模板

模板整理(持续整理中)

二分

while(l<=r)
{
    int mid=(l+r)/2;
    if(check(mid)) l=mid;
    else r=mid-1;
}

并查集

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
const int maxn=10005; 
int f[maxn];
int n,m;
void init()
{
	for(int i=1;i<=10000;i++)
	f[i]=i;
}
int get(int x)
{
	return f[x]=(x==f[x]? x:get(f[x]));
}
void merge(int x,int y)
{
	f[get(x)]=get(y);
}
int main()
{
	
}

快速幂

//位运算版本
#include <iostream>
using namespace std;
int power(int a,int b,int p)
{
	int ans=1%p;
	for( ;b;b>>=1)
	{
		if(b&1)
		ans=(long long)ans*a%p;
		a=(long long)a*a%p; 
	}
	return ans;
}
int main()
{
	
} 
//递归版本
#include <iostream>
#include <cstdio>
using namespace std;
long long t,b,p,k,s,result=1;
int pow(int a,int b,int p)
{
	if(b==0)
	return 1;
	if(b==1)
	return a%p;
	t=pow(a,b/2,p);
	if(b>=2&&b%2==0)
	return t*t%p;
	if(b>=2&&b%2==1)
	return t*t*a%p;
}
int main()
{

} 

线性筛素数

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int maxn=10000005;
int v[maxn],p[maxn];//v代表v是不是质数，是的话为1，p为质数
void primes(int n)
{
	int m=0;
	memset(v,0,sizeof(v));
	for(int i=2;i<=n;i++)
	{
		if(v[i]==0)
		{
			v[i]=i;
			p[++m]=i;
		}
		for(int j=1;j<=m;j++)
		{
			if(p[j]>v[i]||p[j]>(n/i))
			break;
			v[i*p[j]]=p[j];
		}
	}
} 
int main()
{
	
}

高精度（重载运算符）

struct bignum {
	int l,h[1001];
	inline void clear() {
		memset(h,0,sizeof(h)), l = 0;
	}
	inline void arg() {
		re int t = 1;
		while(h[t] || t<l) {
			if(h[t] < 0) h[t] += 10000, h[t+1] -= 1;
			if(h[t] >= 10000) h[t+1] += h[t]/10000;
			h[t++] %= 10000;
		}
		l = t-1;
	}
	inline void input(string s) {
		clear();
		re int p = 1, k = 1, t = 0;
		for(re int i = 0; i < s.length(); ++i)
			if(s[i] != '0') {t = i; break;}
		for(re int i = s.length()-1; i >= t; --i)
			if(k < 10000) h[p] += (s[i]-'0')*k, k *= 10;
			else ++p, h[p] = s[i]-'0', k = 10;
		l = p, arg();
	}
	inline void input(int w){
		clear();
		re int p = 1, k = 1;
		while(w){
			if(k < 10000) h[p] += (w%10)*k, k *= 10;
			else ++p, h[p] = w%10, k = 10;
			w /= 10;
		}
		l = p, arg();
	}
	inline void print() {
		arg();
		if(l<=1 && h[1]==0) {write(0); return;}
		for(re int i = l; i >= 1; --i) {
			if(i==l || h[i]>=1000) write(h[i]);
			else {
				re int l1 = 0, t = h[i];
				while(t) t/=10,++l1;
				while(++l1 <= 4) write(0);
				if(h[i]) write(h[i]);
			}
		}
	}
	inline bignum operator + (const bignum b) const {
		re bignum a = *this, c;	c.clear();
		c.l = max(a.l,b.l);
		for(re int i = 1; i <= max(a.l,b.l); ++i)
			c.h[i] = a.h[i]+b.h[i];
		c.arg(); return c;
	}
	inline bignum operator * (const bignum b) const {
		re bignum a = *this, c; c.clear(), c.l = a.l+b.l;
		for(re int i = 1; i <= a.l; ++i) {
			for(re int j = 1; j <= b.l; ++j)
				c.h[i+j-1] += a.h[i]*b.h[j];
			c.arg();///////////////////
		}
		c.arg(); return c;
	}
	inline bool operator < (bignum b) const {
		bignum a = *this; a.arg(), b.arg();
		if(a.l != b.l) return a.l < b.l;
		for(re int i = a.l; i >= 1; --i)
			if(a.h[i] < b.h[i]) return 1;
			else if(a.h[i] > b.h[i]) return 0;
		return 0;
	}
	inline bool operator > (bignum b) const {
		bignum a = *this; a.arg(), b.arg();
		if(a.l != b.l) return a.l > b.l;
		for(re int i = a.l; i >= 1; --i)
			if(a.h[i] > b.h[i]) return 1;
			else if(a.h[i] < b.h[i]) return 0;
		return 0;
	}
}

