[模板集合]
各种模板的集合。
1.手写堆
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
//#include<set>
//#include<bits/stdc++.h>
using namespace std;
int n,x,r;
int t=0;
int hp[1000005];
void pus(int x) {
int now=++t;
int tp=now/2;
hp[now]=x;
while(now>1) {
int tp=now/2;
if(hp[now]<hp[tp]) {
swap(hp[now],hp[tp]);
now=tp;
} else break;
}
}
void del() {
hp[1]=hp[t];
t--;
int now=1;
while(2*now<=t) {
int tp=2*now;
if(hp[tp]>hp[tp+1]&&tp<t)tp++;
if(hp[tp]<hp[now]) {
std::swap(hp[tp],hp[now]);
now=tp;
} else break;
}
}
int main() {
std::cin>>n;
for(register int i=1; i<=n; i++) {
std::cin>>r;
if(r==1) {
std::cin>>x;
pus(x);
} else if(r==2) {
std::cout<<hp[1]<<endl;
} else if(r==3) {
del();
}
}
}
2.spfa判负环(spfa还活着的证据)
#include<cstdio>
#include<iostream>
#include<set>
#include<queue>
#include<cstring>
using namespace std;
const int N = 6005;
int T,head[N],ecnt;
int n,m,s;
int dis[N],cnt[N];
bool vis[N];
struct Edge {
int nxt,to,val;
} e[N<<2];
void add(int bg,int ed,int val) {
e[++ecnt].nxt=head[bg],e[ecnt].to=ed,e[ecnt].val=val,head[bg]=ecnt;
}
queue<int>q;
bool spfa() {
memset(cnt,0,sizeof cnt);
memset(vis,0,sizeof vis);
memset(dis,0x3f,sizeof dis);
q.push(s);
dis[s]=0;
vis[s]=1;
while(!q.empty()) {
int u=q.front();
q.pop();
vis[u]=0;
for(int i=head[u]; i; i=e[i].nxt) {
int v=e[i].to;
if(dis[v]>dis[u]+e[i].val) {
if(!vis[v]) {
q.push(v);
vis[v]=1;
}
dis[v]=dis[u]+e[i].val;
cnt[v]=cnt[u]+1;
if(cnt[v]==n)return 0;
}
}
}
return 1;
}
int main() {
cin>>T;
while(T--) {
scanf("%d%d",&n,&m);
s=-1;
ecnt=0;
memset(head,0,sizeof head);
int a,b,c;
for(int i=1; i<=m; i++) {
scanf("%d%d%d",&a,&b,&c);
if(c<0) s=a;
add(a,b,c);
}
if(s==-1){
cout<<"YE5\n";continue;
}
if(!spfa()) cout<<"YE5\n";
else cout<<"N0\n";
}
}
3.ST表
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
const int N=1e6+7;
int Max[21][N];
int query(int l,int r){
int k=log2(r-l+1);
return max(Max[k][l],Max[k][r-(1<<k)+1]);
}
int n,m;
int main(){
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++) scanf("%d",&Max[0][i]);
for(int j=1;j<=21;j++){
for(int i=1;i+(1<<j)-1<=n;i++){
Max[j][i]=max(Max[j-1][i],Max[j-1][i+((1<<j-1))]);
}
}
for(int i=1,l,r;i<=m;i++){
scanf("%d%d",&l,&r);
printf("%d\n",query(l,r));
}
}
4.manacher
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
const int N=11000007;
char s[N<<1],tp[N];
int p[N<<1],n,ans;
void manacher() {
int id=0,mx=0;
for(int i=1;i<n;i++) {
if(i<mx) p[i]=min(p[id*2-i],p[id]+id-i);
else p[i]=1;
while(s[i+p[i]]==s[i-p[i]]) p[i]++;
if(i+p[i]>mx) mx=i+p[i],id=i;
ans=max(ans,p[i]);
}
}
int main() {
scanf("%s",tp);
n=strlen(tp);
s[0]=s[1]=';';
for(int i=0;i<n;i++) {
s[i+i+2]=tp[i];
s[i+i+3]=';';
}
n=n+n+2;
s[n]=' ';
manacher();
cout<<ans-1;
return 0;
}
5.EXCRT
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=1e5+5;
typedef long long ll;
ll tor(ll d,ll z,ll m) {
long long res=0;
while(z) {
if(z&1) res=(res+d)%m;
d=(d+d)%m;
z>>=1;
}
return res;
}
ll exgcd(ll &x,ll &y,ll a,ll b) {
if(!b) {
x=1,y=0;
return a;
}
ll g=exgcd(x,y,b,a%b);
ll t=x;
x=y;
y=t-a/b*y;
return g;
}
int n;
ll ai[N],bi[N];
void excrt() {
ll x,y,k,z,h;
ll M=ai[1],ans=bi[1];
for(int i=2;i<=n;i++) {
ll a=M,b=ai[i],c=(bi[i]-ans%b+b)%b;
ll g=exgcd(x,y,a,b);
ll newb=b/g;
