【CSP（NOIP）】主要模板
前言：
今年最后一篇博客了 T T TT TT
下面都是（真）联赛模板，太简单或难的就不放了
一.数学问题
1.快速乘/快速幂
inline int ksc(int a,int b,int mod)
{
int ans=0;
a%=mod;
while(b)
{
if(b&1) ans=(ans+a)%mod;
b>>=1;
a=(a+a)%mod;
}
return ans;
}
inline int mul(int a,int b)//O(1)快速乘
{
return (a*b-(int)((long double)a/mod*b)*mod+mod)%mod;
}
inline int ksm(int a,int b,int c)//a^b%c
{
int ans=1;
a=a%c;
while(b)
{
if(b&1) ans=ans*a%c;
a=(a*a)%c,b>>=1;
}
return ans;
}
2.Lucas定理
#include <bits/stdc++.h>
#define int long long
using namespace std;
const int Max=100005;
int t,n,m,mod;
int mul[Max],inv[Max];
inline void pre()
{
mul[0]=inv[1]=1;
for(int i=1;i<=mod;i++) mul[i]=(mul[i-1]*i)%mod;
for(int i=2;i<=mod;i++) inv[i]=(mod-mod/i)*inv[mod%i]%mod;
}
inline int C(int n,int m)
{
if(n>=0&&m>=0&&n>=m) return (mul[n]*inv[mul[m]]%mod*inv[mul[n-m]])%mod;
return 0;
}
inline int Lucas(int n,int m)
{
if(!m) return 1;
return (Lucas(n/mod,m/mod)*C(n%mod,m%mod))%mod;
}
signed main()
{
scanf("%d",&t);
while(t--)
{
scanf("%d%d%d",&n,&m,&mod);
if(n+m<m) {cout<<"0\n";continue;}
pre();
printf("%d\n",Lucas(n+m,m));
}
return 0;
}
3.exCRT（扩展中国剩余定理）
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cctype>
#define int long long
using namespace std;
const int Max=1000010;
int k,x,y,gcd;
int a[Max],m[Max];
inline int get_int()
{
int x=0,f=1;
char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') {f=-1;c=getchar();}
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void exgcd(int a,int b)
{
if(!b) x=1,y=0,gcd=a;
else
{
exgcd(b,a%b);
int t=x;
x=y;
y=t-a/b*x;
}
}
inline int solve()
{
int pa=a[1],pm=m[1];
for(int i=2;i<=k;i++)
{
exgcd(pm,m[i]);
if((a[i]-pa)%gcd) return -1;
x=(x*(a[i]-pa)/gcd%m[i]+m[i])%m[i];
pa=x*pm+pa;
pm=pm*m[i]/gcd;
pa=(pa%pm+pm)%pm;
}
return pa;
}
signed main()
{
while(~scanf("%d",&k))
{
for(int i=1;i<=k;i++) m[i]=get_int(),a[i]=get_int();
cout<<solve()<<"\n";
}
return 0;
}
4.高斯消元
#include <bits/stdc++.h>
using namespace std;
const int Max=105;
int n,l,tag;
double tmp,num[Max][Max],ans[Max];
inline void solve()
{
for(int i=1;i<=n;i++)
{
l=i;
for(int j=i+1;j<=n;j++) if(fabs(num[l][i])<fabs(num[j][i])) l=j;
for(int j=1;j<=n+1;j++) swap(num[l][j],num[i][j]);
for(int j=i+1;j<=n;++j)
for(int p=i+1;p<=n+1;++p)
num[j][p]-=num[j][i]*num[i][p]/num[i][i];
}
int fg=0;
for(int i=1;i<=n;++i)
{
fg=0;
for(int j=i;j<=n;++j) if(num[i][j]) fg=1;
if(num[i][n+1]&&fg==0) {tag=1;return;}
if(num[i][n+1]==0&&fg==0) {tag=2;return;}
}
for(int i=n;i;i--)
{
tmp=num[i][n+1];
for(int j=i+1;j<=n;j++) tmp-=ans[j]*num[i][j];
ans[i]=tmp/num[i][i];
}
}
int main()
{
freopen("lx.in","r",stdin);
scanf("%d",&n);
for(int i=1;i<=n;i++)
for(int j=1;j<=n+1;j++) scanf("%lf",&num[i][j]);
solve();
if(tag==1) {puts("-1");return 0;}
if(tag==2) {puts("0");return 0;}
for(int i=1;i<=n;i++)
{
if(fabs(ans[i])<1e-8) printf("x%d=0\n",i);
else printf("x%d=%.2f\n",i,ans[i]);
}
return 0;
}
二.图论
1.dijkstra
#include <bits/stdc++.h>
using namespace std;
const int Maxn=10005;
const int Maxm=100005;
