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@miosjfad
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DATA STRUCTURE

单调队列

CPP
#include<bits/stdc++.h>
#define ll long long
#define int long long
using namespace std;
const int mod = 1e9 + 7;
int a[5000100],ans[5000010];
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	deque<int> q;
	int n,k;
	cin>>n>>k;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	for(int i=1;i<=n;i++)
	{
		while(!q.empty() && i-q.front()>=k) q.pop_front();
		while(!q.empty() && a[i]<=a[q.back()]) q.pop_back();
		q.push_back(i);
		if(i>=k)
		{
			ans[i]=a[q.front()];
		}
	}
	for(int i=k;i<=n;i++)
	{
		cout<<ans[i]<<" ";
	}
  cout<<endl;
  q.clear();
	for(int i=1;i<=n;i++)
	{
		while(!q.empty() && i-q.front()>=k) q.pop_front();
		while(!q.empty() && a[i]>=a[q.back()]) q.pop_back();
		q.push_back(i);
		if(i>=k)
		{
			ans[i]=a[q.front()];
		}
	}
	for(int i=k;i<=n;i++)
	{
		cout<<ans[i]<<" ";
	}
	return 0;
}

单调栈

CPP
#include<bits/stdc++.h>
using namespace std;
int n,a[3000005],f[3000005];
stack<int>s;
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	for(int i=n;i>=1;i--)
	{
		while(!s.empty()&& a[s.top()]<=a[i]) s.pop();
		if(s.empty()) f[i]=0;
		else f[i]=s.top();
		s.push(i);
	}
	for(int i=1;i<=n;i++) cout<<f[i]<<" ";
	return 0;
}
CPP
	for(int i=1;i<=n;i++)
	{
		while(top && a[sta[top]]<=a[i]) --top;
		lmx[i]=sta[top];
		sta[++top]=i;
	}

并查集

CPP
#include<bits/stdc++.h>
using namespace std;
int fa[200006];
int find(int x)
{
	if(x==fa[x]) return x;
	return fa[x]=find(fa[x]);
}
void merge(int x,int y)
{
	fa[find(x)]=find(y);
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	 cout.tie(0);
	int n,m;
	cin>>n>>m;
	for(int i=1;i<=n;i++)
	{
		fa[i]=i;
	}
	for(int i=1;i<=m;i++)
	{
		int z,x,y;
		cin>>z>>x>>y;
		if(z==1) merge(x,y);
		else {
			if(find(x)==find(y)) cout<<"Y"<<endl;

			else cout<<"N"<<endl;
		}
	}
	return 0;
}

ST表

CPP
#include<bits/stdc++.h>
using namespace std;
int a[100006];
int f[100006][20];
int lg[100006];
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*10+ch-48;ch=getchar();}
	return x*f;
}
int main()
{
  	int n=read();
  	int m=read();
  	for(int i=1;i<=n;i++)
  	{
	  	a[i]=read();
	  	f[i][0]=a[i];
	}
//	cout<<log2(100000);
	for(int i=2;i<=100000;i++)
	{
		lg[i]=lg[i>>1]+1;
	}
	for(int j=1;j<=lg[n];j++)
	{
		for(int i=1;i<=n-(1<<(j))+1;i++)
		{
			f[i][j]=max(f[i][j-1],f[i+(1<<(j-1))][j-1]);
		}
	}
	for(int i=1;i<=m;i++)
	{
		int l=read();
		int r=read();
		int ler=lg[r-l+1];
		cout<<max(f[l][ler],f[r-(1<<(ler))+1][ler])<<"\n";//forger
	}
	return 0;
}

树状数组

CPP
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int mod = 1e9 + 7;
const int N=5e5+6;
ll c[N],a[N];
ll pre[N];
int n,m;
ll ask(int x)
{
	ll y=0;
	for(;x;x-=x&-x) y+=c[x];
	return y;
}//ask(r)-ask(l-1)
void add(int x,int y)
{
	for(;x<=n;x+=x&-x) c[x]+=y;
}
void init()
{
	for(int i=1;i<=n;i++)
	{
		pre[i]=pre[i-1]+a[i];
		c[i]=pre[i]-pre[i-(i&-i)];
	}
	return;
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	cin>>n>>m;

	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
	}
	init();
	for(int i=1;i<=m;i++)
	{
		int op,b,d;
		cin>>op>>b>>d;
		if(op==1) add(b,d);
		else cout<<ask(d)-ask(b-1)<<endl;
	}
	return 0;
}

线段树

微缩版（带 mod）

CPP
/*
1	区间每个元素加上 k
2	区间每个元素乘上 k
3	区间每个元素变为 k
4	输出区间和
MADE BY SKYx
*/

#include <bits/stdc++.h>
using namespace std;
#define ll long long
// int->ll may useful
#define db double
#define pii pair<int,int>
#define mp make_pair
#define fi first
#define se second

const int N=1e5+5;
int n, q, x, y, k;
int mod=998244353;
struct node
{
	int l,r;
	int s,add,mul;
	int set;

} tr[N<<2];


void build(int c,int l,int r)
{
	auto &t=tr[c];
	t.l=l;
	t.r=r;
	t.add=t.s=0;
	t.mul=1;
	t.set=INT_MIN;
	if(l==r)
	{
		cin>>t.s;
		t.s=t.s%mod;
		return;
	}
	int mid=(l+r)/2;
	build(c*2,l,mid);
	build(c*2+1,mid+1,r);
	t.s=(tr[c*2].s+tr[c*2+1].s)%mod;
	