if(c%g!=0) {cout<<-1;return;}
x=tor(x,c/g,newb);
ans+=x*M;
M*=newb;
ans=(ans%M+M)%M;
}
cout<<(ans+M)%M;
}
int main() {
scanf("%d",&n);
for(int i=1;i<=n;i++) scanf("%lld%lld",&ai[i],&bi[i]);
excrt();
return 0;
}
6.线性基
#include <cstdio>
long long base[70],n;
void insert(long long x){
for(int i=60;~i;i--){
if(x&(1ll<<i)){
if(!base[i]) {base[i]=x;return;}
x=x^base[i];}
}
}
long long query(long long x){
for(int i=60;~i;i--){
if((x^base[i])>x)x^=base[i];
}
return x;
}
int main(){
scanf("%d",&n);
for(long long i=1,a;i<=n;i++) scanf("%lld",&a),insert(a);
printf("%lld",query(0));
}
7.逆元
https://www.cnblogs.com/sdfzhsz/p/9797175.html
8.后缀排序
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=1000005;
int sa[N],rk[N],x[N],y[N],tot,n,m,c[N];
char s[N];
void SA() {
for(int i=1;i<=n;i++) x[i]=s[i];
for(int i=1;i<=n;i++) c[x[i]]++;
for(int i=2;i<=m;i++) c[i]+=c[i-1];
for(int i=n;i;i--) sa[c[x[i]]--]=i;
for(int k=1;k<=n;k<<=1) {
tot=0;
for(int j=n-k+1;j<=n;j++) y[++tot]=j;
for(int j=1;j<=n;j++) if(sa[j]>k) y[++tot]=sa[j]-k;
memset(c,0,sizeof (int)*(m+1));
for(int i=1;i<=n;i++) c[x[i]]++;
for(int i=2;i<=m;i++) c[i]+=c[i-1];
for(int i=n;i;i--) sa[c[x[y[i]]]--]=y[i],y[i]=0;
swap(x,y);
x[sa[1]]=1;tot=1;
for(int i=2;i<=n;i++) {
x[sa[i]]=(y[sa[i]]==y[sa[i-1]]&&y[sa[i]+k]==y[sa[i-1]+k])?tot:++tot;
}
m=tot;
}
for(int i=1;i<=n;i++) printf("%d ",sa[i]);
return;
}
int main() {
scanf("%s",s+1);
n=strlen(s+1);
m='z';
SA();
return 0;
}
9.EXBSGS
#include <cstdio>
#include <cmath>
#include <map>
std::map<int,int> mp;
int a,b,c;
int exgcd( long a, long b, long &x, long &y) {
if(!b) {
x=1,y=0;
return a;
}
long ans=exgcd(b,a%b,x,y),t=x;
x=y,y=t-a/b*y;
return ans;
}
long gcd( long a, long b) {
return b?gcd(b,a%b):a;
}
long ksm( long b, long z, long p) {
long res=1;
while(z) {
if(z&1) res*=b,res%=p;
b*=b,b%=p;
z>>=1;
}
return res;
}
long EXBSGS( long a, long b, long p) {
a%=p,b%=p;
if(b==1)return 0;
int cnt=0,d=1;
for(int g=gcd(a,p); g!=1; g=gcd(a,p)) {
if(b%g) return -1;
p/=g,b/=g;
d=1ll*d*a/g%p;
++cnt;
if(b==d) return cnt;
}
mp.clear();
int m=ceil(sqrt(p)),t=b;
for(int i=0; i<m; i++) {
mp[t]=i;
t=1ll*t*a%p;
}
int g=ksm(a,m,p);
t=1ll*d*g%p;
for(int i=1; i<=m+1; i++) {
if(mp.count(t))
return cnt+i*m-mp[t];
t=1ll*t*g%p;
}
return -1;
}
int main() {
int a,b,p,ans;
while(~scanf("%d%d%d",&a,&p,&b)) {
if(!a&&!b&&!p)return 0;
if(p==1) {
puts("0");
continue;
}
ans=EXBSGS(a,b,p);
if(ans==-1) puts("No Solution");
else printf("%d\n",ans);
}
}
10.杜教筛筛phi和miu
#include <iostream>
#include <cstdio>
#include <map>
using namespace std;
typedef long long ll;
const int N=7000000;
int n;
map<int,ll>ph,mu;
int prime[N>>3],tot;ll phi[N],miu[N];
bool vis[N];
void init() {
miu[1]=phi[1]=1;
for(int i=2;i<=N-5;i++) {
if(!vis[i]) prime[++tot]=i,miu[i]=-1,phi[i]=i-1;
for(int j=1;j<=tot&&prime[j]*i<=N-5;j++) {
vis[i*prime[j]]=1;
if(i%prime[j]==0) {phi[i*prime[j]]=phi[i]*prime[j];break;}
phi[i*prime[j]]=phi[i]*phi[prime[j]];miu[i*prime[j]]=-miu[i];
}
}
for(int i=1;i<=N-5;i++) phi[i]+=phi[i-1],miu[i]+=miu[i-1];
}
ll solvephi(int x) {
if(x<=N-5) return phi[x];
if(ph.count(x)) return ph[x];
ll ans=1ll*x*(x+1)/2;
for(int i=2,nxti;i<=x;i=nxti) {
nxti=x/(x/i)+1;
ans-=(nxti-i)*solvephi(x/i);
}