int n,m,s,tot;
int dis[Maxn],first[Maxn],vis[Maxn];
struct shu{int to,next,len;}edge[Maxm<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-')f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y,int z){edge[++tot].next=first[x],first[x]=tot,edge[tot].to=y,edge[tot].len=z;}
inline void init()
{
n=get_int(),m=get_int(),s=get_int();
memset(dis,0x3f3f3f,sizeof(dis));
for(int i=1;i<=m;i++)
{
int x=get_int(),y=get_int(),z=get_int();
build(x,y,z),build(y,x,z);
}
}
inline void dijkstra()
{
dis[s]=0;
priority_queue<pair<int,int> >q;
q.push(make_pair(0,s));
while(!q.empty())
{
int p=q.top().second;q.pop();
if(vis[p]) continue;vis[p]=1;
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(dis[to]>dis[p]+edge[u].len)
{
dis[to]=dis[p]+edge[u].len;
q.push(make_pair(-dis[to],to));
}
}
}
cout<<dis[n];
}
int main()
{
init();
dijkstra();
return 0;
}
2.最短路计数
#include <bits/stdc++.h>
using namespace std;
const int Max=1000005;
const int mod=100003;
int n,m,s,ans[Max],dis[Max],first[Max],vis[Max];
struct shu{int to,next;}edge[Max<<2];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void print(int x)
{
if(x>9) print(x/10);
putchar('0'+x%10);
}
inline void build(int x,int y){edge[++s].next=first[x],first[x]=s,edge[s].to=y;}
inline void init()
{
n=get_int(),m=get_int();
for(int i=1;i<=m;i++)
{
int x=get_int(),y=get_int();
build(x,y),build(y,x);
}
}
inline void dijkstra()
{
priority_queue<pair<int,int> >q;
memset(dis,0x3f3f3f,sizeof(dis));
ans[1]=1,dis[1]=0,q.push(make_pair(0,1));
while(q.size())
{
int p=q.top().second;q.pop();if(vis[p]) continue;vis[p]=1;
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(dis[to]==dis[p]+1) ans[to]=(ans[to]+ans[p])%mod;
else if(dis[to]>dis[p]+1) dis[to]=dis[p]+1,ans[to]=ans[p],q.push(make_pair(-dis[to],to));
}
}
}
inline void solve()
{
dijkstra();
for(int i=1;i<=n;i++)
if(dis[i]<=n) print(ans[i]),putchar('\n');
else puts("0");
}
int main()
{
init();
solve();
return 0;
}
3.割点
#include <bits/stdc++.h>
using namespace std;
const int Maxn=100005;
const int Maxm=500005;
int n,m,s,Index;
int first[Maxn],vis[Maxn],num[Maxn],low[Maxn],size[Maxn];
long long ans[Maxn];
struct shu{int to,next;}e[Maxm<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void print(long long x)
{
if(x<0) x=-x,putchar('-');
if(x>9) print(x/10);
putchar('0'+x%10);
}
inline void build(int x,int y){e[++s].next=first[x],first[x]=s,e[s].to=y;}
inline void tarjan(int p)
{
int flag=0,sum=0;
low[p]=num[p]=++Index,size[p]=1;
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if(!num[to])
{
tarjan(to),low[p]=min(low[p],low[to]),size[p]+=size[to];
if(low[to]>=num[p])
{
flag++,ans[p]+=(long long)size[to]*(n-size[to]),sum+=size[to];
if(p!=1||flag>1) vis[p]=1;
}
}
else low[p]=min(low[p],num[to]);
}
if(vis[p]) ans[p]+=(long long)(n-sum-1)*(sum+1)+n-1;
else ans[p]=2*(n-1);
}
int main()
{
n=get_int(),m=get_int();
for(int i=1;i<=m;i++)
{
int x=get_int(),y=get_int();
if(x==y) continue;
build(x,y),build(y,x);
}
