{
		int p=++tot;
		if(l==r)return p;
		int mid=(l+r)/2;
		t[p].ls=build(l,mid);
		t[p].rs=build(mid+1,r);
		return p;
	}
	int modify(int pre,int l,int r,int x)
	{
		int p=++tot;
		t[p]=t[pre];
		if(l==r)
		{
			t[p].sum++;
			return p;
		}
		int mid=(l+r)/2;
		if(x<=mid)t[p].ls=modify(t[pre].ls,l,mid,x);
		else t[p].rs=modify(t[pre].rs,mid+1,r,x);
		t[p].sum=t[t[p].ls].sum+t[t[p].rs].sum;
		return p;
	}
	int query(int u,int v,int l,int r,int k)
	{
		int sum=t[t[v].ls].sum-t[t[u].ls].sum;
		if(l==r)return l;
		int mid=(l+r)/2;
		if(sum>=k)return query(t[u].ls,t[v].ls,l,mid,k);
		else return query(t[u].rs,t[v].rs,mid+1,r,k-sum);
	}
}T;
int main()
{
	int n=read(),m=read();
	for(int i=1;i<=n;i++)a[i]=read();
	memcpy(t,a,sizeof(a));int c=n;
	sort(t+1,t+c+1);c=unique(t+1,t+c+1)-t-1;
	for(int i=1;i<=n;i++)a[i]=lower_bound(t+1,t+c+1,a[i])-t;
	rt[0]=T.build(1,c);
	for(int i=1;i<=n;i++)rt[i]=T.modify(rt[i-1],1,c,a[i]);
	for(int i=1;i<=m;i++)
	{
		int l=read(),r=read(),k=read();
		printf("%d\n",t[T.query(rt[l-1],rt[r],1,c,k)]);
	}
	return 0;
}

