【打板进行中】

1.快速排序

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<queue>
#include<ctime>
const int maxn=100005;
using namespace std;
int n,a[maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

void qsort(int *s,int l,int r) {
    int bs=s[rand()%(r-l+1)+l];
    int i=l,j=r;
    while(i<=j) {
        while(s[j]>bs) j--; 
        while(s[i]<bs) i++;
        if(i<=j) {
            swap(s[i],s[j]);
            i++; j--;
        }
    }
    if(j>l) qsort(s,l,j);
    if(i<r) qsort(s,i,r);
}

void work() {
    qsort(a,1,n);
    for(int i=1;i<n;i++) printf("%d ",a[i]);
    printf("%d\n",a[n]);
}

void init() {
    read(n);
    for(int i=1;i<=n;i++) read(a[i]);
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    srand(time(0));
    init();
    work();
    return 0;
}

 

2.归并排序

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<queue>
#include<ctime>
const int maxn=100005;
using namespace std;
int n,a[maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int tp[maxn];
void msort(int *s,int l,int r) {
    if(l>=r) return;
    int mid=((l+r)>>1);
    msort(s,l,mid); msort(s,mid+1,r);
    int tl=l,i=l,j=mid+1;
    while(tl<=r) {
        if(i<=mid&&(j>r||s[i]<s[j])) { tp[tl++]=s[i]; i++;}
        else {tp[tl++]=s[j]; j++;}
    }
    for(int i=l;i<=r;i++) s[i]=tp[i]; 
}

void work() {
    msort(a,1,n);
    for(int i=1;i<n;i++) printf("%d ",a[i]);
    printf("%d\n",a[n]);
}

void init() {
    read(n);
    for(int i=1;i<=n;i++) read(a[i]);
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    srand(time(0));
    init();
    work();
    return 0;
}

 

3.kmp

//Twenty雨欲予鱼愉
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
const int maxn=1000007;
using namespace std;
char a[maxn],b[maxn];
int nxt[maxn],ans[maxn],sza,szb;

void make_nxt(char b[],int nxt[]) {
    for(int i=1,k=0;i<szb;i++) {
        while(k&&b[i]!=b[k]) k=nxt[k-1];
        if(b[i]==b[k]) k++;
        nxt[i]=k;
    }
}

void kmp(char a[],char b[],int nxt[]) {
    make_nxt(b,nxt);
    for(int i=0,k=0;i<sza;i++) {
        while(k&&a[i]!=b[k]) k=nxt[k-1];
        if(a[i]==b[k]) k++;
        if(k==szb) {ans[++ans[0]]=i-szb+2;}
    } 
}

void work() {
    kmp(a,b,nxt);
    for(int i=1;i<=ans[0];i++) 
    printf("%d\n",ans[i]);
    for(int i=0;i<szb-1;i++) printf("%d ",nxt[i]);
    printf("%d\n",nxt[szb-1]);
}

void init() {
    scanf("%s",a);
    getchar();
    scanf("%s",b);
    sza=strlen(a); 
    szb=strlen(b);
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

4.SLF优化的spfa

//Twenty雨欲予鱼愉
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
const int maxn=10005;
const int maxm=500007;
using namespace std;
int dis[maxn],n,m,s;

template<typename T>void read(T &x) {
    char ch=getchar(); x=0; T f=1;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') ch=getchar(),f=-1;
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxm],to[maxm],val[maxm];
void add(int u,int v,int w) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v; val[ecnt]=w;
}

int que[maxm+5],ql=1,qr=0,vis[maxn];
void spfa(int s) {
    for(int i=1;i<=n;i++) dis[i]=2147483647;
    memset(vis,0,sizeof(vis));
    dis[s]=0; 
    vis[s]=1;
    que[++qr]=s;
    while(ql<=qr) {
        int x=que[(ql+maxm)%maxm];
        ql++;
        vis[x]=0;
        for(int i=fir[x];i;i=nxt[i]) {
            if(dis[to[i]]>dis[x]+val[i]) {
                dis[to[i]]=dis[x]+val[i];
                if(!vis[to[i]]) {
                    vis[to[i]]=1;
                    if(ql<=qr&&(dis[que[(ql+maxm)%maxm]]>dis[to[i]])) {
                        ql--;
                        que[(ql+maxm)%maxm]=to[i];
                    }
                    else {
                        qr++;
                        que[(qr+maxm)%maxm]=to[i];
                    }
                }
            }
        }    
    }    
}