}

void pushdown(int c)
{
	auto &t=tr[c];
	if(t.set!=INT_MIN)
	{
		int v=t.set;
		for(int i=0; i<2; i++)
		{
			auto &u=tr[c*2+i];
			u.set=v%mod;
			u.s=v*(u.r-u.l+1)%mod;
			u.add=0;
			u.mul=1;
		}
		t.set=INT_MIN;
	}
	if(t.mul!=1 || t.add!=0)
	{
		for(int i=0; i<2; i++)
		{
			auto &u=tr[c*2+i];
			u.s=(u.s*t.mul%mod+t.add*(u.r-u.l+1)%mod)%mod;
			u.mul=u.mul*t.mul%mod;
			u.add=(u.add*t.mul+t.add)%mod;
		}
		t.mul=1;
		t.add=0;
	}
}
void update(int c, int L, int R, int type, int v)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return;
	if(L<=t.l && t.r<=R)
	{
		if (type==1)
		{
			t.s=(t.s+v*(t.r-t.l+1))%mod;
			t.add=(t.add+v)%mod;
		}
		if (type==2)
		{
			t.s=t.s*v%mod;
			t.mul=t.mul*v%mod;
			t.add=t.add*v%mod;
		}

		if (type==3)
		{
			t.s=v*(t.r-t.l+1)%mod;
			t.set=v%mod;
			t.add=0;
			t.mul=1;
		}
		return;
	}
	pushdown(c);
	update(c*2,L,R,type,v);
	update(c*2+1,L,R,type,v);
	tr[c].s=(tr[c*2].s+tr[c*2+1].s)%mod;
}

int query(int c, int L, int R)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return 0;
	if(L<=t.l && t.r<=R) return t.s%mod;
	pushdown(c);
	return (query(c*2,L,R)+query(c*2+1,L,R))%mod;
}


signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>q;
	build(1,1,n);

	while (q--)
	{
		int op; 
		cin>>op;
		if (op == 1)
		{
			cin>>x>>y>>k;
			update(1,x,y,1,k);
		}
		if (op == 2)
		{
			cin>>x>>y>>k;
			update(1,x,y,2,k);
		}
		if (op == 3)
		{
			cin>>x>>y>>k;
			update(1,x,y,3,k);
		}
		if (op == 4)
		{
			cin>>x>>y;
			cout<<query(1,x,y)<<'\n';
		}
	}
	return 0;
}
/*


*/

全功能

CPP
/*
1	区间每个元素加上 k
2	区间每个元素乘上 k
3	区间每个元素变为 k
4	输出区间和
5	输出区间最大值
6	输出区间最小值
MADE BY SKYx
*/
#include <bits/stdc++.h>
using namespace std;


const int N = 1e5 + 5;
int n, q, m, x, y, k;

struct node
{
	int l,r;
	int s,add,mul;
	int set;
	int mx,mn;
} tr[N<<2];


void build(int c,int l,int r)
{
	auto &t=tr[c];
	t.l=l;
	t.r=r;
	t.add=t.s=t.mx=t.mn=0;
	t.mul=1;
	t.set=INT_MIN;
	if(l==r)
	{
		cin>>t.s;
		t.mx=t.mn=t.s;
		return;
	}
	int mid=(l+r)/2;
	build(c*2,l,mid);
	build(c*2+1,mid+1,r);
	t.s=(tr[c*2].s+tr[c*2+1].s);
	t.mx=max(tr[c*2].mx,tr[c*2+1].mx);
	t.mn=min(tr[c*2].mn,tr[c*2+1].mn);
}

void pushdown(int c)
{
	auto &t=tr[c];
	if(t.set!=INT_MIN)
	{
		int v=t.set;
		for(int i=0; i<2; i++)
		{
			int U=c*2+i;
			auto &u=tr[U];
			u.set=v;
			u.s=v*(u.r-u.l+1);
			u.mx=u.mn=v;
			u.add=0;
			u.mul=1;
		}
		t.set=INT_MIN;
	}
	if(t.mul!=1 || t.add!=0)
	{
		for(int i=0; i<2; i++)
		{
			int U=c*2+i;
			auto &u=tr[U];
			u.s=u.s*t.mul+t.add*(u.r-u.l+1);
			u.mx=u.mx*t.mul+t.add;
			u.mn=u.mn*t.mul+t.add;
			u.mul=u.mul*t.mul;
			u.add=(u.add*t.mul+t.add);
		}
		t.mul=1;
		t.add=0;
	}
}
void update(int c, int L, int R, int type, int v)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return;
	if (L<=t.l && t.r<=R)
	{
		if (type==1)
		{
			t.s=(t.s+v*(t.r-t.l+1));
			t.mx=(t.mx+v);
			t.mn=(t.mn+v);
			t.add=(t.add+v);
		}
		if (type==2)
		{
			t.s=t.s*v;
			int mx1=t.mx*v;
			int mn1=t.mn*v;
			t.mx=max(mx1,mn1);
			t.mn=min(mx1,mn1);
			t.mul=t.mul*v;
			t.add=t.add*v;
		}

		if (type==3)
		{
			t.s=v*(t.r-t.l+1);
			t.mx=t.mn=v;
			t.set=v;
			t.add=0;
			t.mul=1;
		}
		return;
	}
	pushdown(c);
	update(c*2,L,R,type,v);
	update(c*2+1,L,R,type,v);
	t.s=(tr[c*2].s+tr[c*2+1].s);
	t.mx=max(tr[c*2].mx,tr[c*2+1].mx);
	t.mn=min(tr[c*2].mn,tr[c*2+1].mn);
}

int query(int c, int L, int R)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return 0;
	if(L<=t.l && t.r<=R) return t.s;
	pushdown(c);
	return (query(c*2,L,R)+query(c*2+1,L,R));
	
}

int qmax(int c, int L, int R)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return INT_MIN;
	if(L<=t.l && t.r<=R) return t.mx;
	pushdown(c);
	return max(qmax(c*2,L,R),qmax(c*2+1,L,R));
	