轻重链剖分

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=1e5+10,M=2e5+10;
int head[N],ver[M],nxt[M],tot=0,mod;
void add(int x,int y)
{
	ver[++tot]=y;
	nxt[tot]=head[x];
	head[x]=tot;
}
int dfn[N],num,top[N],sz[N],son[N],fa[N],dep[N],pos[N],a[N];
void dfs(int x)
{
//	printf("x=%d\n",x);
	sz[x]=1;
	for(int i=head[x];i;i=nxt[i])
	{
		int y=ver[i];if(dep[y])continue;
		dep[y]=dep[x]+1,fa[y]=x;
		dfs(y),sz[x]+=sz[y];
		if(!son[x]||(sz[y]>sz[son[x]]))son[x]=y;
	}
}
void dfs1(int x,int t)
{
	dfn[x]=++num,pos[dfn[x]]=x,top[x]=t;
	if(son[x])dfs1(son[x],t); 
	for(int i=head[x];i;i=nxt[i])
	{
		int y=ver[i];
		if(y==fa[x]||y==son[x])continue;
		dfs1(y,y);
	}
}
struct sgt{
	struct seg{
		int l,r;
		int add,sum;
	}t[N<<2];
	void build(int p,int l,int r)
	{
		t[p].l=l,t[p].r=r;
		t[p].add=0;
		if(l==r)return t[p].sum=a[pos[l]],void();
		int mid=(l+r)>>1;
		build(p*2,l,mid),build(p*2+1,mid+1,r);
		t[p].sum=t[p*2].sum+t[p*2+1].sum,t[p].sum%=mod;
	}
	void pd(int p)
	{
		if(t[p].add)
		{
			t[p*2].add+=t[p].add,t[p*2].add%=mod;
			t[p*2+1].add+=t[p].add,t[p*2+1].add%=mod;
			t[p*2].sum+=1ll*(t[p*2].r-t[p*2].l+1)*t[p].add%mod,t[p*2].sum%=mod;
			t[p*2+1].sum+=1ll*(t[p*2+1].r-t[p*2+1].l+1)*t[p].add%mod,t[p*2+1].sum%=mod;
			t[p].add=0;
		}
	}
	int query(int p,int l,int r)
	{
		if(l<=t[p].l&&t[p].r<=r)return t[p].sum;
		pd(p);int mid=(t[p].l+t[p].r)>>1,ans=0;
		if(l<=mid)ans+=query(p*2,l,r),ans%=mod;
		if(r>mid)ans+=query(p*2+1,l,r),ans%=mod;
		return ans;
	}
	void modify(int p,int l,int r,int d)
	{
		if(l<=t[p].l&&t[p].r<=r)
		{
			t[p].sum+=1ll*(t[p].r-t[p].l+1)*d%mod,t[p].sum%=mod;
			t[p].add+=d,t[p].add%=mod;
			return;
		}
		pd(p);int mid=(t[p].l+t[p].r)>>1;
		if(l<=mid)modify(p*2,l,r,d);
		if(r>mid)modify(p*2+1,l,r,d);
		t[p].sum=t[p*2].sum+t[p*2+1].sum,t[p].sum%=mod; 
	}
}T;
void modify(int x,int y,int d)
{
	int fx=top[x],fy=top[y];
	while(fx!=fy)
	{
		if(dep[fx]>=dep[fy])
		{
			T.modify(1,dfn[fx],dfn[x],d);
			x=fa[fx];
		}
		else
		{
			T.modify(1,dfn[fy],dfn[y],d);
			y=fa[fy];
		}
		fx=top[x],fy=top[y];
	}
	T.modify(1,min(dfn[x],dfn[y]),max(dfn[x],dfn[y]),d);
}
int query(int x,int y)
{
	int ans=0,fx=top[x],fy=top[y];
	while(fx!=fy)
	{
		if(dep[fx]>=dep[fy])
		{
			ans+=T.query(1,dfn[fx],dfn[x]),ans%=mod;
			x=fa[fx];
		}
		else
		{
			ans+=T.query(1,dfn[fy],dfn[y]),ans%=mod;
			y=fa[fy];
		}
		fx=top[x],fy=top[y];
	}
	ans+=T.query(1,min(dfn[x],dfn[y]),max(dfn[x],dfn[y])),ans%=mod;
	return ans;
}
int main()
{
	int n=read(),m=read(),rt=read();mod=read();
	for(int i=1;i<=n;i++)a[i]=read();
	for(int i=1;i<n;i++){int u=read(),v=read();add(u,v),add(v,u);}
	dep[rt]=1,dfs(rt),dfs1(rt,rt),T.build(1,1,n);
	while(m--)
	{
		int pos=read();
		if(pos==1){int u=read(),v=read(),w=read();modify(u,v,w);}
		else if(pos==2){int u=read(),v=read();printf("%d\n",query(u,v));}
		else if(pos==3){int x=read(),d=read();T.modify(1,dfn[x],dfn[x]+sz[x]-1,d);}
		else {int x=read();printf("%d\n",T.query(1,dfn[x],dfn[x]+sz[x]-1));}
	}
}
//zzt qwq