void work() {
    spfa(s);
    for(int i=1;i<=n;i++) 
        printf("%d ",dis[i]);
    printf("\n");
}

void init() {
    read(n);
    read(m);
    read(s);
    for(int i=1;i<=m;i++) {
        int x,y,z;
        read(x); read(y); read(z);
        add(x,y,z);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

5.堆优化的dijkstra

//Twenty雨欲予鱼愉
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
const int maxn=10005;
const int maxm=500007;
using namespace std;
int dis[maxn],n,m,s;

template<typename T>void read(T &x) {
    char ch=getchar(); x=0; T f=1;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') ch=getchar(),f=-1;
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxm],to[maxm],val[maxm];
void add(int u,int v,int w) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v; val[ecnt]=w;
}

struct node {
    int x,dis;
    node(){}
    node(int x,int dis):x(x),dis(dis){}
    friend bool operator <(const node&A,const node&B) {
        return A.dis>B.dis;
    }
};

priority_queue<node>que;
int vis[maxn];
void spfa(int s) {
    for(int i=1;i<=n;i++) dis[i]=2147483647;
    memset(vis,0,sizeof(vis));
    dis[s]=0; 
    que.push(node(s,0));
    while(!que.empty()) {
        node tp=que.top();
        int x=tp.x;
        que.pop();
        if(vis[x]) continue;
        vis[x]=1;
        for(int i=fir[x];i;i=nxt[i]) 
            if(!vis[to[i]]&&dis[to[i]]>dis[x]+val[i]) {
                dis[to[i]]=dis[x]+val[i];
                que.push(node(to[i],dis[to[i]]));
            }
    }    
}

void work() {
    spfa(s);
    for(int i=1;i<=n;i++) 
        printf("%d ",dis[i]);
    printf("\n");
}

void init() {
    read(n);
    read(m);
    read(s);
    for(int i=1;i<=m;i++) {
        int x,y,z;
        read(x); read(y); read(z);
        add(x,y,z);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

6.左偏树

//Twenty雨欲予鱼愉
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
const int maxn=100000+299;
using namespace std;
int a[maxn],n,m,bo[maxn],fa[maxn],dis[maxn],ch[maxn][2];

template<typename T>void read(T &x) {
    char ch=getchar(); x=0; T f=1;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') ch=getchar(),f=-1;
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int find(int x) {return x==fa[x]?x:fa[x]=find(fa[x]);}

#define lc ch[x][0]
#define rc ch[x][1]
int merge(int x,int y) {
    if(!(x*y)) return x^y;
    if(a[x]>a[y]) swap(x,y);
    fa[y]=x;
    rc=merge(rc,y);
    if(dis[rc]>dis[lc]) swap(lc,rc);
    if(!rc) dis[x]=0;
    else dis[x]=dis[rc]+1;
    return x;
}

void work() {
    for(int i=1;i<=m;i++) {
        int o,x,y;
        read(o);
        if(o==1) {
            read(x);
            read(y);
            if(!bo[x]&&!bo[y]&&(find(x)!=find(y)))
                x=merge(find(x),find(y));
        }
        else {
            read(x);
            if(bo[x]) {
                printf("-1\n");
                continue;
            }
            x=find(x);
            printf("%d\n",a[x]);
            fa[lc]=lc; fa[rc]=rc;
            lc=merge(lc,rc);
            if(!lc) fa[x]=rc;
            else fa[x]=lc;
            lc=rc=0;
            bo[x]=1;
        }
    }
}

void init() {
    read(n); 
    read(m);
    for(int i=1;i<=n;i++) {
        read(a[i]);
        fa[i]=i;
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