tarjan(1);
for(int i=1;i<=n;i++) print(ans[i]),putchar('\n');
return 0;
}
4.tarjan强连通
#include <bits/stdc++.h>
using namespace std;
const int Maxn=10005;
const int Maxm=50005;
int n,m,s,ans1,ans2,cnt,tot,Index;
int first[Maxn],fr[Maxn],to[Maxn],fa[Maxn],q[Maxn],vis[Maxn],low[Maxn],num[Maxn];
struct shu{int to,next;}e[Maxm<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y){e[++s].next=first[x],first[x]=s,e[s].to=y;}
inline void tarjan(int p)
{
low[p]=num[p]=++Index;
q[++tot]=p,vis[p]=1;
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if(!num[to]) tarjan(to),low[p]=min(low[p],low[to]);
else if(vis[to]) low[p]=min(low[p],num[to]);
}
if(num[p]==low[p])
{
cnt++;
while(1)
{
int x=q[tot--];
vis[x]=0,fa[x]=cnt;
if(x==p) break;
}
}
}
int main()
{
freopen("lx.in","r",stdin);
n=get_int(),m=get_int();
for(int i=1;i<=m;i++)
{
int x=get_int(),y=get_int();
build(x,y);
}
for(int i=1;i<=n;i++) if(!num[i]) tarjan(i);
for(int i=1;i<=n;i++)
for(int u=first[i];u;u=e[u].next)
if(fa[i]!=fa[e[u].to]) fr[fa[i]]++,to[fa[e[u].to]]++;
for(int i=1;i<=cnt;i++)
{
if(!to[i]) ans1++;
if(!fr[i]&&to[i]) ans2++;
}
cout<<ans1<<"\n"<<ans1*ans2<<"\n";
return 0;
}
5.边双联通
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
using namespace std;
const int Max=50005;
int n,m,s=1,tot,cnt,sum,Index;
int first[Max],num[Max],low[Max],fa[Max],q[Max],to[Max];
struct shu{int to,next;}e[Max<<1];
inline int get_int()
{
int x=0;char c;
for(c=getchar();!isdigit(c);c=getchar());
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x;
}
inline void build(int x,int y)
{
e[++s].next=first[x],first[x]=s,e[s].to=y;
e[++s].next=first[y],first[y]=s,e[s].to=x;
}
inline void tarjan(int p,int f)
{
num[p]=low[p]=++Index,q[++tot]=p;
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if((u^1)!=f)
{
if(!num[to]) tarjan(to,u),low[p]=min(low[p],low[to]);
else low[p]=min(low[p],num[p]);
}
}
if(low[p]==num[p])
{
cnt++;
while(1)
{
int x=q[tot--];
fa[x]=cnt;
if(x==p) break;
}
}
}
int main()
{
freopen("lx.in","r",stdin);
n=get_int(),m=get_int();
while(m--)
{
int x=get_int(),y=get_int();
build(x,y);
}
tarjan(1,0);
for(int i=1;i<=n;i++)
for(int u=first[i];u;u=e[u].next)
if(fa[i]!=fa[e[u].to])
to[fa[i]]++;
for(int i=1;i<=cnt;i++) if(to[i]==1) sum++;
cout<<(sum+1)/2;
return 0;
}
6.最大流
#include <bits/stdc++.h>
using namespace std;
const int inf=1e9;
const int Maxn=105;
const int Maxm=5005;
int n,m,size=1,s,t;
long long ans;
int first[Maxn],dep[Maxn],tmp[Maxn];
struct shu{int to,next,len;}e[Maxm<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y,int z)
{
e[++size].next=first[x],first[x]=size,e[size].to=y,e[size].len=z;
e[++size].next=first[y],first[y]=size,e[size].to=x,e[size].len=0;
}
inline void init()
{
n=get_int(),m=get_int(),s=get_int(),t=get_int();
for(int i=1;i<=m;i++)
{
int x=get_int(),y=get_int(),z=get_int();
build(x,y,z);
}
}
inline bool bfs()
{
queue<int>q;
for(int i=1;i<=n;i++) dep[i]=0;
q.push(s),dep[s]=1;
while(q.size())
{
int p=q.front();q.pop();