普通平衡树（FHQ Treap）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch^48);ch=getchar();}
	return x*f;
}
const int N=1e5+10;
int ch[N][2],val[N],pri[N],sz[N],cnt=0;
void maintain(int x){sz[x]=1+sz[ch[x][0]]+sz[ch[x][1]];}
int build(int v)
{
	val[++cnt]=v;
	pri[cnt]=rand();
	sz[cnt]=1;
	return cnt;
}
int merge(int x,int y)
{
	if(!x||!y)return x+y;
	if(pri[x]<pri[y])
	{
		ch[x][1]=merge(ch[x][1],y);
		maintain(x);
		return x;
	}
	else
	{
		ch[y][0]=merge(x,ch[y][0]);
		maintain(y);
		return y;
	}
}
void split(int now,int k,int &x,int &y)
{
	if(!now)x=y=0;
	else
	{
		if(val[now]<=k)x=now,split(ch[now][1],k,ch[x][1],y);
		else y=now,split(ch[now][0],k,x,ch[y][0]);
		maintain(now);
	}
}
int kth(int now,int k)
{
	while(114514)
	{
		if(sz[ch[now][0]]>=k)now=ch[now][0];
		else if(sz[ch[now][0]]+1==k)return val[now];
		else k-=sz[ch[now][0]]+1,now=ch[now][1];
	}
}
int main()
{
	int n=read(),rt=0,x,y,z;
	for(int i=1;i<=n;i++)
	{
		int p=read(),v=read();
		if(p==1)//insert 
		{
			split(rt,v-1,x,y);
			rt=merge(merge(x,build(v)),y);
		}
		else if(p==2)//delete
		{
			split(rt,v,x,z);
			split(x,v-1,x,y);
			y=merge(ch[y][0],ch[y][1]);
			rt=merge(merge(x,y),z);
		}
		else if(p==3)//rank
		{
			split(rt,v-1,x,y);
			printf("%d\n",sz[x]+1);
			rt=merge(x,y);
		}
		else if(p==4)//kth
			printf("%d\n",kth(rt,v));
		else if(p==5)//pre
		{
			split(rt,v-1,x,y);
			printf("%d\n",kth(x,sz[x]));
			rt=merge(x,y);
		}
		else//nxt
		{
			split(rt,v,x,y);
			printf("%d\n",kth(y,1));
			rt=merge(x,y);
		}
	}
	return 0;
}

普通平衡树（Splay）

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int N=1e5;
int rt,tot,sz[N+10],ch[N+10][2],fa[N+10],cnt[N+10],val[N+10];
void maintain(int x) {sz[x]=sz[ch[x][0]]+sz[ch[x][1]]+cnt[x];}
void clear(int x) {sz[x]=ch[x][0]=ch[x][1]=fa[x]=cnt[x]=val[x]=0;}
int get(int x) {return ch[fa[x]][1]==x;}
void rorate(int x)
{
	int y=fa[x],z=fa[y],w=get(x);
	ch[y][w]=ch[x][w^1];
	fa[ch[x][w^1]]=y;
	ch[x][w^1]=y;
	fa[y]=x;
	fa[x]=z;
	if(z) ch[z][y==ch[z][1]]=x;
	maintain(y);
	maintain(x);
}
void splay(int x)
{
	for(int f=fa[x];f=fa[x],f;rorate(x))
		if(fa[f]) rorate(get(f)==get(x)?f:x);
	rt=x;
}
void ins(int k)
{
	if(!rt)
	{
		val[++tot]=k;
		cnt[tot]++;
		rt=tot;
		maintain(rt);
		return;
	}
	int cur=rt,f=0;
	while(1)
	{
		if(val[cur]==k)
		{
			cnt[cur]++;
			maintain(cur);
			maintain(f);
			splay(cur);
			break;
		}
		f=cur;
		cur=ch[cur][val[cur]<k];
		if(!cur)
		{
			val[++tot]=k;
			cnt[tot]++;
			fa[tot]=f;
			ch[f][val[f]<k]=tot;
			maintain(tot);
			maintain(f);
			splay(tot);
			break;
		}
	}
}
int rk(int k)
{
	int cur=rt,res=0;
	while(1)
	{
		if(k<val[cur]) cur=ch[cur][0];
		else
		{
			res+=sz[ch[cur][0]];
			if(val[cur]==k)
			{
				splay(cur);
				return res+1;
			}
			res+=cnt[cur];
			cur=ch[cur][1];
		}
	}
}
int kth(int k)
{
	int cur=rt;
	while(1)
	{
		if(k<=sz[ch[cur][0]] && ch[cur][0]) cur=ch[cur][0];
		else
		{
			k-=sz[ch[cur][0]]+cnt[cur];
			if(k<=0)
			{
				splay(cur);
				return val[cur];
			}
			cur=ch[cur][1];
		}
	}
}
int pre()
{
	int cur=ch[rt][0];
	while(ch[cur][1]) cur=ch[cur][1];
	return cur;
}
int nxt()
{
	int cur=ch[rt][1];
	while(ch[cur][0]) cur=ch[cur][0];
	return cur;
}
void del(int k)
{
	rk(k);
	if(cnt[rt]>1) 
	{
		cnt[rt]--;
		maintain(rt);
		return;
	}
	if(!ch[rt][0] && !ch[rt][1])
	{
		clear(rt);
		rt=0;
		return;
	}
	if(!ch[rt][0])
	{
		int cur=rt;
		rt=ch[rt][1];
		fa[rt]=0;
		clear(cur);
		return;
	}
	if(!ch[rt][1])
	{
		int cur=rt;
		rt=ch[rt][0];
		fa[rt]=0;
		clear(cur);
		return;
	}
	int cur=rt,x=pre();
	splay(x);
	fa[ch[cur][1]]=x;
	ch[x][1]=ch[cur][1];
	clear(cur);
	maintain(rt);
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int p,x;
		scanf("%d %d",&p,&x);
		if(p==1) ins(x);
		else if(p==2) del(x);
		else if(p==3) printf("%d\n",rk(x));
		else if(p==4) printf("%d\n",kth(x));
		else if(p==5)
		{
			ins(x);
			printf("%d\n",val[pre()]);
			del(x);
		}
		else
		{
			ins(x);
			printf("%d\n",val[nxt()]);
			del(x);
		}
	}
	return 0;
}