7.线性筛素数

//Twenty
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
using namespace std;
const int maxn=10000007;
int n,m,p[maxn];
bool bo[maxn];

template<typename T>void read(T &x) {
    char ch=getchar(); x=0; T f=1;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') ch=getchar(),f=-1;
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

void get_prime(int n) {
    bo[1]=1;
    for(int i=2;i<=n;i++) {
        if(!bo[i]) p[++p[0]]=i;
        for(int j=1;j<=p[0]&&p[j]*i<=n;j++) {
            bo[p[j]*i]=1;
            if(i%p[j]==0) break;
        }
    }
}

void init() {
    read(n);
    get_prime(n);
    read(m);
    for(int i=1;i<=m;i++) {
        int x; read(x);
        if(bo[x]) printf("No\n");
        else printf("Yes\n");
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    return 0;
}

 

8.二分图最大匹配 匈牙利

//Twenty雨欲予鱼愉
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<ctime>
#include<queue>
const int maxn=2005;
using namespace std;
int n,m,e,pr[maxn],vis[maxn],ans;

template<typename T>void read(T &x) {
    char ch=getchar(); x=0; T f=1;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') ch=getchar(),f=-1;
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxn*maxn],to[maxn*maxn];
void add(int u,int v) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v;
}

int find(int x) {
    for(int i=fir[x];i;i=nxt[i]) if(!vis[to[i]]){
        int y=to[i];
        vis[y]=1;
        if(!pr[y]||find(pr[y])) {
            pr[y]=x;
            return 1;
        }
    }
    return 0;
}

void work() {
    for(int i=1;i<=n;i++) {
        memset(vis,0,sizeof(vis));
        ans+=find(i);
    }
    printf("%d\n",ans);
}

void init() {
    read(n);
    read(m);
    read(e);
    for(int i=1;i<=e;i++) {
        int x,y;
        read(x);
        read(y);
        if(x<=n&&y<=m)
        add(x,y);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

9.二分图匹配 km算法

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<queue>
#include<ctime>
#define INF 0xfffffff
const int maxn=305;
typedef long long LL;
using namespace std;
int n,cx[maxn],cy[maxn],x[maxn],y[maxn],pr[maxn],slack[maxn];
int a[maxn][maxn];
 
int find(int u) {
    x[u]=1;
    for(int i=1;i<=n;i++) if(!y[i]){
        if(cx[u]+cy[i]==a[u][i]) {
            y[i]=1;
            if(pr[i]==-1||find(pr[i])) {
                pr[i]=u;
                return 1;
            }
        }
        else slack[i]=min(slack[i],-a[u][i]+cx[u]+cy[i]);
    }
    return 0;
}
 
void work() {
    memset(pr,-1,sizeof(pr));
    memset(cy,0,sizeof(cy));
    for(int i=1;i<=n;i++) {
        for(int j=1;j<=n;j++) slack[j]=INF;
        for(;;) {
            memset(x,0,sizeof(x));
            memset(y,0,sizeof(y));
            if(find(i)) break;
            int d=INF;
            for(int j=1;j<=n;j++)
                if(!y[j]&&d>slack[j])
                    d=slack[j];
            if(d==INF) return;
            for(int j=1;j<=n;j++) {
                if(x[j]) cx[j]-=d;
                if(y[j]) cy[j]+=d;
                else slack[j]-=d;
            }
        }
    }
    int ans=0;
    for(int i=1;i<=n;i++)
        ans+=a[pr[i]][i];
    printf("%d\n",ans);
}
 
void init() {
    while(~scanf("%d",&n)) {
        for(int i=1;i<=n;i++) {
            cx[i]=-INF;
            for(int j=1;j<=n;j++) {
                scanf("%d",&a[i][j]);
                cx[i]=max(cx[i],a[i][j]);
            }
        }
        work();
    }
}
 
int main()  {
    init();
    return 0;
}

 