return ph[x]=ans;
}
ll solvemiu(int x) {
if(x<=N-5) return miu[x];
if(mu.count(x)) return mu[x];
ll ans=1;
for(int i=2,nxti;i<=x;i=nxti) {
nxti=x/(x/i)+1;
ans-=(nxti-i)*solvemiu(x/i);
}
return mu[x]=ans;
}
int T;
int main() {
init();
cin>>T;
while(T--){
cin>>n;
cout<<solvephi(n)<<' '<<solvemiu(n)<<endl;
}
}
11.树剖+线段树
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<vector>
#include<stack>
#include<algorithm>
#include<cstdlib>
#define int long long
using namespace std;
const int N=400005;
int n,m,r,p,a[N],head[N],ecnt,siz[N],fa[N],dep[N],son[N],dfn1[N],dfn2[N],top[N],ncnt,rnk[N];
struct Segtree {
int sum,lazy,l,r;
} seg[N<<2];
struct Edge {
int to,nxt;
} e[N<<1];
void pushup(int x) {
seg[x].sum=seg[x<<1].sum+seg[x<<1|1].sum;
seg[x].sum%=p;
}
void add(int bg,int ed){
e[++ecnt].nxt=head[bg];
e[ecnt].to=ed;
head[bg]=ecnt;
}
void build(int L,int R,int x) {
seg[x].l=L,seg[x].r=R;
if(L==R) {
seg[x].sum=a[rnk[L]];
return;
}
int mid=(L+R)>>1;
build(L,mid,x<<1);
build(mid+1,R,x<<1|1);
pushup(x);
}
void pushdown(int x) {
if(seg[x].lazy) {
if(seg[x].l!=seg[x].r) {
seg[x<<1].sum+=seg[x].lazy*(seg[x<<1].r-seg[x<<1].l+1);
seg[x<<1].sum%=p;
seg[x<<1|1].sum+=(seg[x].lazy)*(seg[x<<1|1].r-seg[x<<1|1].l+1);
seg[x<<1|1].sum%=p;
seg[x<<1].lazy+=seg[x].lazy;
seg[x<<1].lazy%=p;
seg[x<<1|1].lazy+=seg[x].lazy;
seg[x<<1|1].lazy%=p;
}
seg[x].lazy=0;
}
}
void update(int L,int R,int x,int c) {
if(R<seg[x].l||L>seg[x].r)return;
if(L<=seg[x].l&&seg[x].r<=R) {
seg[x].lazy+=c;
seg[x].sum+=(seg[x].r-seg[x].l+1)*c;
seg[x].sum%=p;
return;
}
pushdown(x);
update(L,R,x<<1,c);
update(L,R,x<<1|1,c);
pushup(x);
}
int query(int L,int R,int x){
if(L>seg[x].r||R<seg[x].l)return 0;
if(L<=seg[x].l&&seg[x].r<=R){
return seg[x].sum%p;
}
pushdown(x);
return (query(L,R,x<<1)%p+query(L,R,x<<1|1)%p)%p;
}
void dfs1(int x){
siz[x]=1;
for(int i=head[x];i;i=e[i].nxt){
int v=e[i].to;
if(fa[x]==v) continue;
fa[v]=x;
dep[v]=dep[x]+1;
dfs1(v);
siz[x]+=siz[v];
if(siz[v]>siz[son[x]]) son[x]=v;
}
}
void dfs2(int x,int qtop){
top[x]=qtop;dfn1[x]=++ncnt;
rnk[dfn1[x]]=x;
if(son[x]) dfs2(son[x],qtop);
for(int i=head[x];i;i=e[i].nxt){
int v=e[i].to;
if(v==fa[x]||v==son[x]) continue;
dfs2(v,v);
}
dfn2[x]=ncnt;
}
void add_v(int x,int y,int z){
int f1=top[x],f2=top[y];
while(f1!=f2){
if(dep[f1]<dep[f2]) swap(f1,f2),swap(x,y);
update(dfn1[f1],dfn1[x],1,z);
x=fa[f1],f1=top[x];
}
if(dep[x]>dep[y]) update(dfn1[y],dfn1[x],1,z);
else update(dfn1[x],dfn1[y],1,z);
}
int query_path(int x,int y){
int f1=top[x],f2=top[y],ans=0;
while(f1!=f2){
if(dep[f1]<dep[f2]) swap(f1,f2),swap(x,y);
ans+=query(dfn1[f1],dfn1[x],1);
ans%=p;
x=fa[f1],f1=top[x];
}
if(dep[x]>dep[y]) ans+=query(dfn1[y],dfn1[x],1);
else ans+=query(dfn1[x],dfn1[y],1)%p;
return ans%p;
}
signed main() {
cin>>n>>m>>r>>p;
int u,v,b,c;
for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
for(int i=1;i<n;i++){
scanf("%lld%lld",&u,&v);
add(u,v);
add(v,u);
}
dfs1(r);
dfs2(r,r);
build(1,n,1);
for(int i=1;i<=m;i++){
scanf("%lld",&u);
switch (u){
case 1:scanf("%lld%lld%lld",&c,&b,&v);add_v(c,b,v);break;
case 2:scanf("%lld%lld",&c,&b);printf("%lld\n",query_path(c,b));break;
case 3:scanf("%lld%lld",&b,&c);update(dfn1[b],dfn2[b],1,c);break;