文艺平衡树（FHQ Treap）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e5+10;
int ch[N][2],val[N],pri[N],sz[N],cnt=0,tag[N];
void maintain(int x){sz[x]=1+sz[ch[x][0]]+sz[ch[x][1]];}
void pd(int p)
{
	if(!tag[p])return;
	swap(ch[p][0],ch[p][1]);
	if(ch[p][0])tag[ch[p][0]]^=1;
	if(ch[p][1])tag[ch[p][1]]^=1;
	tag[p]=0;
}
int build(int v)
{
	val[++cnt]=v;
	pri[cnt]=rand();
	sz[cnt]=1;
	return cnt;
}
int merge(int x,int y)
{
	if(!x||!y)return x+y;
	if(pri[x]<pri[y])
	{
		pd(x);
		ch[x][1]=merge(ch[x][1],y);
		maintain(x);
		return x;
	}
	else
	{
		pd(y);
		ch[y][0]=merge(x,ch[y][0]);
		maintain(y);
		return y;
	}
}
void split(int now,int k,int &x,int &y)
{
	if(!now)x=y=0;
	else
	{
		pd(now);
		if(k<=sz[ch[now][0]])y=now,split(ch[now][0],k,x,ch[y][0]);
		else x=now,split(ch[now][1],k-sz[ch[now][0]]-1,ch[x][1],y);
		maintain(now);
	}
}
void print(int p)
{
	if(!p)return;
	pd(p);
	print(ch[p][0]);
	printf("%d ",val[p]);
	print(ch[p][1]);
}
int main()
{
	int n=read(),rt=0,x,y,z,m=read();
	for(int i=1;i<=n;i++)rt=merge(rt,build(i));
	for(int i=1;i<=m;i++)
	{
		int l=read(),r=read();
		split(rt,l-1,x,y);
		split(y,r-l+1,y,z);
		tag[y]^=1;
		rt=merge(merge(x,y),z);
	}
	print(rt);
	return 0;
}