10.线性基

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<queue>
#include<ctime>
const int maxn=101;
typedef long long LL;
using namespace std;
int n;
LL a[maxn],b[maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

void work() {
    for(int i=1;i<=n;i++) 
        for(int j=60;j>=0;j--) 
            if((1LL<<j)&a[i]) {
                if(b[j]) a[i]^=b[j];
                else { b[j]=a[i]; break;}
            }
    LL ans=0;
    for(int i=60;i>=0;i--) 
        if((ans^b[i])>ans) ans^=b[i];
    printf("%lld\n",ans);
}

void init() {
    read(n);
    for(int i=1;i<=n;i++) read(a[i]); 
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

11.高斯消元

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=105;
typedef long long LL;
using namespace std;
int n;
double a[maxn][maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int gauss(double a[][105],int n) {
    for(int i=1;i<=n;i++) {
        int now=i;
        for(int j=i+1;j<=n;j++) 
            if(a[j][i]>a[now][i]) now=j;
        if(now!=i) 
            for(int j=i;j<=n+1;j++)
                swap(a[i][j],a[now][j]);
        if(a[now][i]==0) return 0;
        for(int j=i+1;j<=n+1;j++) 
            a[i][j]/=a[i][i];
        a[i][i]=1;
        for(int j=i+1;j<=n;j++) {
            for(int k=i+1;k<=n+1;k++) 
                a[j][k]-=a[i][k]*a[j][i];
            a[j][i]=0;    
        }
    }
    for(int i=n-1;i>=1;i--) 
        for(int j=i+1;j<=n;j++) 
            a[i][n+1]-=a[i][j]*a[j][n+1];
    return 1;
}

void work() 
{
    if(!gauss(a,n)) printf("No Solution\n");
    else 
        for(int i=1;i<=n;i++)
            printf("%.2lf\n",a[i][n+1]); 
}

void init() {
    read(n);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n+1;j++) 
              read(a[i][j]);
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

12.tarjan割点

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=100005; 
typedef long long LL;
using namespace std;
int n,m,ans[maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxn<<1],to[maxn<<1];
void add(int u,int v) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v;
    nxt[++ecnt]=fir[v]; fir[v]=ecnt; to[ecnt]=u;
}

int rc,dfs_clock,dfn[maxn],low[maxn],cut[maxn];
void tarjan(int x,int rt) {
    dfn[x]=low[x]=++dfs_clock;
    for(int i=fir[x];i;i=nxt[i]) {
            if(!dfn[to[i]]) {    
            if(x==rt) rc++;
            tarjan(to[i],rt);
            low[x]=min(low[x],low[to[i]]);
            if(x!=rt&&low[to[i]]>=dfn[x]) cut[x]=1;
        }
        else low[x]=min(low[x],dfn[to[i]]);
    }
    if(x==rt&&rc>=2) cut[x]=1;
}

void work() {
    for(int i=1;i<=n;i++) 
        if(!dfn[i]) {rc=0;tarjan(i,i);}
    for(int i=1;i<=n;i++) 
        if(cut[i])
            ans[++ans[0]]=i;
    printf("%d\n",ans[0]);
    for(int i=1;i<ans[0];i++) printf("%d ",ans[i]);
    if(ans[0]) printf("%d\n",ans[ans[0]]); 
}

void init() {
    read(n);
    read(m);
    for(int i=1;i<=m;i++) {
        int x,y;
        read(x); read(y);
        add(x,y);
    }
}

int main() {
    init();
    work();
    return 0;
}

 