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if(dep[to]||!e[u].len) continue;
dep[to]=dep[p]+1,q.push(to);
if(to==t) return 1;
}
}
return 0;
}
inline int dinic(int p,int flow)
{
if(p==t) return flow;
int sum=0;
for(int &u=tmp[p];u;u=e[u].next)
{
int to=e[u].to;
if(dep[to]!=dep[p]+1||!e[u].len) continue;
int minn=dinic(to,min(e[u].len,flow-sum));
sum+=minn,e[u].len-=minn,e[u^1].len+=minn;
if(sum==flow) return sum;
}
return dep[p]=0,sum;
}
inline void solve()
{
while(bfs())
{
for(int i=1;i<=n;i++) tmp[i]=first[i];
ans+=dinic(s,inf);
}
cout<<ans;
}
int main()
{
init();
solve();
return 0;
}
7.二分图最大匹配
#include <bits/stdc++.h>
using namespace std;
const int inf=1e9+7;
const int Maxn=2005;
const int Maxm=1005000;
int k,n,m,tot,s,t,ans;
int first[Maxn],dep[Maxn],tmp[Maxn];
struct shu{int to,next,len;}edge[Maxm<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y,int z){edge[++tot].next=first[x],first[x]=tot,edge[tot].to=y,edge[tot].len=z;}
inline void init()
{
n=get_int(),m=get_int(),k=get_int();
tot=1,s=0,t=n+m+1;
for(int i=1;i<=k;i++)
{
int x=get_int(),y=get_int();
if(x>n||y>m) continue;
build(x,y+n,1),build(y+n,x,0);
}
for(int i=1;i<=n;i++) build(0,i,1),build(i,0,0);
for(int i=n+1;i<=n+m;i++) build(i,t,1),build(t,i,0);
}
inline bool bfs()
{
queue<int>q;
for(int i=s;i<=t;i++) dep[i]=0;
dep[s]=1,q.push(s);
while(q.size())
{
int p=q.front();q.pop();
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(dep[to]||!edge[u].len) continue;
dep[to]=dep[p]+1,q.push(to);
if(to==t) return 1;
}
}
return 0;
}
inline int dinic(int p,int flow)
{
if(p==t) return flow;
int res=flow;
for(int &u=tmp[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(dep[to]!=dep[p]+1||!edge[u].len) continue;
int sum=dinic(to,min(edge[u].len,res));
res-=sum,edge[u].len-=sum,edge[u^1].len+=sum;
if(!res) return flow;
}
return flow-res;
}
inline void solve()
{
while(bfs())
{
for(int i=0;i<=t;i++) tmp[i]=first[i];
ans+=dinic(s,inf);
}
cout<<ans;
}
int main()
{
freopen("lx.in","r",stdin);
init();
solve();
return 0;
}
8.SPFA判负环
#include <bits/stdc++.h>
#define Max 2010
using namespace std;
int n,m,t,s;
int first[Max],cnt[Max],dis[Max],vis[Max];
struct shu{int to,next,len;};
shu edge[6010];
queue<int>q;
inline int get_int()
{
int x=0,f=1;
char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') {f=-1;c=getchar();}
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y,int z)
{
edge[++s].next=first[x];
first[x]=s;
edge[s].to=y;
edge[s].len=z;
}
inline int SPFA()
{
while(!q.empty()) q.pop();
dis[1] = 0,cnt[1] = 1;
q.push(1);
while(!q.empty())
{
int point = q.front();
q.pop();
vis[point] = 0;
for(register int u=first[point];u;u=edge[u].next)
{
int to=edge[u].to;
if(dis[to] > dis[point] + edge[u].len)
{
dis[to] = dis[point] + edge[u].len;
if(!vis[to])
{
cnt[to] = cnt[to] + 1;
if(cnt[to] >= n) return 1;
vis[to] = 1;
q.push(to);
}
}
}
}
return 0;
}
int main()
{
t=get_int();
while(t--)
{
s=0;
n=get_int(),m=get_int();