三维偏序（CDQ分治）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=2e5+10;
struct node{
	int x,y,z,c,pos;
	node(){x=y=z=c=pos=0;}
}a[N],b[N];
bool cmp(node a,node b){return a.x!=b.x?a.x<b.x:(a.y!=b.y?a.y<b.y:a.z<b.z);}
bool cmp1(node a,node b){return a.y!=b.y?a.y<b.y:a.z<b.z;}
//bool cmp2(node a,node b){return a.pos<b.pos;}
int m;
struct bit{
	int c[N];
	bit(){memset(c,0,sizeof(c));}
	int query(int x){int ans=0;for(;x;x-=x&-x)ans+=c[x];return ans;}
	void modify(int x,int d){for(;x<=m;x+=x&-x)c[x]+=d;}
}T;
int f[N];
void cdq(int l,int r)
{
	if(l==r)return;
	int mid=(l+r)>>1;
	cdq(l,mid),cdq(mid+1,r);
	sort(a+l,a+mid+1,cmp1),sort(a+mid+1,a+r+1,cmp1);
	int j=l;
	for(int i=mid+1;i<=r;i++)
	{
		while(j<=mid&&a[j].y<=a[i].y)T.modify(a[j].z,a[j].c),j++;
		f[a[i].pos]+=T.query(a[i].z);
	}
	for(int i=l;i<j;i++)T.modify(a[i].z,-a[i].c);
}
int Ans[N];
int main()
{
	int nn=read(),n=0;m=read();
	for(int i=1;i<=nn;i++)b[i].x=read(),b[i].y=read(),b[i].z=read();
	sort(b+1,b+nn+1,cmp);
	a[n=1]=b[1],a[1].c=1;
	for(int i=2;i<=nn;i++)
	{
		if(a[n].x==b[i].x&&a[n].y==b[i].y&&a[n].z==b[i].z)a[n].c++;
		else a[++n]=b[i],a[n].c=1;
	}
	for(int i=1;i<=n;i++)a[i].pos=i;
	cdq(1,n);
	for(int i=1;i<=n;i++)f[a[i].pos]+=a[i].c-1;
//	sort(a+1,a+n+1,cmp2);
//	for(int i=1;i<=n;i++)printf("(%d, %d, %d), cnt=%d, f=%d\n",a[i].x,a[i].y,a[i].z,a[i].c,f[i]);
	for(int i=1;i<=n;i++)Ans[f[a[i].pos]]+=a[i].c;
	for(int i=0;i<nn;i++)printf("%d\n",Ans[i]);
	return 0;
}
//zzt qwq

笛卡尔树

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e7+10;
int p[N],st[N],top=0,ls[N],rs[N];
int main()
{
	int n=read();
	for(int i=1;i<=n;i++)p[i]=read();
	for(int i=1;i<=n;i++)
	{
		int k=top;
		while(k&&p[i]<p[st[k]])k--;
		if(k)rs[st[k]]=i;
		if(k<top)ls[i]=st[k+1];
		st[++k]=i,top=k;
	}
	ll ans1=0,ans2=0;
	for(int i=1;i<=n;i++)ans1^=1ll*i*(ls[i]+1),ans2^=1ll*i*(rs[i]+1);
	printf("%lld %lld\n",ans1,ans2);
	return 0;
}
//zzt qwq 

数学

线性筛

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
bitset<100000010>vis;
const int N=5e7+10,maxn=1e8;
int pri[N],tot=0;
void init()
{
	for(int i=2;i<=maxn;i++)
	{
		if(!vis[i])
			pri[++tot]=i;
		for(int j=1;j<=tot&&pri[j]*i<=maxn;j++)
		{
			vis[i*pri[j]]=1;
			if(i%pri[j]==0)break;
		}
	}
}
int main()
{
	init();
	int n=read(),q=read();
	while(q--)
	{
		int k=read();
		printf("%d\n",pri[k]);
	}
}

高斯消元&行列式求值

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=110;
const double eps=1e-4;
double a[N][N];
int main()
{
	int n=read();
	for(int i=1;i<=n;i++)for(int j=1;j<=n+1;j++)a[i][j]=read();
	for(int i=1;i<=n;i++)
	{
		int p=i;
		for(int j=i+1;j<=n;j++)if(fabs(a[j][i])>=fabs(a[p][i]))p=j;
		for(int j=1;j<=n+1;j++)swap(a[i][j],a[p][j]);
		if(fabs(a[i][i])<=eps)return puts("No Solution"),0;
		for(int j=i+1;j<=n;j++)
		{
			double r=a[j][i]/a[i][i];
			for(int k=1;k<=n+1;k++)a[j][k]-=a[i][k]*r;
		}
		for(int k=i+1;k<=n+1;k++)a[i][k]/=a[i][i];
		a[i][i]=1;
	}
	for(int i=n-1;i;i--)for(int j=i+1;j<=n;j++)a[i][n+1]-=a[j][n+1]*a[i][j];
	for(int i=1;i<=n;i++)printf("%.2lf\n",a[i][n+1]);
}
//zzt qwq