13.tarjan求桥

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<queue>
#include<vector>
typedef long long LL;
using namespace std;
const int maxn=10000+299;
const int maxm=100000*2+299;
int T,n,m,x,y,fir[maxn],nxt[maxm],to[maxm],fa[maxn],cc,cut[maxm],dfn[maxn],id[maxm],low[maxn],dfs_clock,ecnt;

void add(int x,int y,int tot) { 
    nxt[++ecnt]=fir[x]; fir[x]=ecnt; to[ecnt]=y; id[ecnt]=tot;
    nxt[++ecnt]=fir[y]; fir[y]=ecnt; to[ecnt]=x; id[ecnt]=tot;
}
void clear() {
    memset(fir,0,sizeof(fir));
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    memset(cut,0,sizeof(cut));
    memset(fa,0,sizeof(fa)); ecnt=0;
    dfs_clock=0;
}

void tarjan(int x) {
    dfn[x]=low[x]=++dfs_clock;
    for(int i=fir[x];i;i=nxt[i]) {
        if(!dfn[to[i]]) {
            fa[to[i]]=i;
            tarjan(to[i]);
            low[x]=min(low[x],low[to[i]]);
        }
        else if(id[fa[x]]!=id[i]) low[x]=min(low[x],dfn[to[i]]);
    }
    if(fa[x]&&dfn[x]==low[x]) {
        cc++;
        cut[id[fa[x]]]=1;
    }
}

int main()
{
    scanf("%d",&T);
    while(T) {
        clear();
        scanf("%d%d",&n,&m);
        for(int i=1;i<=m;i++) {
            scanf("%d%d",&x,&y);
            add(x,y,i);    
        }
        for(int i=1;i<=n;i++)
            if(!dfn[i]) tarjan(i);
        printf("%d\n",cc);
        for(int i=1;i<=m;i++) 
            if(cut[i]) { cc--; if(cc) printf("%d ",i); else printf("%d\n",i);}
        --T;
        if(T) printf("\n");
    }
    return 0;
}

 

14.网络最大流

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
#define inf 0xfffffff
const int N=10007;
const int M=100007;
typedef long long LL;
using namespace std;
int n,m,s,t,d[N],c[N],ecnt=1;

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

struct edge {
    int from,to,cap,flow,nxt;
    edge(){}
    edge(int from,int to,int cap,int flow,int nxt):from(from),to(to),cap(cap),flow(flow),nxt(nxt){}
}e[M<<1];

int fir[N],cur[N];
void add(int u,int v,int w) {
    e[++ecnt]=edge(u,v,w,0,fir[u]);
    e[++ecnt]=edge(v,u,0,0,fir[v]);
    fir[u]=ecnt-1; fir[v]=ecnt;
}

queue<int>que;
void bfs() {
    for(int i=1;i<=n;i++) d[i]=n;
    d[t]=0; 
    que.push(t);
     while(!que.empty()) {
         int x=que.front();
         que.pop();
         for(int i=fir[x];i;i=e[i].nxt) {
             int y=e[i].to;
            if(d[y]==n&&e[i].cap==e[i].flow) {
                d[y]=d[x]+1;
                que.push(y); 
            } 
        }
    } 
}

int p[N];
int cal() {
    int fl=inf;
    for(int x=t;x!=s;x=e[p[x]].from) 
        fl=min(fl,e[p[x]].cap-e[p[x]].flow);
    for(int x=t;x!=s;x=e[p[x]].from) {
        e[p[x]].flow+=fl;
        e[p[x]^1].flow-=fl;
    }
    return fl;
}

int max_flow() {
    bfs();
    for(int i=1;i<=n;i++) cur[i]=fir[i],c[d[i]]++; 
    int res=0;
    for(int x=s;d[x]<n;) {
        if(x==t) {
            res+=cal();
            x=s;
        }
        int ok=0;
        for(int &i=cur[x];i;i=e[i].nxt) {
            int y=e[i].to;
            if(d[y]+1==d[x]&&e[i].cap>e[i].flow) {
                ok=1;    
                p[y]=i;
                x=y; 
                break;
            }
        }
        if(!ok) {
            cur[x]=fir[x];
            int M=n;
            for(int i=cur[x];i;i=e[i].nxt) {
                int y=e[i].to;
                if(e[i].flow<e[i].cap&&d[y]+1<M) M=d[y]+1;
            }
            if(!(--c[d[x]])) break;
            c[d[x]=M]++;
            if(x!=s) x=e[p[x]].from;
        }
    }
    return res;
} 

void work() {
    printf("%d\n",max_flow());
}

void init() {
    read(n);
    read(m);
    read(s);
    read(t);
    for(int i=1;i<=m;i++) {
        int u,v,w;
        read(u);
        read(v);
        read(w);
        add(u,v,w);
    } 
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