for(register int i=1;i<=n;++i) vis[i] = cnt[i] = first[i] = 0,dis[i] = 1e9;
for(register int i=1;i<=m;++i)
{
int x=get_int(),y=get_int(),z=get_int();
build(x,y,z);
if(z >= 0) build(y,x,z);
}
SPFA() ? printf("YE5\n") : printf("N0\n");
}
}
9.树的直径
#include <bits/stdc++.h>
using namespace std;
const int Max=100010;
int n,m,size,ans;
int first[Max],f[Max],d[Max];
struct shu{int to,next,len;}edge[Max<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y,int z){edge[++size].next=first[x],first[x]=size,edge[size].to=y,edge[size].len=z;}
inline void dfs(int p,int fa)
{
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(to==fa) continue;
dfs(to,p);
f[p]=max(f[p],d[p]+edge[u].len+d[to]);
d[p]=max(d[p],edge[u].len+d[to]);
}
}
int main()
{
n=get_int();
for(int i=1;i<n;i++)
{
int x=get_int(),y=get_int(),z=get_int();
build(x,y,z),build(y,x,z);
}
dfs(1,0);
for(int i=1;i<=n;i++) ans=max(ans,f[i]);
cout<<ans;
return 0;
}
10.树的重心
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <cstring>
using namespace std;
const int Max=20005;
int n,m,t,s,id,ans;
int first[Max],size[Max];
struct shu{int to,next;}edge[Max<<1];
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='0');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void build(int x,int y){edge[++s].next=first[x],first[x]=s,edge[s].to=y;}
inline void init()
{
n=get_int(),s=0,id=ans=1e9;
for(int i=1;i<=n;i++) size[i]=first[i]=0;
for(int i=1;i<n;i++)
{
int x=get_int(),y=get_int();
build(x,y),build(y,x);
}
}
inline void dfs(int p,int fa)
{
size[p]=1;int mx=0;
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(to==fa) continue;
dfs(to,p),size[p]+=size[to],mx=max(mx,size[to]);
}
mx=max(mx,n-size[p]);
if(ans>mx) ans=mx,id=p;
else if(ans==mx) id=min(id,p);
}
inline void solve()
{
dfs(1,0);
cout<<id<<" "<<ans<<"\n";
}
int main()
{
t=get_int();
while(t--)
{
init();
solve();
}
return 0;
}
11.树剖求LCA
inline void dfs1(int p)
{
size[p]=vis[p]=1;
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(vis[to]) continue;
fa[to]=p,dep[to]=dep[p]+1,dfs1(to),size[p]+=size[to];
if(size[son[p]]<size[to]) son[p]=to;
}
}
inline void dfs2(int p,int tp)
{
top[p]=tp;
if(!son[p]) return;
dfs2(son[p],tp);
for(int u=first[p];u;u=edge[u].next)
{
int to=edge[u].to;
if(to==fa[p]||to==son[p]) continue;
dfs2(to,to);
}
}
inline int LCA(int x,int y)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]]) swap(x,y);
x=fa[top[x]];
}
return dep[x]<dep[y] ? x : y;
}
12.树链剖分
#include <bits/stdc++.h>
using namespace std;
const int Max=30005;
int n,m,tot,s;
int first[Max],num[Max];
int tree[Max<<2],sum[Max<<2];
int top[Max],dep[Max],son[Max],size[Max],fa[Max],rev[Max],seg[Max];
struct shu{int to,next;}e[Max<<1];
////////////////////////////////////////////
inline int get_int()
{
int x=0,f=1;char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void print(int x)
{
if(x<0) x=-x,putchar('-');
if(x>9) print(x/10);
putchar('0'+x%10);
}
inline int max(int a,int b){return a<b?b:a;}
////////////////////////////////////////////