}

int qmin(int c, int L, int R)
{
	auto &t=tr[c];
	if(R<t.l || t.r<L) return INT_MAX;
	if(L<=t.l && t.r<=R) return t.mn;
	pushdown(c);
	return min(qmin(c*2,L,R),qmin(c*2+1,L,R));
}

signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>q;
	build(1,1,n);

	while (q--)
	{
		int op; 
		cin>>op;
		if (op == 1)
		{
			cin>>x>>y>>k;
			update(1,x,y,1,k);
		}
		if (op == 2)
		{
			cin>>x>>y>>k;
			update(1,x,y,2,k);
		}
		if (op == 3)
		{
			cin>>x>>y>>k;
			update(1,x,y,3,k);
		}
		if (op == 4)
		{
			cin>>x>>y;
			cout<<query(1,x,y)<<'\n';
		}
		if (op == 5)
		{
			cin>>x>>y;
			cout<<qmax(1,x,y)<<'\n';
		}
		if (op == 6)
		{
			cin>>x>>y;
			cout<<qmin(1,x,y)<<'\n';
		}
	}
	return 0;
}
/*


*/

异或版

CPP
/*
1	输出区间和
2	区间每个元素异或上 k
把每个整数看成 $B$ 位二进制 ，对第 $b$ 位分别构建一棵线段树，
维护这棵树节点上该区间内“1 的个数”以及一个翻转懒标记，
当要对区间异或上 $k$ 时，只需对 $k$ 的二进制表示中为 1 的那些位的线段树，执行一次“翻转区间”操作
当要查询区间和时，对于每一位 $b$，查询该位线段树上 [l,r] 内 1 的个数，然后累加贡献
query(b, 1, l, r) 查询的是第 b 位在区间 [l, r] 内 1 的数量。
最终的答案是这些 1 的数量按其二进制位加权求和。通过 1LL * cnt1 * (1LL << b) 计算对应的贡献值并加到答案上。
MADE BY SKYx
*/
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 1e5 + 5;
const int B = 20;

int n, m;

struct node
{
	int l, r;
	int s;
	bool rev;
} tr[B][N<<2];

int a[N];

void build(int b, int c, int l, int r)
{
	auto &t = tr[b][c];
	t.l=l;
	t.r=r;
	t.rev=0;

	if(l==r)
	{
		t.s=((a[l]>>b)&1);
		return;
	}
	int mid = (l+r)/2;
	build(b,c*2,l,mid);
	build(b,c*2+1,mid+1,r);
	t.s=tr[b][c*2].s+tr[b][c*2+1].s;
}

void pushdown(int b, int c)
{
	auto &t = tr[b][c];
	if(!t.rev) return;
	for(int i=0; i<2; i++)
	{
		int U = c*2+i;
		auto &u=tr[b][U];
		u.rev^=1;
		int len=u.r-u.l+1;
		u.s=len-u.s;
	}
	t.rev = 0;
}

void update(int b,int c,int L,int R)
{
	auto &t = tr[b][c];
	if(R<t.l || t.r<L) return;
	if(L<=t.l && t.r<=R)
	{

		int len=t.r-t.l+1;
		t.s = len - t.s;
		t.rev ^= 1;
		return;
	}
	pushdown(b,c);
	update(b,c*2,L,R);
	update(b,c*2+1,L,R);
	t.s = tr[b][c*2].s + tr[b][c*2+1].s;
}

int query(int b,int c,int L,int R)
{
	auto &t = tr[b][c];
	if(R<t.l || t.r<L) return 0;
	if(L<=t.l && t.r<=R) return t.s;
	pushdown(b,c);
	return query(b,c*2,L,R)+query(b,c*2+1,L,R);
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin >> n;
	for(int i=1; i<=n; i++) cin >> a[i];

	for(int b=0; b<B; b++) build(b,1,1,n);

	cin >> m;
	while(m--)
	{
		int op;
		cin >> op;
		if(op==1)
		{
			int l,r;
			cin>>l>>r;
			ll ans=0;
			for(int b=0;b<B;b++)
			{
				ans += 1LL*query(b,1,l,r)*(1LL<<b);
			}
			cout<<ans<<"\n";
		}
		if(op==2)
		{
			int l,r,k;
			cin>>l>>r>>k;
			for(int b=0;b<B;b++)
			{
				if((k>>b)&1)
				{
					update(b,1,l,r);
				}
			}
		}
	}
	return 0;
}

GRAPH THEORY & TREE

LCA

CPP
#include <bits/stdc++.h>
using namespace std;
int n, m, s;
int f[500006][21], dep[500006];
vector<int> g[500006];
void dfs(int u, int fa)
{
	f[u][0] = fa;
	dep[u] = dep[fa] + 1;
	for (auto v : g[u])
	{
		if (v != fa) dfs(v, u);
	}
}
int lca(int u, int v)
{
	if (dep[u] < dep[v]) swap(u, v);
	for (int i = 20; i >= 0; i--)
	{
		if (dep[f[u][i]] >= dep[v]) u = f[u][i];
	}
	if (u == v) return u;
	for (int i = 20; i >= 0; i--)
	{
		if (f[u][i] != f[v][i])
		{
			u = f[u][i];
			v = f[v][i];
		}
	}
	return f[u][0];
}
void init()
{
	for (int j = 1; (1 << j) <= n; j++)
	{
		for (int i = 1; i <= n; i++)
		{
			f[i][j] = f[f[i][j - 1]][j - 1];
		}
	}
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> m >> s;
	for (int i = 1; i < n; i++)
	{
		int x, y;
		cin >> x >> y;
		g[x].push_back(y);
		g[y].push_back(x);
	}
	dfs(s, 0);
	init();
	for (int i = 1; i <= m; i++)
	{
		int u, v;
		cin >> u >> v;
		cout << lca(u, v) << endl;
	}
	return 0;
}