case 4:scanf("%lld",&b);printf("%lld\n",query(dfn1[b],dfn2[b],1));break;
}
}
return 0;
}
12.树状数组
void add(int x,int y) {
for(; x<=n; x+=x&-x) {
f[x]+=y;
}
}
int query(int x) {
int sum=0;
for(; x; x-=x&-x) {
sum+=f[x];
}
return sum;
}
13.Treap
#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <ctime>
using namespace std;
const int N=100005;
int ch[N][2],fa[N],siz[N],cnt[N],val[N],prio[N],rt,tot,ans,n;
inline void pushup(int x){siz[x]=siz[ch[x][0]]+siz[ch[x][1]]+cnt[x];}
bool is_right(int x) {return x==ch[fa[x]][1];}
inline void rotate(int &x,int tag) {
int y=ch[x][tag^1];
ch[x][tag^1]=ch[y][tag];
ch[y][tag]=x;
siz[y]=siz[x];
pushup(x);
x=y;
}
void insert(int &x,int k) {
if(x==0) {x=++tot;val[x]=k,prio[x]=rand(),siz[x]=cnt[x]=1;return;}
siz[x]++;
if(k<val[x]) {insert(ch[x][0],k);if(prio[ch[x][0]]<prio[x]) rotate(x,1);}
else if(k>val[x]) {insert(ch[x][1],k);if(prio[ch[x][1]]<prio[x]) rotate(x,0);}
else if(k==val[x]) cnt[x]++;
}
void del(int &x,int k) {
if(x==0) return;
if(val[x]==k) {
if(cnt[x]>1) {cnt[x]--,siz[x]--;return;}
if(ch[x][0]==0||ch[x][1]==0) {x=ch[x][0]+ch[x][1];return;}
if(prio[ch[x][0]]<prio[ch[x][1]]) rotate(x,1),del(x,k);
else rotate(x,0),del(x,k);
return;
}
if(val[x]<k) {
siz[x]--;
del(ch[x][1],k);
}
else if(val[x]>k) {
siz[x]--;
del(ch[x][0],k);
}
pushup(x);
}
int rnk(int x,int k) {
if(x==0) return 0;
if(val[x]==k) return siz[ch[x][0]]+1;
if(val[x]<k) return rnk(ch[x][1],k)+siz[ch[x][0]]+cnt[x];
if(val[x]>k) return rnk(ch[x][0],k);
}
int getval(int x,int k) {
if(x==0) return 0;
if(k<=siz[ch[x][0]]) return getval(ch[x][0],k);
if(siz[ch[x][0]]+cnt[x]<k) return getval(ch[x][1],k-siz[ch[x][0]]-cnt[x]);
return val[x];
}
void pre(int x,int k) {
if(!x) return;
if(val[x]<k) ans=x,pre(ch[x][1],k);
else pre(ch[x][0],k);
}
void nxt(int x,int k) {
if(!x) return;
if(val[x]>k) ans=x,nxt(ch[x][0],k);
else nxt(ch[x][1],k);
}
int main() {
scanf("%d",&n);
srand(19260817);
int opt,x;
for(int i=1;i<=n;i++) {
scanf("%d%d",&opt,&x);
if(opt==1)insert(rt,x);
if(opt==2)del(rt,x);
if(opt==3)printf("%d\n",rnk(rt,x));
if(opt==4)printf("%d\n",getval(rt,x));
if(opt==5)pre(rt,x),printf("%d\n",val[ans]);
if(opt==6)nxt(rt,x),printf("%d\n",val[ans]);
}
}
14.Splay
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
const int N=100005;
int n,m,a[N];
int val[N],ch[N][2],fa[N],siz[N],rt,tot;
bool rev[N];
inline void pushup(int x) {siz[x]=siz[ch[x][0]]+siz[ch[x][1]]+1;}
int build(int x,int l,int r) {
if(l>r) return 0;
int mid=l+r>>1,now=++tot;
val[now]=a[mid],fa[now]=x;//siz[now]=1;
ch[now][0]=build(now,l,mid-1);
ch[now][1]=build(now,mid+1,r);
pushup(now);
return now;
}
inline void pushdown(int x) {
if(!rev[x]) return;
swap(ch[x][0],ch[x][1]);
rev[ch[x][0]]^=1;rev[ch[x][1]]^=1;
rev[x]=0;
}
inline void rotate(int x) {
int f=fa[x],ff=fa[f];
bool tag=x==ch[fa[x]][1];
pushdown(f),pushdown(x);
ch[f][tag]=ch[x][tag^1];
fa[ch[f][tag]]=f;
fa[f]=x;
fa[x]=ff;
ch[x][tag^1]=f;
if(ff) ch[ff][f==ch[ff][1]]=x;
pushup(f);
pushup(x);
}
inline void splay(int x,int tar) {
for(int f;(f=fa[x])!=tar;rotate(x)) if(fa[f]!=tar)rotate((x==ch[fa[x]][0])==(f==ch[fa[f]][0])?f:x);
if(!tar)
rt=x;
}
inline int getval(int x) {
int now=rt;
while(1) {
pushdown(now);
if(x<=siz[ch[now][0]]) now=ch[now][0];