inline void build(int x,int y)
{
e[++s].next=first[x],first[x]=s,e[s].to=y;
e[++s].next=first[y],first[y]=s,e[s].to=x;
}
inline void dfs1(int p)
{
size[p]=1;
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if(to==fa[p]) continue;
fa[to]=p,dep[to]=dep[p]+1,dfs1(to),size[p]+=size[to];
if(size[to]>size[son[p]]) son[p]=to;
}
}
inline void dfs2(int p,int tp)
{
top[p]=tp,seg[rev[p]=++tot]=p;
if(!son[p]) return;
dfs2(son[p],tp);
for(int u=first[p];u;u=e[u].next)
{
int to=e[u].to;
if(to==fa[p]||to==son[p]) continue;
dfs2(to,to);
}
}
////////////////////////////////////////////
inline void update(int rt){tree[rt]=max(tree[rt<<1],tree[rt<<1|1]),sum[rt]=sum[rt<<1]+sum[rt<<1|1];}
inline void buildtree(int rt,int l,int r)
{
if(l==r){tree[rt]=sum[rt]=num[seg[l]];return;}
int mid=(l+r)>>1;
buildtree(rt<<1,l,mid),buildtree(rt<<1|1,mid+1,r);
update(rt);
}
inline void modify(int rt,int l,int r,int pos,int x)
{
if(l==r){tree[rt]=sum[rt]=x;return;}
int mid=(l+r)>>1;
if(pos<=mid) modify(rt<<1,l,mid,pos,x);
else modify(rt<<1|1,mid+1,r,pos,x);
update(rt);
}
inline int Qmax(int rt,int l,int r,int L,int R)
{
if(L<=l&&R>=r) return tree[rt];
int mid=(l+r)>>1,ans=-1e9;
if(L<=mid) ans=max(ans,Qmax(rt<<1,l,mid,L,R));
if(R>mid) ans=max(ans,Qmax(rt<<1|1,mid+1,r,L,R));
return ans;
}
inline int Qsum(int rt,int l,int r,int L,int R)
{
if(L<=l&&R>=r) return sum[rt];
int mid=(l+r)>>1,ans=0;
if(L<=mid) ans+=Qsum(rt<<1,l,mid,L,R);
if(R>mid) ans+=Qsum(rt<<1|1,mid+1,r,L,R);
return ans;
}
////////////////////////////////////////////
inline int ask(int x,int y,int tag)
{
int ans=(tag==1)?-1e9:0;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]]) swap(x,y);
if(tag==1) ans=max(ans,Qmax(1,1,tot,rev[top[x]],rev[x]));
else ans+=Qsum(1,1,tot,rev[top[x]],rev[x]);
x=fa[top[x]];
}
if(dep[x]>dep[y]) swap(x,y);
if(tag==1) ans=max(ans,Qmax(1,1,tot,rev[x],rev[y]));
else ans+=Qsum(1,1,tot,rev[x],rev[y]);
return ans;
}
////////////////////////////////////////////
int main()
{
freopen("lx.in","r",stdin);
n=get_int();
for(int i=1;i<n;i++)
{
int x=get_int(),y=get_int();
build(x,y);
}
for(int i=1;i<=n;i++) num[i]=get_int();
dfs1(1),dfs2(1,1),buildtree(1,1,tot);
m=get_int();
while(m--)
{
char ch[10];scanf("%s",ch);int x=get_int(),y=get_int();
if(ch[1]=='H') modify(1,1,tot,rev[x],y);
else if(ch[1]=='M') print(ask(x,y,1)),putchar('\n');
else print(ask(x,y,2)),putchar('\n');
}
return 0;
}
三.字符串
1.KMP
#include <bits/stdc++.h>
using namespace std;
const int Max=1000005;
int n,m,tag,first[Max];
char a[Max],b[Max];
inline void init()
{
scanf("%s\n%s",a+1,b+1);
n=strlen(a+1),m=strlen(b+1);
}
inline void pre()
{
for(int i=2,j=0;i<=m;i++)
{
while(b[i]!=b[j+1]&&j) j=first[j];
if(b[i]==b[j+1]) j++;first[i]=j;
}
}
inline void solve()
{
for(int i=1,j=0;i<=n;i++)
{
while(j&&a[i]!=b[j+1]) j=first[j];
if(a[i]==b[j+1]) j++;
if(j==m) tag=1,cout<<i-m+1<<"\n";
}
if(!tag) puts("NO");
}
int main()
{
init();
pre();
solve();
return 0;
}
2.字符串哈希