最小生成树

kruskal

CPP
#include <bits/stdc++.h>
using namespace std;
#define ll long long
int fa[8010];
int n, m;
struct edge
{
	int u, v, w;
}g[4000010];
int cnt;
void add(int u, int v, int w)
{
	cnt++;
	g[cnt].u = u;
	g[cnt].v = v;
	g[cnt].w = w;
}

int find(int x)
{
	if(fa[x]==x) return fa[x];
	else return fa[x]=find(fa[x]);
}
void merge(int x,int y)
{
	x=find(x);
	y=find(y);
	fa[x]=y;
}
bool cmp(edge q, edge e)
{
	return q.w < e.w;
}
void kruskal()
{
	int tot=0;
	ll ans=0;
	for(int i=1;i<=2*m;i++)
	{
		int xr=find(g[i].u);
		int yr=find(g[i].v);
		if(xr!=yr)
		{
			merge(xr,yr);
			tot++;
			ans+=g[i].w;
		 } 
		if(tot==n-1)
		{
			cout<<ans<<endl;
			return;
		}
	}
	cout<<"orz"<<endl;
}

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= n; i++)
	{
		fa[i] = i;
	}
	for (int i = 1; i <= m; i++)
	{
		int u, v, w;
		cin >> u >> v >> w;
		add(u, v, w);
		add(v,u,w);
	}
	sort(g+1,g+2*m+1,cmp);
	kruskal();
	return 0;
}

prim

CPP
#include<bits/stdc++.h>
using namespace std;

struct edge
{
	int to, dis, nxt;
} e[4000005];

struct node
{
	int pos, dis;
};
bool operator < (node q,node w)
{
	return q.dis>w.dis;
}

int head[5005], d[5005], cnt, n, m, ans;
bool vis[5005];

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

priority_queue<node> q;
int prim(int s)
{

	q.push((node){s,0});
	d[s]=0;
	int tot=0;
	while(!q.empty() && tot<n)
	{
		node t=q.top();
		q.pop();
		int x=t.pos;
		if(vis[x]) continue;
		vis[x]=1;
		ans+=t.dis;
		tot++;
		for(int i=head[x];i;i=e[i].nxt)
		{
			int v=e[i].to;
			int w=e[i].dis;
			if(!vis[v] && w<d[v])
			{
				d[v]=w;
				q.push((node){v,d[v]});
			}
		}
	}
	if(tot==n) return ans;
	else return -1;
}

int main()
{
	cin>>n>>m;
	for(int i=1;i<=m;i++)
	{
		int u,v,w;
		cin>>u>>v>>w;
		add(u,v,w);
		add(v,u,w);
	}

	for(int i=1;i<=n;i++)
	{
		d[i]=INT_MAX;
	}
	int res=prim(1);
	if(res==-1)
	{
		cout<<"orz"<<endl;
	}
	else cout<<res;

	return 0;
}

DIJ

CPP
#include <bits/stdc++.h>
using namespace std;
struct edge
{
	int to;
	int dis;
	int nxt;
}e[500006];
int head[500006];
int d[500006];
bool vis[500006];
int cnt;
struct node
{
	int dis,pos;
};
bool operator <(node q,node w)
{
	return q.dis>w.dis;
}
priority_queue<node> q; 
void dij(int s)
{
	d[s]=0;
	q.push((node){0,s});
	while(!q.empty())
	{
		node t=q.top();
		q.pop();
		int x=t.pos;
		if(vis[x]) continue;
		vis[x]=1;
		for(int i=head[x];i;i=e[i].nxt)
		{
			int y=e[i].to;
			if(d[y]>d[x]+e[i].dis)
			{
				d[y]=d[x]+e[i].dis;	
				if(!vis[y]) q.push((node){d[y],y});
			}
		}
	}
	return ;
}
void add(int u,int v,int di)
{
	cnt++;
	e[cnt].dis=di;
	e[cnt].to=v;
	e[cnt].nxt=head[u];
	head[u]=cnt;
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	int n,m,s;	
	cin>>n>>m>>s;
	for(int i=1;i<=n;i++)d[i] = INT_MAX;
	for(int i=1;i<=m;i++)
	{
		int u,v,di;
		cin>>u>>v>>di;
		add(u,v,di);
	}
	dij(s);
	for(int i=1;i<=n;i++)
	{
		cout<<d[i]<<" ";
	}
	return 0;
}

SPFA

CPP
#include<bits/stdc++.h>
using namespace std;
struct edge
{
    int to, dis, nxt;
}e[500010];
int head[100010], dis[100010], cnt;
bool vis[100010];
inline void add( int u, int v, int d )
{
    cnt++;
    e[cnt].dis = d;
    e[cnt].to = v;
    e[cnt].nxt = head[u];
    head[u] = cnt;
}
struct node
{
    int dis;
    int pos;
};
queue<node> q;
inline void spfa(int s)
{
	dis[s]=0;
	vis[s]=1;
	q.push((node){0,s});
	while(!q.empty())
	{
		node t=q.front();
		q.pop();
		int x=t.pos;
		vis[x]=0;
		for(int i=head[x];i;i=e[i].nxt)
		{
			int y=e[i].to;
			if(dis[y]>dis[x]+e[i].dis)
			{
				dis[y]=dis[x]+e[i].dis;
				if(!vis[y])
			{
				q.push((node){dis[y],y});
				vis[y]=1;
			}
			}

		}
	}
	return;
}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n,m,s;
	cin>>n>>m>>s;
    for(int i=1;i<=n;i++)dis[i] = INT_MAX;
    for(int i=1;i<=m;i++)
    {
        int u, v, d;
       cin>>u>>v>>d;
        add( u, v, d );
    }
    spfa(s);
    for(int i=1;i<=n;i++)
       cout<<dis[i]<<" ";
    return 0;
}

Floyd

CPP
	for(int k=1;k<=n;k++)
	{
		for(int i=1;i<=n;i++)
		{
			for(int j=1;j<=n;j++)
			{
				dp[i][j]=min(dp[i][j],dp[i][k]+dp[k][j]);
				dp[j][i]=dp[i][j];
			}
		}
	}