else {
x-=siz[ch[now][0]]+1;
if(!x) return now;
now=ch[now][1];
}
}
}
void print(int x) {
pushdown(x);
if(ch[x][0]) print(ch[x][0]);
if(abs(val[x])!=0x3f3f3f3f) printf("%d ",val[x]);
if(ch[x][1])print(ch[x][1]);
}
int main() {
scanf("%d%d",&n,&m);
a[1]=-0x3f3f3f3f,a[n+2]=0x3f3f3f3f;
for(int i=1;i<=n;i++) a[i+1]=i;
rt=build(0,1,n+2);int l,r;
while(m--) {
scanf("%d%d",&l,&r);
l=getval(l),r=getval(r+2);
splay(l,0);
splay(r,l);
rev[ch[ch[rt][1]][0]]^=1;
}
print(rt);
}
15.Dinic
//Writer:jr HSZ;%%%GhostCai
#include<bits/stdc++.h>
#define int long long
#define reg register int
#define inf 0x7fffffff
using namespace std;
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-'0',ch=getchar();
return x*f;
}
struct Edge {
int to,nxt,val;
} e[2000005];
int n,m,s,t,mx;
int mxflow;
int cur[20005];
int head[20005],cnt=1;
void add(int bg,int ed,int val) {
e[++cnt].to=ed;
e[cnt].nxt=head[bg];
e[cnt].val=val;
head[bg]=cnt;
}
int h[20005];
queue<int>q;
bool bfs() {
memset(h,-1,sizeof h);
q.push(s);
h[s]=0;
while(!q.empty()) {
int x=q.front();
q.pop();
for(int i=head[x]; i; i=e[i].nxt) {
if(e[i].val&&h[e[i].to]==-1) {
h[e[i].to]=h[x]+1;
q.push(e[i].to);
}
}
}
return h[t]!=-1;
}
int dfs(int x,int f) {
if(x==t)return f;
int tp,used=0;
for(int i=cur[x]; i; i=e[i].nxt) {
if(e[i].val&&h[e[i].to]==h[x]+1) {
tp=dfs(e[i].to,min(e[i].val,f-used));
e[i].val-=tp;
if(e[i].val)cur[x]=i;
e[i^1].val+=tp;
used+=tp;
if(used==f)return f;
}
}
if(!used)h[x]=-1;
return used;
}
void dinic() {
while(bfs()) {
memcpy(cur,head,sizeof head);
mxflow+=dfs(s,inf);
}
}
int x,y,v;
signed main() {
n=read();m=read();s=read();t=read();
for(int i=1; i<=m; i++) {
x=read();y=read();v=read();
add(x,y,v);
add(y,x,0);
}
dinic();
cout<<mxflow;
return 0;
}
16.高斯消元
//Writer : Hsz %WJMZBMR%tourist%hzwer
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<stack>
#include<vector>
#include<cstdlib>
#include<algorithm>
#define LL long long
using namespace std;
int n,w[105];
const double eps=1e-8;
double a[105][105],b[105],v[105];
void gauss(){
for(int i=1;i<=n;i++)
{
int p=0;
double mx=0;
for(int j=1;j<=n;j++) {
if(fabs(a[i][j])-eps>mx) mx=fabs(a[i][j]),p=j;
}
if(!p) {
printf("No Solution");
return;
}
w[i]=p;
for(int j=1;j<=n;j++)
{
if(i!=j){
double tt=a[j][p]/a[i][p];
for(int k=1;k<=n+1;k++)
{
a[j][k]-=a[i][k]*tt;
}
}
}
}
for(int i=1;i<=n;i++) v[w[i]]=a[i][n+1]/a[i][w[i]];
for(int i=1;i<=n;i++) printf("%.2lf\n" ,v[i]);
}
int main() {
cin>>n;
for(int i=1;i<=n;i++){
for(int j=1;j<=n+1;j++)
scanf("%lf",&a[i][j]);
// scanf("%lf",&b[i]);
}
gauss();
return 0;
}
17.Lucas
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=1e7+7;
int T,n,m,mod;
long long fac[N];
void ready(int x)
{
fac[0]=1;
for(int i=1;i<=x;i++) fac[i]=fac[i-1]*i%mod;
}
long long ksm(long long d,long long z)
{
long long res=1;
d%=mod;
while(z)
{
if(z&1) res*=d,res%=mod;
d*=d;
d%=mod;
z>>=1;
}
return res%mod;
}
long long fermat(long long m,long long n)
{
if(n<m)return 0;
return fac[n]*ksm(fac[m],mod-2)%mod*ksm(fac[n-m],mod-2)%mod;
}
long long lucas(int m,int n)
{
long long ans=1;
while(n and m and ans)
{
ans=(ans*(fermat(m%mod,n%mod)))%mod;
n/=mod;
m/=mod;
}
return ans;
}
int main()
{
scanf("%d",&T);
while(T--)