15.最小费用最大流

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
#define inf 0xfffffff
const int N=5007;
const int M=50007;
typedef long long LL;
using namespace std;
int n,m,s,t,ecnt=1;

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

struct edge {
    int from,to,cap,flow,cost,nxt;
    edge(){}
    edge(int from,int to,int cap,int flow,int cost,int nxt):from(from),to(to),cap(cap),flow(flow),cost(cost),nxt(nxt){}
}e[M<<1];

int fir[N],cur[N];
void add(int u,int v,int w,int c) {
    e[++ecnt]=edge(u,v,w,0,c,fir[u]);
    e[++ecnt]=edge(v,u,0,0,-c,fir[v]);
    fir[u]=ecnt-1; fir[v]=ecnt;
}

int p[N];
int cal() {
    int fl=inf;
    for(int x=t;x!=s;x=e[p[x]].from) 
        fl=min(fl,e[p[x]].cap-e[p[x]].flow);
    for(int x=t;x!=s;x=e[p[x]].from) {
        e[p[x]].flow+=fl;
        e[p[x]^1].flow-=fl;
    }
    return fl;
}

queue<int>que;
int dis[N],vis[N];
int spfa() {
    for(int i=1;i<=n;i++) dis[i]=inf;
    dis[s]=0; vis[s]=1; que.push(s);
    while(!que.empty()) {
        int x=que.front();
        que.pop(); vis[x]=0;
        for(int i=fir[x];i;i=e[i].nxt) {
            int y=e[i].to;
            if(e[i].cap>e[i].flow&&dis[y]>dis[x]+e[i].cost) {
                p[y]=i; 
                dis[y]=dis[x]+e[i].cost;
                if(!vis[y]) {
                    vis[y]=1;
                    que.push(y); 
                }
            }
        }
    }
    return (dis[t]!=inf); 
} 

int ans2=0;
int max_flow() {
    int res=0;
    while(spfa()) {
        int tp=cal();
        res+=tp;
        ans2+=tp*dis[t];
    }
    return res;
} 

void work() {
    printf("%d ",max_flow());
    printf("%d\n",ans2);
}

void init() {
    read(n);
    read(m);
    read(s);
    read(t);
    for(int i=1;i<=m;i++) {
        int u,v,w,c;
        read(u);
        read(v);
        read(w);
        read(c);
        add(u,v,w,c);
    } 
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

 16.倍增求lca

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=500007;
typedef long long LL;
using namespace std;
int n,m,rt;

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxn<<1],to[maxn<<1];
void add(int u,int v) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v;
    nxt[++ecnt]=fir[v]; fir[v]=ecnt; to[ecnt]=u;
}

int f[maxn][20],R[maxn];
void dfs(int x,int fa) {
    f[x][0]=fa; R[x]=R[fa]+1;
    for(int i=1;i<=19;i++) 
        f[x][i]=f[f[x][i-1]][i-1];
    for(int i=fir[x];i;i=nxt[i]) if(to[i]!=fa) {
        dfs(to[i],x);
    }
}

int get_lca(int x,int y) {
    if(R[x]<R[y]) swap(x,y);
    for(int i=19;i>=0;i--) 
        if(f[x][i]&&R[f[x][i]]>=R[y])
            x=f[x][i];
    if(x==y) return x;
    for(int i=19;i>=0;i--) 
        if(f[x][i]&&f[x][i]!=f[y][i])
            x=f[x][i],y=f[y][i];
    return f[x][0];
}

void work() {
    dfs(rt,0);
    for(int i=1;i<=m;i++) {
        int x,y;
        read(x); read(y);
        printf("%d\n",get_lca(x,y));
    }
}

void init() {
    read(n);
    read(m);
    read(rt);
    for(int i=1;i<n;i++) {
        int u,v;
        read(u); read(v);
        add(u,v);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