强连通分量

CPP
#include<bits/stdc++.h>
using namespace std;
int n,m;
const int N=1e4+10,M=1e5+10;
vector<int>g[N],ng[N];

int u[M],v[M];
int a[N];

int low[N],dfn[N],idx;
stack<int> st;

int rd[N],dp[N];
int num,scc[N],w[1000005];

void tarjan(int u)
{
	dfn[u]=low[u]=++idx;
	st.push(u);
	for(int v:g[u])
	{
		if(!dfn[v])
		{
			tarjan(v);
			low[u]=min(low[u],low[v]);
		}
		else if(!scc[v]) low[u]=min(low[u],dfn[v]);
	}
		if(low[u]==dfn[u])
		{
			int t;
			num++;
			do
			{
				t=st.top();
				st.pop();
				scc[t]=num;
				w[num]+=a[t];
			}
			while(t!=u);
		}

}
queue<int> q;

void toposort()
{
	while(!q.empty())
	{
		q.pop();
	}
	for(int i=1; i<=num; i++)
	{
		if(!rd[i])
		{
			q.push(i);
			dp[i]=w[i];
		}
	}
	while(!q.empty())
	{
		int u=q.front();
		q.pop();
		for(int v:ng[u])
		{
			dp[v]=max(dp[v],dp[u]+w[v]);
			if(--rd[v]==0)
			{
				q.push(v);
			}
		}
	}
	return;
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>m;
	for(int i=1; i<=n; i++)
	{
		cin>>a[i];
	}

	for(int i=1; i<=m; i++)
	{
		cin>>u[i]>>v[i];
		g[u[i]].push_back(v[i]);
	}

	for(int i=1; i<=n; i++)
	{
		if(!dfn[i]) tarjan(i);
	}
	for(int i=1; i<=m; i++)
	{
		int x=scc[u[i]];
		int y=scc[v[i]];
		if(x!=y)
		{
			ng[x].push_back(y);
			rd[y]++;
		}
	}
	toposort();
	int ans=0;
	for(int i=1; i<=num; i++)
	{
		ans=max(ans,dp[i]);
	}
	cout<<ans;
	return 0;
}

割点

CPP
#include <bits/stdc++.h>
using namespace std;
int n, m;
int dfn[100004], low[100004], idx, res;
bool vis[100004], flag[100004];
vector<int> g[100004];

void tarjan(int u, int fa)
{
	vis[u] = 1;
	low[u] = dfn[u] = ++idx;
	int child = 0;
	vis[u]=1;
	low[u]=dfn[u]=++idx;
	for(int v : g[u])
	{
		if(!vis[v])
		{
			child++;
			tarjan(v,u);
			low[u]=min(low[u],low[v]);
			if(fa!=u && low[v]>=dfn[u])
			{
				flag[u]=1;
			 } 
		}
		else if(v!=fa)
		{
			low[u]=min(low[u],dfn[v]);
		}
	}
	if(fa==u && child>=2)
	{
		flag[u]=1;
	}
}

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= m; i++)
	{
		int x, y;
		cin >> x >> y;
		g[x].push_back(y);
		g[y].push_back(x);
	}
	for (int i = 1; i <= n; i++)
		if (!vis[i])
		{
			idx = 0;
			tarjan(i, i);
		}
	for (int i = 1; i <= n; i++)
	{
		if (flag[i]) res++;
	}
	cout << res << endl;
	for (int i = 1; i <= n; i++)
		if (flag[i]) cout << i << " ";
	return 0;
}

割边

CPP
#include <bits/stdc++.h>
using namespace std;
#define PP pair<int,int>
#define mp make_pair
const int MAXN = 100005; 
int n, m;
vector<int> g[MAXN];
int dfn[MAXN], low[MAXN], idx;
bool vis[MAXN];
vector<PP> bd;

void tarjan(int u, int father)
{

    vis[u]=1;
    dfn[u]=low[u]=++idx;
    for(int v:g[u])
    {
    	if(!vis[v])
    	{
    		tarjan(v,u);
    		low[u]=min(low[u],low[v]);
    		if(low[v]>dfn[u])
    		{
    			int a=u;int b=v;
    			if(a>b) swap(a,b);
    			bd.push_back(mp(a,b));
    		}
		}
		else if(v!=father)
		{
			low[u]=min(low[u],dfn[v]);
		}
	}
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);

    cin>>n>>m;
    for (int i = 0; i < m;i++)
    {
        int a, b;
        cin >> a >> b;
        g[a].push_back(b);
        g[b].push_back(a);
    }

    for (int i = 1; i <= n;i++)
        if (!vis[i]) tarjan(i, i);

    sort(bd.begin(), bd.end());

    for (auto e : bd)
    {
        cout << e.first << ' ' << e.second << '\n';   	
	}


    return 0;
}

点双

CPP
#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 5, M = 2e6 + 5;
int n, m;

struct edge
{
	int to, nxt;
} e[M << 2];

int head[N << 1], cnt = 1;

void add(int u,int v)
{
	cnt++;
	e[cnt].to=v;
	e[cnt].nxt=head[u];
	head[u]=cnt;
}

int ans;
int dfn[N], low[N], idx;

stack<int> st;
bool cut[N];
vector<int> dcc[N];
int root;int num;

void tarjan(int u,int lst)
{
	dfn[u] = low[u] = ++idx;
	st.push(u);
	if (u == root && head[u] == 0)
	{
		dcc[++num].push_back(u);
		return;
	}
	int child = 0;
	for(int i=head[u];i;i=e[i].nxt)
	{
		if(i==(lst^1)) continue;
		int v=e[i].to;
		if(!dfn[v])
		{
			tarjan(v,i);
			low[u]=min(low[u],low[v]);
			if(low[v]>=dfn[u])
			{
				if(++child>1 || u!=root) 
				{
					cut[u]=1;//??
				}
				num++;
				int tt;
				do
				{
					tt=st.top();
					dcc[num].emplace_back(tt);
					st.pop();
				}while(tt!=v);
				dcc[num].emplace_back(u);
			}
		}
		else
			low[u] = min(low[u], dfn[v]);
	}
}

int main()
{
	cin >> n >> m;
	int u, v;
	for (int i = 1; i <= m; i++)
	{
		cin >> u >> v;
		if (u != v)
		{
			add(u,v);
			add(v,u);
		}
	}
	for (int i = 1; i <= n; i++)
		if (!dfn[i]) 
		{
			root=i;
			tarjan(i,0);
		}
		
	cout << num << '\n';
	for (int i = 1; i <= num; i++)
	{
		cout << dcc[i].size() << ' ';
		for (int j = 0; j < dcc[i].size(); j++) cout << dcc[i][j] << ' ';
		cout << '\n';
	}
	return 0;
}