{
scanf("%d%d%d",&n,&m,&mod);
ready(n+m);
printf("%lld\n",lucas(n,m+n));
}
}
18.左偏树
//Writer : Hsz %WJMZBMR%tourist%hzwer
#include <iostream>
#include <cstring>
#include <cstdio>
int in(){
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-'0';ch=getchar();}
return x*f;
}
void out(int x)
{
int a[25],wei=0;
if(x<0) putchar('-'),x=-x;
for(;x;x/=10) a[++wei]=x%10;
if(wei==0){ puts("0"); return;}
for(int j=wei;j>=1;--j) putchar('0'+a[j]);
putchar('\n');
}
void swap(int &x,int &y){int t=x;x=y,y=t;}
const size_t N=100005;
int n,m,val[N],ch[N][2],fa[N],dis[N];
int merge(int x,int y){
if(!x||!y)return x+y;
if(val[x]>val[y]||(val[x]==val[y]&&x>y)){swap(x,y);}
ch[x][1]=merge(ch[x][1],y);
fa[ch[x][1]]=x;
if(dis[ch[x][0]]<dis[ch[x][1]])swap(ch[x][0],ch[x][1]);
dis[x]=dis[ch[x][1]]+1;
return x;
}
int find(int x){while(fa[x]) x=fa[x];return x;}
void pop(int x){val[x]=-1;fa[ch[x][0]]=fa[ch[x][1]]=0;merge(ch[x][0],ch[x][1]);}
int main()
{
n=in(),m=in();
for(int i=1;i<=n;i++) val[i]=in();
for(int i=1,opt,x,y;i<=m;i++){
opt=in();x=in();
if(opt==1){y=in();if(val[x]==-1||val[y]==-1||x==y) continue;int ffff=find(x),fff=find(y);merge(ffff,fff);}
else {if(val[x]==-1) out(val[x]) ;else {int fmx=find(x);out(val[fmx]);pop(fmx);}}
}
return 0;
}
19.LCT
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=300005;
int n,m,a[N],fa[N],ch[N][2],sum[N];
bool rev[N];
bool is_rt(int x) {
// if(x==0) return 1;
return ch[fa[x]][0]!=x&&ch[fa[x]][1]!=x;
}
void pushup(int x) {
sum[x]=a[x]^sum[ch[x][0]]^sum[ch[x][1]];
}
void pushdown(int x) {
if(rev[x])
swap(ch[x][0],ch[x][1]),
rev[ch[x][0]]^=1,
rev[ch[x][1]]^=1,
rev[x]=0;
}
bool ck(int x) {
return x==ch[fa[x]][1];
}
void rotate(int x) {
int f=fa[x],ff=fa[f];bool tag=ck(x);
if(!is_rt(f)) ch[ff][f==ch[ff][1]]=x;
ch[f][tag]=ch[x][tag^1];
fa[ch[f][tag]]=f;
ch[x][tag^1]=f;
fa[f]=x;
fa[x]=ff;
pushup(f);pushup(x);
}
int top,stk[N];
void splay(int x) {
top=0;
stk[++top]=x;
for(int i=x;!is_rt(i);i=fa[i]) stk[++top]=fa[i];
for(int i=top;i;i--) pushdown(stk[i]);
for(int f;!is_rt(x);rotate(x))
if(!is_rt(f=fa[x]))rotate(ck(x)==ck(f)?f:x);
}
void access(int x) {
for(int t=0;x;t=x,x=fa[x])
splay(x),ch[x][1]=t,pushup(x);
}
void makeroot(int x) {
access(x);
splay(x);
swap(ch[x][0],ch[x][1]);
rev[ch[x][0]]^=1;rev[ch[x][1]]^=1;
}
int findroot(int x) {
access(x);
splay(x);
while(ch[x][0]) x=ch[x][0];
return x;
}
void link(int x,int y) {
makeroot(x);
fa[x]=y;
}
void cut(int x,int y) {
makeroot(x);
access(y);
splay(y);
if(ch[x][0]||ch[x][1]||fa[x]!=y||ch[y][ck(x)^1]) return;
ch[y][0]=fa[x]=0;
}
void change(int x,int v) {
a[x]=v;
access(x);
splay(x);
}
int query(int x,int y) {
makeroot(x);
access(y);
splay(y);
return sum[y];
}
int main() {
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++) scanf("%d",&a[i]);
for(int i=1,opt,x,y;i<=m;i++) {
scanf("%d%d%d",&opt,&x,&y);
switch (opt) {
case 0:printf("%d\n",query(x,y));break;
case 1:if(findroot(x)!=findroot(y)) link(x,y);break;
case 2:if(findroot(x)==findroot(y))cut(x,y);break;
case 3:change(x,y);break;
}
}
}
20.FFT
include <iostream>
#include <complex>
#include <cmath>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=2097153;
const double pi=acos(-1.0);
struct complexd{