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=610;
int n,mod;
struct mat{
	int a[N][N];
	mat(){memset(a,0,sizeof(a));}
	int det()
	{
		int ans=1;
		for(int i=1;i<=n;i++)
		{
			for(int j=i+1;j<=n;j++)
			{
				while(a[i][i])
				{
					int r=a[j][i]/a[i][i];
					for(int k=1;k<=n;k++)a[j][k]-=1ll*r*a[i][k]%mod,a[j][k]=(a[j][k]+mod)%mod;
					for(int k=1;k<=n;k++)swap(a[i][k],a[j][k]);
					ans=1ll*ans*(mod-1)%mod;
				}
				ans=1ll*ans*(mod-1)%mod;
				for(int k=1;k<=n;k++)swap(a[i][k],a[j][k]);
			}
		}
		for(int i=1;i<=n;i++)ans=1ll*ans*a[i][i]%mod;
		return ans;
	}
}x;
int main()
{
	n=read(),mod=read();
	for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)x.a[i][j]=read();
	printf("%d\n",x.det());
	return 0;
}
//zzt qwq

CRT/EXCRT

太丑了，有时间重新写一份

拉格朗日插值

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int mod=998244353;
int qpow(int a,int n)
{
	int ans=1;
	while(n)
	{
		if(n&1)ans=1ll*a*ans%mod;
		a=1ll*a*a%mod;
		n>>=1;
	}
	return ans;
}
const int N=2e3+10;
int x[N],y[N];
int main()
{
	int n=read(),k=read();
	for(int i=1;i<=n;i++)x[i]=read(),y[i]=read();
	int ans=0;
	for(int i=1;i<=n;i++)
	{
		int s2=1,s1=1;
		for(int j=1;j<=n;j++)
		{
			if(i==j)continue;
			s1=(k-x[j]+mod)%mod*1ll*s1%mod;
			s2=(x[i]-x[j]+mod)%mod*1ll*s2%mod;
		}
		ans+=1ll*s1*qpow(s2,mod-2)%mod*y[i]%mod,ans%=mod; 
	}
	printf("%d",ans);
	return 0;
}