边双

CPP
#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 5, M = 2e6 + 5;
int n, m;

struct edge
{
	int to, nxt;
} e[M << 2];

int head[N << 1], cnt = 1;

void add(int u,int v)
{
	cnt++;
	e[cnt].to=v;
	e[cnt].nxt=head[u];
	head[u]=cnt;
}
int idx, sum;
int dfn[N], low[N];
bool vis[N];
vector<vector<int>> ans;
stack<int> st;

void tarjan(int u, int in)
{
	low[u] = dfn[u] = ++idx;
	st.push(u);
	vis[u]=1;
	for(int i=head[u]; i; i=e[i].nxt)
	{
		int v=e[i].to;
		if(i==(in^1)) continue;
		if(!dfn[v])
		{
			tarjan(v,i);
			low[u]=min(low[u],low[v]);
		}
		else if(vis[v])
		{
			low[u]=min(low[u],dfn[v]);
		}
	}

	if(dfn[u]==low[u])
	{
		vector<int> t;
		int tt;

		do
		{
			tt=st.top();
			st.pop();
			t.push_back(tt);
			vis[tt]=0;


		}
		while(tt!=u);
		ans.push_back(t);
	}
	return;
}

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(0);
	cin >> n >> m;
	int u, v;
	for (int i = 1; i <= m; i++)
	{
		cin >> u >> v;
		if (u != v)
		{
			add(u, v);
			add(v, u);
		}
	}
	for (int i = 1; i <= n; i++)
	{
		if (!dfn[i]) tarjan(i, 0);

	}

	cout << ans.size() << '\n';
	for (int i = 0; i < ans.size(); i++)
	{
		cout << ans[i].size() << ' ';
		for (int j = 0; j < ans[i].size(); j++) cout << ans[i][j] << ' ';
		cout << '\n';
	}
	return 0;
}

STRING

KMP

CPP
#include <bits/stdc++.h>
using namespace std;

char s[1000010];
char t[1000010];
int nxt[1000010];

int main()
{
	cin>>(s+1);
	cin>>(t+1);

	int n=strlen(s+1);
	int m=strlen(t+1);
	int p;
	nxt[0]=0;
	p=0;
	for(int i=1;i<m;i++)
	{
		while(t[p+1]!=t[i+1] && p) p=nxt[p];
		if(t[p+1]==t[i+1])
		{
			p++;
		}
		nxt[i+1]=p;
	} 

	p=0;
	for(int i=1;i<=n;i++)
	{
		while(t[p+1]!=s[i] && p) p=nxt[p];
		if(t[p+1]==s[i])
		{
			p++;
		}
		if(p==m)
		{
			cout<<i-m+1<<endl;
			p=nxt[p];
		}
	}
	for(int i=1;i<=m;i++)
	{
		cout<<nxt[i]<<' ';
	}
	return 0;
}

Manacher

CPP
#include<bits/stdc++.h>
using namespace std;

char s[60000005], S[30000005];
int p[30000005], n;

int manacher(char s[])
{

	int m=0;
	int r=0;
	for(int i=1;i<=n;i++)
	{
		if(i>r) p[i]=1;
		else p[i]=min(p[2*m-i],r-i+1); 
		while(i-p[i]>=1 && i+p[i]<=n && s[i-p[i]]==s[i+p[i]])
		{
			p[i]++;
		} 
		if(i+p[i]-1>r)
		{
			m=i;
			r=i+p[i]-1;
		}
	}
	int ans=0;
	for(int i=1;i<=n;i++)
	{
		ans=max(ans,p[i]);
	}
	return ans-1;
}

signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	cin >> S;
	s[0]=' ';
	int idx=1;
	int ls=strlen(S);
	for(int i=0;i<ls;i++)
	{
		s[idx++]='#';
		s[idx++]=S[i];
	}
	s[idx++]='#';
	n=idx-1;

	cout << manacher(s) << endl;
	return 0;
}

字典树

CPP
#include<bits/stdc++.h>
using namespace std;
int t[3000005][127],cnt[3000005],idx;
char s[3000005];
int getnum(char x)
{
	if(x>='A'&&x<='Z')
		return x-'A';
	else if(x>='a'&&x<='z')
		return x-'a'+26;
	else
		return x-'0'+52;
}
void insert(char str[])
{
	int p=0;
	int len=strlen(str);
	for(int i=0;i<len;i++)
	{
		int c=getnum(str[i]);
		if(!t[p][c]) t[p][c]=++idx;
		p=t[p][c];
		cnt[p]++;
	}
}
int find(char str[])
{
	int p=0;
	int len=strlen(str);
	for(int i=0;i<len;i++)
	{
		int c=getnum(str[i]);
		if(!t[p][c]) return 0;
		p=t[p][c];
	}
	return cnt[p];
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int T;
	cin>>T;
	while(T--)
	{
		for(int i=0; i<=idx; i++)
		{
			for(int j=0;j<=122;j++)
			{
				t[i][j]=0;
			}
		}
		for(int i=0; i<=idx; i++)
		{
			cnt[i]=0;	
		}
		int n,q;
		idx=0;
		cin>>n>>q;
		for(int i=1; i<=n; i++)
		{
			cin>>s;
			insert(s);
		}
		for(int i=1; i<=q; i++)
		{
			cin>>s;
			cout<<find(s)<<'\n';
		}
	}
	return 0;
}