double x,y;
complexd (double xx=0,double yy=0){x=xx,y=yy;}
complexd operator + (const complexd &rhs) const {return complexd(x+rhs.x,y+rhs.y);}
complexd operator - (const complexd &rhs) const {return complexd(x-rhs.x,y-rhs.y);}
complexd operator * (const complexd &rhs) const {return complexd(x*rhs.x-y*rhs.y,x*rhs.y+y*rhs.x);}
};
inline int rd() {
static int x;x=0;static char ch;ch=getchar();
while(!isdigit(ch)) ch=getchar();
while(isdigit(ch)) x=x*10+(ch^48),ch=getchar();
return x;
}
int n,m,l,r[N];
void fft(complexd *b,short tag) {
for(int i=0;i<n;i++) if(i<r[i]) swap(b[i],b[r[i]]);
for(int mid=1;mid<n;mid<<=1) {
complexd tp(cos(pi/mid),tag*sin(pi/mid));
for(int j=0;j<n;j+=mid<<1) {
complexd w(1,0);
for(int k=0;k<mid;k++,w=w*tp) {
complexd x=b[j+k],y=w*b[j+mid+k];
b[j+k]=x+y;
b[j+mid+k]=x-y;
}
}
}
}
complexd a[N],b[N];
int main() {
n=rd(),m=rd();
for(int i=0,x;i<=n;i++) a[i]=rd();
for(int j=0,x;j<=m;j++) b[j]=rd();
m+=n;
n=1;
while(n<=m) n<<=1,l++;
for(int i=0;i<n;i++) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
fft(a,1);
fft(b,1);
for(int i=0;i<=n;i++) a[i]=a[i]*b[i];
fft(a,-1);
for(int i=0;i<=m;i++) printf("%d ",(int)(a[i].x/n+0.5));
return 0;
}
21.KMP
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
char s1[1000005],s2[1000005],s[2000005];
int nxt[2000005];
int main() {
scanf("%s%s",s1,s2);
int len=strlen(s2);
for(int i=1;i<=len;i++) s[i]=s2[i-1];
s[len+1]=' ';
int len1=strlen(s1);
for(int i=0;i<len1;i++) s[i+len+2]=s1[i];
nxt[0]=0;
for(int i=2,j=0;i<=1+len+len1;i++) {
while(j&&s[i]!=s[j+1]) j=nxt[j];
if(s[i]==s[j+1]) j++;
nxt[i]=j;
if(nxt[i]==len&&i>len+1) printf("%d\n",i-len-len);
}
// putchar('\n');
for(int i=1;i<=len;i++) printf("%d ",nxt[i]);
return 0;
}
22.LCA
https://www.cnblogs.com/sdfzhsz/p/9280879.html
23.EK求mcf
#include <queue>
#include <cctype>
#include <cstdio>
#include <cstring>
const int inf=0x3f3f3f3f,N=50005<<1;
std::queue<int> q;
int n,m,S,T,dis[N],from[N],head[N],ecnt=1,ans1,ans2;
bool inq[N];
struct Edge{int to,nxt,val,cost,from;}e[N<<1];
void add(int bg,int ed,int val,int cost){e[++ecnt].cost=cost;e[ecnt].from=bg;e[ecnt].nxt=head[bg];e[ecnt].to=ed;e[ecnt].val=val;head[bg]=ecnt;}
bool spfa(){
q.push(S);
std::memset(dis,0x3f,sizeof dis);
std::memset(inq,0,sizeof inq);
dis[S]=0;inq[S]=1;
while(!q.empty()){
int u=q.front();q.pop();inq[u]=0;
for(int i=head[u],v;i;i=e[i].nxt){
v=e[i].to;
if(dis[v]>dis[u]+e[i].cost&&e[i].val){
dis[v]=dis[u]+e[i].cost;
from[v]=i;
if(!inq[v]) q.push(v),inq[v]=1;
}
}
}
return dis[T]!=inf;
}
void min(int &x,int y){x=x<y?x:y;}
void mcf() {
int x=inf,i=from[T];
while(i) {min(x,e[i].val);i=from[e[i].from];}
ans1+=x;i=from[T];
while(i){
e[i].val-=x;e[i^1].val+=x;
ans2+=x*e[i].cost;i=from[e[i].from];
}
}
inline void read(int &x){
x=0;int f=1;char ch=getchar();
while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
x=x*f;
}
int main(){
read(n);read(m);read(S);read(T);
for(int i=1,a,b,c,v;i<=m;i++)read(a),read(b),read(v),read(c),add(a,b,v,c),add(b,a,0,-c);
while(spfa())mcf();
printf("%d %d",ans1,ans2);
}
24.AC自动机
#include <iostream>
#include <cstdio>
#include <queue>
#include <cstring>
using namespace std;
int n;
const int N=500010;
struct ACZDJ {
int tr[N][26],fail[N],val[N],cnt;