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
using namespace std;
const int Max=1000005;
int n,m,tag,t;
unsigned long long Pow[Max],hash1[Max],hash2[Max];
char ch1[Max],ch2[Max];
const void solve()
{
Pow[0]=1,tag=0;
for(int i=1;i<=m;i++) hash2[i]=hash2[i-1]*131+ch2[i]-'a',Pow[i]=Pow[i-1]*131;
for(int i=1;i<=n;i++)
{
hash1[i]=hash1[i-1]*131+ch1[i]-'a';
if(i>=m&&hash1[i]==hash1[i-m]*Pow[m]+hash2[m]) tag=1,cout<<i-m+1<<"\n";
}
}
int main()
{
scanf("%s",ch1+1);
n=strlen(ch1+1);
scanf("%s",ch2+1);
m=strlen(ch2+1);
solve();
if(!tag) puts("NO");
return 0;
}
四.数据结构
1.RMQ
#include <bits/stdc++.h>
using namespace std;
const int Max=50005;
int n,m;
int f[Max][18],g[Max][18],Log[Max];
inline int get_int()
{
int x=0,f=1;
char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') f=-1,c=getchar();
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void print(int x)
{
if(x>9) print(x/10);
putchar('0'+x%10);
}
inline int mx(int x,int y){return x < y ? y : x;}
inline int mn(int x,int y){return x < y ? x : y;}
inline void pre()
{
Log[0]=-1;
for(int i=1;i<=n;i++) Log[i]=Log[i>>1]+1;
for(int j=1;(1<<j)<=n;j++)
for(int i=1;i+(1<<j)-1<=n;i++)
f[i][j]=max(f[i][j-1],f[i+(1<<j-1)][j-1]),g[i][j]=min(g[i][j-1],g[i+(1<<j-1)][j-1]);
}
int main()
{
n=get_int(),m=get_int();
for(int i=1;i<=n;i++) g[i][0]=f[i][0]=get_int();
pre();
while(m--)
{
int x=get_int(),y=get_int(),len=Log[y-x+1];
print(mx(f[x][len],f[y-(1<<len)+1][len])-mn(g[x][len],g[y-(1<<len)+1][len])),putchar('\n');
}
return 0;
}
2.线段树
线段树的模板实在是太多了，如果考到应该不会太复杂，所以就略过了。
3.主席树
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
using namespace std;
const int Max=100010;
int n,m,q,s;
int num[Max],a[Max],sum[Max*20],lc[Max*20],rc[Max*20],root[Max*20];
inline int get_int()
{
int x=0,f=1;
char c;
for(c=getchar();(!isdigit(c))&&(c!='-');c=getchar());
if(c=='-') {f=-1;c=getchar();}
for(;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+c-'0';
return x*f;
}
inline void pre()
{
sort(a+1,a+n+1);
m=unique(a+1,a+n+1)-a-1;
for(int i=1;i<=n;i++) num[i] = lower_bound(a+1,a+m+1,num[i]) - a;
}
inline void build(int fa,int &now,int l,int r,int num)
{
now = ++s;
sum[now] = sum[fa] + 1;
lc[now] = lc[fa],rc[now] = rc[fa];
if(l==r) return;
int mid = l + r >> 1;
if(num <= mid) build(lc[fa],lc[now],l,mid,num);
else build(rc[fa],rc[now],mid+1,r,num);
}
inline int Q(int root1,int root2,int l,int r,int k)
{
if(l==r) return l;
int mid = l + r >> 1,num = sum[lc[root1]] - sum[lc[root2]];
if(num >= k) return Q(lc[root1],lc[root2],l,mid,k);
else return Q(rc[root1],rc[root2],mid+1,r,k-num);
}
inline void print(int x)
{
if(x < 0) putchar('-'),x=-x;
if(x > 9) print(x/10);
putchar('0' + x % 10);
}
int main()
{
n=get_int(),q=get_int();
for(int i=1;i<=n;i++) num[i] = a[i] = get_int();
pre();
for(int i=1;i<=n;i++) build(root[i-1],root[i],1,m,num[i]);
while(q--)
{
int l=get_int(),r=get_int(),k=get_int();
print(a[Q(root[r],root[l-1],1,m,k)]),putchar('\n');
}
return 0;
}
五.动态规划
我觉得 D P DP DP是没有所谓模板的。。。