01 Trie

P10471。
CPP
#include<bits/stdc++.h>
using namespace std;

int t[3000005][2], idx;

void insert(int x)
{
	int p = 0;
	for(int i = 30; i >= 0; i--)
	{
		int c = (x >> i) & 1;
		if(!t[p][c]) t[p][c] = ++idx;
		p = t[p][c];
	}
}

int find(int x)
{
	int p = 0;
	int res = 0;
	for(int i = 30; i >= 0; i--)
	{
		int c = (x >> i) & 1;
		int want = c ^ 1;
		if(t[p][want])
		{
			res |= (1 << i);
			p = t[p][want];
		}
		else
		{
			p = t[p][c];
		}
	}
	return res;
}
int a[31000005]; 
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	int n;
	cin >> n;

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

	int ans = 0;
	insert(a[1]);
	for(int i = 2; i <= n; i++)
	{
		ans = max(ans, find(a[i]));
		insert(a[i]);
	}
	cout << ans << "\n";
	return 0;
}

MATH

有理数取模

CPP
#include<bits/stdc++.h>
#define int long long 
using namespace std;
const int mod=19260817;
int a,b;
int qpow(int a,int b)
{
	int ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
		b>>=1; 
	}
	return ans;
}
inline int read()
{
    int x=0,ch=getchar();
    while(!isdigit(ch)&&ch!=EOF) ch=getchar();
    while(isdigit(ch)) x=(x<<3)+(x<<1)+(ch-'0'),x%=mod,ch=getchar();
    return x;
}

signed main(){
    a=read();
	b=read();
    cout<<(a%mod*qpow(b,mod-2))%mod;
    return 0;
}

排列组合

C(a,b)=a!b!(a−b)!C(a, b) = \dfrac{a!}{b! (a-b)!}
P(a,b)=a!(a−b)!P(a, b) = \dfrac{a!}{(a-b)!}
CPP
#include <bits/stdc++.h>
using namespace std;
#define ll long long
ll n, m;

const ll mod=998244353;
ll a[5005];
ll ans[5005];

ll qpow(ll a,ll b)
{
	ll ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
ll cheng[10005005];
ll numinv[10005005];
ll inv[10005005];
ll c(ll a,ll b)
{
    if(b==0) return 1;
	return cheng[a]*inv[a-b]%mod*inv[b]%mod;
}
ll p(ll a,ll b)
{
	if(b==0) return 1;
	return cheng[a]*inv[a-b]%mod;
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cheng[0]=1;numinv[1]=1;
	for(int i=1;i<=10000;i++) //上界 
	{
		cheng[i]=cheng[i-1]*i%mod;
		if(i>1) numinv[i]=(mod-mod/i)*numinv[mod%i]%mod;
	}
	inv[0]=1;
/*
另外一种递推写法
    inv[n+m+3]=qpow(cheng[n+m+3],mod-2);
    for(int i=n+m+2;i>=1;i--)
    {
    	inv[i]=inv[i+1]*(i+1)%mod;
	}

*/
    for(int i=1;i<=10000;i++)
    {
        inv[i]=inv[i-1]*numinv[i]%mod;
    }
	ll x,y;
	cin>>x>>y;
	// x should > y
	cout<<c(x,y)<<endl;
	cout<<p(x,y)<<endl;
	return 0;
}
CPP
	c[0][0]=1;
	for(int i=1;i<=N;i++)
	{
		c[i][0]=1;
		for(int j=1;j<=N;j++)
		{
			c[i][j]=(c[i-1][j]+c[i-1][j-1])%mod;
		}
	}

卡特兰数

CPP
    printf("%d",c[2*n][n]-c[2*n][n-1]);

欧拉筛

CPP
	int cnt=1;
	for(int i=2;i<=n;i++)
	{
		if(!vis[i]) {
			p[cnt]=i;
			cnt++;
		}
		for(int j=1;j<=cnt;j++)
		{
			if(p[j]*i>n) break;
			vis[p[j]*i]=1;
			if(i%p[j]==0) break;
		}
	}

欧拉函数

CPP
for (int i = 2 ; i < n ; i ++)
	{
		if (!is[i])
			p[++ tot]=i, e[i] =i-1;
		for (int j = 1 ; j <= tot ; j ++)
		{
			if (i * p[j] >n-1) break ;
			is[i * p[j]] = 1 ;
			if (i % p[j] == 0)
			{
				e[i * p[j]] =e[i]*p[j] ;
//φ(i*p[j])=φ(i)*p[j]，互质的再乘个质数还是互质
				break;
			}
			else e[i*p[j]] =e[i]*e[p[j]];
//φ(i*p[j])=φ(i)*φ(p[j])=φ(i)*(p[j]-1)
		}
	}
单个数求 phi。
CPP
int phi(int n)
{
	int ans=n;
	for(int i=2; i*i<=n; i++)
	{
		if(n%i==0) ans=ans/i*(i-1);
		while(n%i==0) n/=i;
	}
	if(n==1) return ans;
	else return ans=ans/n*(n-1);
}

杂项

矩阵快速幂

CPP
#include<bits/stdc++.h>
using namespace std;
const int Mod = 1000000007;
#define ll long long
struct M
{
	long long c[101][101];
} A, ANS;
const int n=3;

M operator * ( M &x, M &y)
{
	M guo;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 1; j <= n; j++)
		{
			guo.c[i][j] = 0;
		}
	}
	for (int i = 1; i <= n; i++)
	{
		for (int j = 1; j <= n; j++)
		{
			for (int k = 1; k <= n; k++)
			{
				guo.c[i][j] += x.c[i][k] * y.c[k][j] % Mod;
				guo.c[i][j] %= Mod;
			}
		}
	}
	return guo;
}