AND/OR/XOR 卷积

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0)putchar('-'),n=-n;
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=1<<17,mod=998244353,inv2=(mod+1)>>1;
int a[N],b[N],c[N],n;
int ta[N],tb[N];
void fwt_and()
{
	memcpy(ta,a,sizeof(a)),memcpy(tb,b,sizeof(b));
	for(int i=0;i<n;i++)
	{
		for(int s=0;s<(1<<n);s++)
		{
			if(!(s&(1<<i)))continue;
			a[s^(1<<i)]+=a[s],b[s^(1<<i)]+=b[s],a[s^(1<<i)]%=mod,b[s^(1<<i)]%=mod;
		}
	}
	for(int s=0;s<(1<<n);s++)c[s]=1ll*a[s]*b[s]%mod;
	for(int i=0;i<n;i++)
	{
		for(int s=0;s<(1<<n);s++)
		{
			if(!(s&(1<<i)))continue;
			c[s^(1<<i)]-=c[s],c[s^(1<<i)]=(c[s^(1<<i)]+mod)%mod;
		}
	}
	memcpy(a,ta,sizeof(ta)),memcpy(b,tb,sizeof(tb));
}
void fwt_or()
{
	memcpy(ta,a,sizeof(a)),memcpy(tb,b,sizeof(b));
	for(int i=0;i<n;i++)
	{
		for(int s=0;s<(1<<n);s++)
		{
			if(s&(1<<i))continue;
			a[s^(1<<i)]+=a[s],b[s^(1<<i)]+=b[s],a[s^(1<<i)]%=mod,b[s^(1<<i)]%=mod;
		}
	}
	for(int s=0;s<(1<<n);s++)c[s]=1ll*a[s]*b[s]%mod;
	for(int i=0;i<n;i++)
	{
		for(int s=0;s<(1<<n);s++)
		{
			if(s&(1<<i))continue;
			c[s^(1<<i)]-=c[s],c[s^(1<<i)]=(c[s^(1<<i)]+mod)%mod;
		}
	}
	memcpy(a,ta,sizeof(ta)),memcpy(b,tb,sizeof(tb));
}
void fwt_xor()
{
	memcpy(ta,a,sizeof(a)),memcpy(tb,b,sizeof(b));
	for(int i=1;i<(1<<n);i<<=1)
	{
		for(int j=0;j<(1<<n);j+=(i<<1))
		{
			for(int s=j;s<j+i;s++)
			{
				int x=a[s],y=a[s+i];
				a[s]=(x+y)%mod,a[s+i]=(x-y+mod)%mod;
			}
		}
	}
	for(int i=1;i<(1<<n);i<<=1)
	{
		for(int j=0;j<(1<<n);j+=(i<<1))
		{
			for(int s=j;s<j+i;s++)
			{
				int x=b[s],y=b[s+i];
				b[s]=(x+y)%mod,b[s+i]=(x-y+mod)%mod;
			}
		}
	}
	for(int s=0;s<(1<<n);s++)c[s]=1ll*a[s]*b[s]%mod;
	for(int i=1;i<(1<<n);i<<=1)
	{
		for(int j=0;j<(1<<n);j+=(i<<1))
		{
			for(int s=j;s<j+i;s++)
			{
				int x=c[s],y=c[s+i];
				c[s]=(x+y)%mod,c[s+i]=(x-y+mod)%mod;
				c[s]=1ll*c[s]*inv2%mod,c[s+i]=1ll*c[s+i]*inv2%mod;
			}
		}
	}
	memcpy(a,ta,sizeof(ta)),memcpy(b,tb,sizeof(tb));
}
int main()
{
	n=read();
	for(int i=0;i<(1<<n);i++)a[i]=read();
	for(int i=0;i<(1<<n);i++)b[i]=read();
	fwt_or();for(int i=0;i<(1<<n);i++)printf("%d ",c[i]);puts("");
	fwt_and();for(int i=0;i<(1<<n);i++)printf("%d ",c[i]);puts("");
	fwt_xor();for(int i=0;i<(1<<n);i++)printf("%d ",c[i]);puts("");
	return 0;
}
//zzt qwq

子集卷积

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0)putchar('-'),n=-n;
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=1<<20,mod=1e9+9;
int a[N],n,f[25][N],g[25][N],h[25][N],pop[N];
void fwt_or(int *a,int tp)
{
	for(int i=0;i<n;i++)
	{
		for(int s=0;s<(1<<n);s++)
		{
			if(s&(1<<i))continue;
			if(tp==1)a[s^(1<<i)]+=a[s],a[s^(1<<i)]%=mod;
			else a[s^(1<<i)]+=mod-a[s],a[s^(1<<i)]%=mod;
		}
	}
}
int main()
{
	for(int i=1;i<N;i++)pop[i]=pop[i>>1]+(i&1);
	n=read();
	for(int i=0;i<(1<<n);i++)f[pop[i]][i]=read();
	for(int i=0;i<(1<<n);i++)g[pop[i]][i]=read();
	for(int i=0;i<=n;i++)fwt_or(f[i],1),fwt_or(g[i],1);
	for(int i=0;i<=n;i++)for(int j=0;j+i<=n;j++)for(int s=0;s<(1<<n);s++)
	h[i+j][s]+=1ll*f[i][s]*g[j][s]%mod,h[i+j][s]%=mod;
	for(int i=0;i<=n;i++)fwt_or(h[i],-1);
	for(int i=0;i<(1<<n);i++)printf("%d ",h[pop[i]][i]);
	return 0;
}
//zzt qwq