void insert(char *s) {
int len=strlen(s),p=0;
for(int i=0; i<len; i++) {
if(!tr[p][s[i]-'a']) tr[p][s[i]-'a']=++cnt;
p=tr[p][s[i]-'a'];
}
val[p]++;
}
void build() {
queue<int>q;
for(int i=0; i<26; i++)
if(tr[0][i]) q.push(tr[0][i]),fail[tr[0][i]]=0;
while(!q.empty()) {
int u=q.front();
q.pop();
for(int i=0; i<26; i++) {
if(tr[u][i]) q.push(tr[u][i]),fail[tr[u][i]]=tr[fail[u]][i];
else tr[u][i]=tr[fail[u]][i];
}
}
}
int query(char *s) {
int len=strlen(s),p=0,ans=0;
for(int i=0; i<len; i++) {
int v=s[i]-'a';
p=tr[p][v];
for(int j=p; ~val[j]&&j; j=fail[j]) {
ans+=val[j];
val[j]=-1;
}
}
return ans;
}
} AC;
char s[2000005];
int main() {
scanf("%d",&n);
while(n--) {
scanf("%s",s);
AC.insert(s);
}
AC.build();
scanf("%s",s);
cout<<AC.query(s);
}
25.主席树
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <queue>
#include <map>
#include <set>
#include <stack>
#include <vector>
#include <cstdlib>
#include <algorithm>
#define LL long long
using namespace std;
const int N=200005<<5;
int l[N],r[N],sum[N],b[N],p[N];
int n,m,a[N],root[N],tot;
void build(int &k,int L,int R) {
k=++tot;
if(L<R) {
int mid=L+R>>1;
build(l[k],L,mid);
build(r[k],mid+1,R);
}
}
void update(int &k,int pre,int L,int R,int c) {
k=++tot;
l[k]=l[pre],r[k]=r[pre],sum[k]=sum[pre]+1;
if(L<R) {
int mid=L+R>>1;
if(c<=mid)update(l[k],l[pre],L,mid,c);
else update(r[k],r[pre],mid+1,R,c);
}
}
int query(int u,int v,int L,int R,int k) {
if(L==R) return L;
int x=sum[l[v]]-sum[l[u]];
if(x>=k) return query(l[u],l[v],L,(L+R)>>1,k);
else return query(r[u],r[v],(L+R)/2+1,R,k-x);
}
int main() {
cin>>n>>m;
for(int i=1; i<=n; i++) scanf("%d",&a[i]),b[i]=a[i];
sort(a+1,a+1+n);
int u=unique(a+1,a+1+n)-a-1;
build(root[0],1,u);
for(int i=1; i<=n; i++) {
b[i]=lower_bound(a+1,a+1+u,b[i])-a;
update(root[i],root[i-1],1,u,b[i]);
}
int q,v,k;
for(int i=1; i<=m; i++) {
scanf("%d%d%d",&q,&v,&k);
printf("%d\n",a[query(root[q-1],root[v],1,u,k)]);
}
return 0;
}
26.割点
#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <vector>
#include <bitset>
#include <cmath>
#include <queue>
#include <ctime>
#include <set>
#include <map>
#define fo(i,j,k) for(int i=j;i<=k;i++)
#define fd(i,j,k) for(int i=j;i>=k;i--)
#define go(i,k) for(int i=head[k],v=e[i].to;i;i=e[i].nxt,v=e[i].to)
using namespace std;
typedef long long ll;
typedef double db;
const int inf=0x3f3f3f3f;
inline int rd() {
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;
}
const int N=100005,M=1000005;
struct Edge{int to,nxt;}e[M];
int head[N],ecnt,dfn[N],low[N],tim,n,m;
bool cut[N];
inline void add(int bg,int ed) {e[++ecnt]=(Edge) {ed,head[bg]};head[bg]=ecnt;}
void tarjan(int x,int rt) {
dfn[x]=low[x]=++tim;
int f=0;
go(i,x) {
if(!dfn[v]) {
tarjan(v,rt);
low[x]=min(low[v],low[x]);
if(low[v]>=dfn[x]&&x!=rt) cut[x]=1;
if(x==rt) f++;
}
else low[x]=min(low[x],dfn[v]);
}
if(f>=2) {cut[rt]=1;}
}
int main() {
#ifdef HSZ
freopen(".in","r",stdin);
freopen(".out","w",stdout);
#endif
n=rd(),m=rd();
int a,b;
fo(i,1,m) a=rd(),b=rd(),add(a,b),add(b,a);
fo(i,1,n) if(!dfn[i])tarjan(i,i);
int ans=0;
fo(i,1,n) if(cut[i]) ans++;
printf("%d\n",ans);
fo(i,1,n) if(cut[i]) printf("%d ",i);
return 0;
}
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