M qpow(M A,ll m)
{
	M ANS;
	ANS.c[1][1]=1;
	ANS.c[1][2]=1;
	ANS.c[1][3]=1;
	while (m > 0)
	{
		if (m & 1) ANS = ANS * A;
		A = A * A;
		m >>= 1;
	}
	return ANS;
}

int main()
{


	int t;
	cin>>t;
	while(t--)
	{
		ll N;
		cin>>N;
		if (N <= 3)
		{
			cout<<1<<endl;
			continue;
		}
		A.c[1][1]=0;
		A.c[1][2]=0;
		A.c[1][3]=1;
		A.c[2][1]=1;
		A.c[2][2]=0;
		A.c[2][3]=0;
		A.c[3][1]=0;
		A.c[3][2]=1;
		A.c[3][3]=1;

		M ANS=qpow(A,N-3);
		cout<<ANS.c[1][3]%Mod<<endl;

	}
	return 0;
}

二维前缀和

以模板题为例：
CPP
for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=m;j++)
		{		
			cin>>a[i][j];
			sum[i][j]=a[i][j]+sum[i-1][j]+sum[i][j-1]-sum[i-1][j-1];
		}
	}
		ull ans=0;
		for(int i=1;i<=q;i++)
		{
			int u,v,x,y;
			cin>>u>>v>>x>>y;
			ans^=sum[x][y]-sum[u-1][y]-sum[x][v-1]+sum[u-1][v-1];
		}

高精度

CPP
#include <bits/stdc++.h>
using namespace std;
#define ll unsigned long long

const int maxn = 10001;

struct bign
{
	int d[maxn], len;

	void clean()
	{
		while(len > 1 && !d[len-1]) len--;
	}

	bign()
	{
		memset(d, 0, sizeof(d));
		len = 1;
	}
	bign(int num)
	{
		*this = num;
	}
	bign(char* num)
	{
		*this = num;
	}
	bign operator = (const char* num)
	{
		memset(d, 0, sizeof(d));
		len = strlen(num);
		for(int i = 0; i < len; i++) d[i] = num[len-1-i] - '0';
		clean();
		return *this;
	}
	bign operator = (int num)
	{
		char s[20];
		sprintf(s, "%d", num);
		*this = s;
		return *this;
	}

	bign operator + (const bign& b)
	{
		bign c = *this;
		int i;
		for (i = 0; i < b.len; i++)
		{
			c.d[i] += b.d[i];
			if (c.d[i] > 9) c.d[i]%=10, c.d[i+1]++;
		}
		while (c.d[i] > 9) c.d[i++]%=10, c.d[i]++;
		c.len = max(len, b.len);
		if (c.d[i] && c.len <= i) c.len = i+1;
		return c;
	}
	bign operator - (const bign& b)
	{
		bign c = *this;
		int i;
		for (i = 0; i < b.len; i++)
		{
			c.d[i] -= b.d[i];
			if (c.d[i] < 0) c.d[i]+=10, c.d[i+1]--;
		}
		while (c.d[i] < 0) c.d[i++]+=10, c.d[i]--;
		c.clean();
		return c;
	}
	bign operator * (const bign& b)const
	{
		int i, j;
		bign c;
		c.len = len + b.len;
		for(j = 0; j < b.len; j++) for(i = 0; i < len; i++)
				c.d[i+j] += d[i] * b.d[j];
		for(i = 0; i < c.len-1; i++)
			c.d[i+1] += c.d[i]/10, c.d[i] %= 10;
		c.clean();
		return c;
	}
	bign operator / (const bign& b)
	{
		int i, j;
		bign c = *this, a = 0;
		for (i = len - 1; i >= 0; i--)
		{
			a = a*10 + d[i];
			for (j = 0; j < 10; j++) if (a < b*(j+1)) break;
			c.d[i] = j;
			a = a - b*j;
		}
		c.clean();
		return c;
	}
	bign operator % (const bign& b)
	{
		int i, j;
		bign a = 0;
		for (i = len - 1; i >= 0; i--)
		{
			a = a*10 + d[i];
			for (j = 0; j < 10; j++) if (a < b*(j+1)) break;
			a = a - b*j;
		}
		return a;
	}
	bign operator += (const bign& b)
	{
		*this = *this + b;
		return *this;
	}

	bool operator <(const bign& b) const
	{
		if(len != b.len) return len < b.len;
		for(int i = len-1; i >= 0; i--)
			if(d[i] != b.d[i]) return d[i] < b.d[i];
		return false;
	}
	bool operator >(const bign& b) const
	{
		return b < *this;
	}
	bool operator<=(const bign& b) const
	{
		return !(b < *this);
	}
	bool operator>=(const bign& b) const
	{
		return !(*this < b);
	}
	bool operator!=(const bign& b) const
	{
		return b < *this || *this < b;
	}
	bool operator==(const bign& b) const
	{
		return !(b < *this) && !(b > *this);
	}

	string str() const
	{
		char s[maxn]= {};
		for(int i = 0; i < len; i++) s[len-1-i] = d[i]+'0';
		return s;
	}
};

istream& operator >> (istream& in, bign& x)
{
	string s;
	in >> s;
	x = s.c_str();
	return in;
}

ostream& operator << (ostream& out, const bign& x)
{
	out << x.str();
	return out;
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	bign a,b;
	cin>>a>>b;
	cout<<a+b;
	return 0;
}

对拍

make.cpp

CPP
#include <bits/stdc++.h>
using namespace std;
#define ll long long

int random(int mod)
{
    int ans=114514;
    ans=ans*rand()%mod;
    return (ans+mod)%mod+1;
}// 1 to mod
int main()
{
	srand(time(0));
	
	int n=random(10000);
	cout<<n<<endl;
	return 0;
}

pai.cpp

CPP
#include <bits/stdc++.h>
using namespace std;
#define ll long long

int main()
{
	while (1)
	{
		system("make.exe > make.in");
		system("baoli.exe < make.in > baoli.out");
		system("ceshi.exe < make.in > ceshi.out");
		if(system("fc baoli.out ceshi.out"))
		{
			cout<<"WARN!"<<endl;
			break;
		}
		else cout<<"NO PROBLEM"<<endl;
	}
    return 0;
}

END

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