邻接表存树，邻接表存图

const int N=100010,M=1000010;
int head[N],ver[M],edge[M],next[M],d[N],tot;
bool v[N];
void (int x,int y,int z)
{
    ver[++tot]=y,edge[tot]=z,next[i]=head[x],head[x]=tot;
}

dfs

void dfs(int x){
    v[x]=1;//记录点x被访问过，v是visit的缩写
    for(int i=head[x];i;i=next[i]){
        int y=ver[i];
        if(v[y]) continue;
        dfs(y);
    }
}

dfs序

void dfs(int x){
    a[++m]=x;
    v[x]=1;
    for(int i=head[x];i;i=next[i]){
        int y=ver[i];
        if(v[y]) continue;
        dfs(y);
    }
    a[++m]=x;
}

求树的深度

void dfs(int x){
    v[x]=1;
    for(int i=head[x];i;i=next[i]){
        int y=ver[i];
        if(v[y]) continue;
        d[y]=d[x]+1;
        dfs(y);
    }
}

树的重心

void dfs(int x){
    v[x]=1;size[i]=1;
    int max_part=0;
    for(int i=head[x];i;i=next[i]){
        int y=ver[i];
        if(v[y]) continue;
        dfs(y);
        size[x]+=size[y];
        max_part=max(max_part,size[y]);
    }
    max_part=max(max_part,n-size[x]);
    if(max_part<ans){
        ans=max_part;
        pos=x;
    }
}

bfs

void bfs()
{
    memset(d,0,sizeof(d));
    queue<int> q;
    q.push(1);d[1]=1;
    while(q.size()>0){
        int x=q.front();
        q.pop;
        for(int i=head[x];i;next[i]){
            int y=ver[i];
            if(d[y]) continue;
            d[y]=d[x]+1；
            q.push(y);
        }
    }
}

单源最短路径

//spfa 慎用
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <cstring>
#include <queue>
using namespace std;
const int N=100010,M=1000010;
int head[N],ver[M],edge[M],next[M],d[N];
bool v[N];
int n,m,s,tot;
queue <int> q;
void add(int x,int y,int z)
{
	ver[++tot]=y,edge[tot]=z,next[tot]=head[x],head[x]=tot;
}
void spfa()
{
	for(int i=1;i<=n;i++)
	d[i]=2147483647;
	memset(v,0,sizeof(v));
	d[s]=0,v[s]=1;
	q.push(s);
	while(q.size())
	{
		int x=q.front();
		q.pop();
		for(int i=head[x];i;i=next[i])
		{
			int y=ver[i],z=edge[i];
			if(d[y]>d[x]+z)
			{
				d[y]=d[x]+z;
				if(!v[y]) q.push(y);
			}
		}
	}
}
int main()
{
	cin>>n>>m>>s;
	for(int i=1;i<=m;i++)
	{
		int x,y,z;
		cin>>x>>y>>z;
		add(x,y,z); 
	}
	spfa();
	for(int i=1;i<=n;i++)
	cout<<d[i]<<" ";
	return 0;
}
//dijkstra 常用
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
using namespace std;
const int N=100010,M=1000010;
int head[N],ver[M],edge[M],next[M],d[N];
bool v[N];
int n,m,s,tot;
priority_queue <pair<int ,int> > q;
void add(int x,int y,int z)
{
	ver[++tot]=y,edge[tot]=z,next[tot]=head[x],head[x]=tot;
}
void dijkstra()
{
	for(int i=1;i<=n;i++)
	d[i]=2147483647;
	memset(v,0,sizeof(v));
	d[s]=0;
	q.push(make_pair(0,s));
	while(q.size())
	{
		int x=q.top().second;
		q.pop();
		if(v[x]) continue;
		v[x]=1;
		for(int i=head[x];i;i=next[i])
		{
			int y=ver[i],z=edge[i];
			if(d[y]>d[x]+z)
			{
				d[y]=d[x]+z;
				q.push(make_pair(-d[y],y)); 
			}
		}
	}
}
int main()
{
	cin>>n>>m>>s;
	for(int i=1;i<=m;i++)
	{
		int x,y,z;
		cin>>x>>y>>z;
		add(x,y,z); 
	}
	dijkstra();
	for(int i=1;i<=n;i++)
	cout<<d[i]<<" ";
	return 0;
}

最小生成树

//Prim 
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <string>
#define re register
#define ll long long
using namespace std;
int a[5005][5005],n,m,ans,d[5005];
bool v[5005];
void prim()
{
	memset(d,0x3f,sizeof(d));
	memset(v,0,sizeof(v));
	d[1]=0;
	for(re int i=1;i<=n;i++)
	{
		int x=0;
		for(re int j=1;j<=n;j++)
		if(!v[j]&&(x==0||d[x]>d[j])) x=j;
		v[x]=1;
		for(re int y=1;y<=n;y++)
		if(!v[y]) d[y]=min(d[y],a[x][y]);
	}
}
int main()
{
	cin>>n>>m;
	memset(a,0x3f,sizeof(a));
	for(int i=1;i<=m;i++)
	{
		int x,y,z;
		cin>>x>>y>>z;
		a[y][x]=a[x][y]=min(a[x][y],z);
	}
	prim();
	for(int i=2;i<=n;i++) ans+=d[i];
	cout<<ans<<endl;
	return 0;
}
//克鲁斯卡尔
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#define re register
#define ll long long
using namespace std;
struct rec{int x,y,z;}edge[500010];
int fa[100010],n,m,ans;
bool operator <(rec a,rec b)
{
	return a.z<b.z;
}
int get(int x)
{
	return fa[x]=(x==fa[x])? x:get(fa[x]);
}
int main()
{
	cin>>n>>m;
	for(re int i=1;i<=m;i++)
		cin>>edge[i].x>>edge[i].y>>edge[i].z;
	sort(edge+1,edge+m+1);
	for(re int i=1;i<=n;i++) fa[i]=i;
	for(re int i=1;i<=m;i++)
	{
		int x=get(edge[i].x);
		int y=get(edge[i].y);
		if(x==y) continue;
		fa[x]=y;
		ans+=edge[i].z;
	}
	cout<<ans<<endl;
	return 0;
}