字符串

KMP

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1000010;
int nxt[N],la,lb;
char a[N],b[N];
int main()
{
	scanf("%s%s",a+1,b+1);
	la=strlen(a+1);
	lb=strlen(b+1);
	for(int i=2,j=0;i<=lb;i++)
	{
		while(j&&b[i]!=b[j+1])j=nxt[j];
		if(b[j+1]==b[i])j++;
		nxt[i]=j;
	}
	for(int i=1,j=0;i<=la;i++)
	{
		while(j>0&&b[j+1]!=a[i])j=nxt[j];
		if(b[j+1]==a[i])j++;
		if(j==lb)
		{
			printf("%d\n",i-lb+1);
			j=nxt[j];
		}
	}

	for(int i=1;i<=lb;i++)printf("%d ",nxt[i]);
	return 0;
}

AC自动机

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
const int N=1e6+10;
struct ACAM{
	int tot,tr[N][26],e[N],fail[N];
	ACAM(){tot=0;memset(tr,0,sizeof(tr)),memset(e,0,sizeof(e)),memset(fail,0,sizeof(fail));}
	void ins(char *s)
	{
		int u=0;
		for(int i=1;s[i];i++)
		{
			if(!tr[u][s[i]-'a'])tr[u][s[i]-'a']=++tot;
			u=tr[u][s[i]-'a'];
		}
		e[u]++;
	}
	void getfail()
	{
		queue<int> que;
		for(int i=0;i<26;i++)if(tr[0][i])que.push(tr[0][i]);
		while(!que.empty())
		{
			int x=que.front();que.pop();
			for(int i=0;i<26;i++)
			{
				if(tr[x][i])fail[tr[x][i]]=tr[fail[x]][i],que.push(tr[x][i]);
				else tr[x][i]=tr[fail[x]][i];
			}
		}
	}
	int query(char *s)
	{
		int ans=0,p=0;
		for(int i=1;s[i];i++)
		{
			int x=s[i]-'a';
			p=tr[p][x];
			for(int j=p;j&&~e[j];j=fail[j])ans+=e[j],e[j]=-1;
		}
		return ans;
	}
}T;
char s[N];
int main()
{
	int n=read();
	for(int i=1;i<=n;i++)scanf("%s",s+1),T.ins(s);
	T.getfail();scanf("%s",s+1);
	printf("%d\n",T.query(s));
	return 0;
}

SA

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
inline int read()
{
	int x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return x*f;
}
void write(int n)
{
	if(n<0){putchar('-');n=-n;}
	if(n>9)write(n/10);
	putchar(n%10^48);
}
const int N=2e6+10;
char s[N];int id[N],cnt[N],sa[N],rk[N],old[N];
bool cmp(int x,int y,int w){return old[x]==old[y]&&old[x+w]==old[y+w];}
int main()
{
	scanf("%s",s+1);int n=strlen(s+1),m=300;
	for(int i=1;i<=n;i++)cnt[rk[i]=s[i]]++;
	for(int i=1;i<=m;i++)cnt[i]+=cnt[i-1];
	for(int i=n;i;i--)sa[cnt[rk[i]]--]=i;
	for(int p=0,w=1;;m=p,w<<=1)
	{
		p=0;for(int i=n;i>n-w;i--)id[++p]=i;
		for(int i=1;i<=n;i++)if(sa[i]>w)id[++p]=sa[i]-w;
		memset(cnt,0,sizeof(cnt));
		for(int i=1;i<=n;i++)cnt[rk[id[i]]]++;
		for(int i=1;i<=m;i++)cnt[i]+=cnt[i-1];
		for(int i=n;i;i--)sa[cnt[rk[id[i]]]--]=id[i];
		memcpy(old,rk,sizeof(rk));
		p=0;for(int i=1;i<=n;i++)rk[sa[i]]=cmp(sa[i],sa[i-1],w)?p:++p;
		if(p==n)break;
	}
	for(int i=1;i<=n;i++)printf("%d ",sa[i]);
}