树状数组

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
using namespace std;
int n,m;
int a[500005],c[500005];
int lowbit(int x)
{
	return x&(-x);
}
void add(int x,int y)
{
	for( ;x<=n;x+=lowbit(x)) c[x]+=y;
}
int ask(int x)
{
	int ans=0;
	for(;x;x-=lowbit(x)) ans+=c[x];
	return ans;
}
int main()
{
    
}

求乘法逆元

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
long long n,p;
long long inv[3000010];
int main()
{
	cin>>n>>p;
	inv[1]=1;
	printf("1
");
	for(int i=2;i<=n;i++)
	{
		inv[i]=(long long)(p-p/i)*inv[p%i]%p;
		printf("%lld
",inv[i]);
	}
	return 0;
}

最近公共祖先

//LCA
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
#define re register
#define ll long long 
using namespace std;
const int size=50010;
int f[size][20],d[size],dist[size];
int ver[2*size],edge[2*size],next[2*size],head[size];
int T,n,m,tot,t;
queue <int>q; 
void add(int x,int y,int z)
{
	ver[++tot]=y,edge[tot]=z,next[tot]=head[x],head[x]=tot;
}
void bfs()
{
	q.push(1);
	d[1]=1;
	while(q.size())
	{
		int x=q.front();
		q.pop();
		for(re int i=head[x];i;i=next[i]);
		{
			int y=ver[i],z=edge[i];
			if(d[y]) continue
			d[y]=d[x]+1;
			dist[y]=dist[x]+z;
			f[y][0]=x;
			for(int j=1;j<=t;j++)
			f[y][j]=f[y][f[y][j-1]][j-1];
			q.push(y); 
		}
	} 
}
int lca(int x,int y)
{
	if(d[x]>d[y]) swap(x,y);
	for(re int i=t;i>=0;i--)
	if(d[f[y][i]]>=d[x]) y=f[y][i];
	if(x==y) return x;
	for(re int i=t;i>=0;i--)
	if(f[x][i]!=f[y][i]) x=f[x][i],y=f[y][i];
	return f[x][0];
}
int main()
{
	cin>>T;
	while(T--)
	{
		cin>>n>>m;
		t=(int)(log(n)/log(2))+1;
		for(re int i=1;i<=n;i++)
		head[i]=d[i]=0;
		tot=0;
		for(re int i=1;i<n;i++)
		{
			int x,y,z;
			scanf("%d%d%d",&x,&y,&z);
			add(x,y,z),add(y,x,z);
		}
		bfs();
		for(re int i=1;i<=m;i++)
		{
			int x,y;
			scanf("%d%d",&x,&y);
			printf("%d
",dist[x]+dist[y]-2*dist[lca(x,y)]);
		}
	}
	return 0;
} 

矩阵快速幂

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int maxn=1005;
const int mod=1000000007; 
struct mat
{
	long long m[maxn][maxn];
};
mat a,e;
long long n,p;
mat mul(mat x,mat y)
{
	mat c;
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		c.m[i][j]=0;
	}
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		{
			for(int k=1;k<=n;k++)
			c.m[i][j]=(c.m[i][j]%mod+(x.m[i][k]*y.m[k][j])%mod)%mod;
		}
	}
	return c;
}
mat pow(mat a,long long b)
{
	mat ans=e;
	while(b)
	{
		if(b&1)
		ans=mul(ans,a);
		a=mul(a,a);
		b>>=1;
	}
	return ans;
}
int main()
{
	cin>>n>>p;
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		cin>>a.m[i][j];
	}
	for(int i=1;i<=n;i++)
	e.m[i][i]=1;
	mat s=pow(a,p);
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		cout<<s.m[i][j]<<" ";
		cout<<endl;
	}
	return 0;
}

nim游戏

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
int t,n;
int main()
{
	cin>>t;
	while(t--)
	{
		int ans=0;
		cin>>n;
		for(int i=1;i<=n;i++)
		{
			int a;
			cin>>a;
			ans=ans^a;
		}
		if(ans)
		cout<<"Yes"<<endl;
		else
		cout<<"No"<<endl;
	}
	return 0;
}