17.tarjan求lca

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=500007;
typedef long long LL;
using namespace std;
int n,m,rt;

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxn<<1],to[maxn<<1];
void add(int u,int v) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v;
    nxt[++ecnt]=fir[v]; fir[v]=ecnt; to[ecnt]=u;
}

int cnt,fi[maxn],nx[maxn<<1],tt[maxn<<1],id[maxn<<1],ans[maxn];
void add_ask(int u,int v,int i) {
    nx[++cnt]=fi[u]; fi[u]=cnt; tt[cnt]=v; id[cnt]=i;
    nx[++cnt]=fi[v]; fi[v]=cnt; tt[cnt]=u; id[cnt]=i;
}

int fa[maxn],vis[maxn];
int find(int x) { return x==fa[x]?x:fa[x]=find(fa[x]);} 

void dfs(int x,int f) {
    for(int i=fi[x];i;i=nx[i]) 
        if(vis[tt[i]]) 
            ans[id[i]]=find(tt[i]);
    vis[x]=1;
    for(int i=fir[x];i;i=nxt[i]) if(to[i]!=f) 
        dfs(to[i],x);
    fa[x]=f;
}

void work() {
    for(int i=1;i<=n;i++) fa[i]=i;
    for(int i=1;i<=m;i++) {
        int x,y;
        read(x); read(y);
        add_ask(x,y,i);
    }
    dfs(rt,0);
    for(int i=1;i<=m;i++)
        printf("%d\n",ans[i]);
}

void init() {
    read(n);
    read(m);
    read(rt);
    for(int i=1;i<n;i++) {
        int u,v;
        read(u); read(v);
        add(u,v);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

 18.树剖求lca

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=500007;
typedef long long LL;
using namespace std;
int n,m,rt;

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

int ecnt,fir[maxn],nxt[maxn<<1],to[maxn<<1];
void add(int u,int v) {
    nxt[++ecnt]=fir[u]; fir[u]=ecnt; to[ecnt]=v;
    nxt[++ecnt]=fir[v]; fir[v]=ecnt; to[ecnt]=u;
}

int R[maxn],sz[maxn],top[maxn],fa[maxn];
void dfs(int x,int f) {
    R[x]=R[f]+1;
    sz[x]=1; fa[x]=f;
    for(int i=fir[x];i;i=nxt[i]) if(to[i]!=f) {
        dfs(to[i],x);
        sz[x]+=sz[to[i]];
    }
}

void DFS(int x,int tt) {
    top[x]=tt;
    int mson=0;
    for(int i=fir[x];i;i=nxt[i]) if(to[i]!=fa[x]&&sz[to[i]]>sz[mson]){
        mson=to[i];
    } 
    if(!mson) return;
    DFS(mson,tt);
    for(int i=fir[x];i;i=nxt[i]) if(to[i]!=fa[x]&&to[i]!=mson){
        DFS(to[i],to[i]);
    } 
}

int get_lca(int x,int y) {
    while(top[x]!=top[y]) {
        if(R[top[x]]<R[top[y]]) swap(x,y);
        x=fa[top[x]];
    } 
    if(R[x]>R[y]) swap(x,y);
    return x;
} 

void work() {
    dfs(rt,0);
    DFS(rt,rt);
    for(int i=1;i<=m;i++) {
        int x,y;
        read(x); read(y);
        printf("%d\n",get_lca(x,y));
    }
}

void init() {
    read(n);
    read(m);
    read(rt);
    for(int i=1;i<n;i++) {
        int u,v;
        read(u); read(v);
        add(u,v);
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    work();
    return 0;
}

 

19.manacher

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=11000007;
typedef long long LL;
using namespace std;
int tot,ans,rad[maxn<<1];
char a[maxn<<1];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

void manacher() {
    for(int i=0,j=0,k;i<tot;) {
        while(a[i-j-1]==a[i+j+1]) j++;
        rad[i]=j;
        ans=max(ans,j);
        for(k=1;k<=j&&rad[i-k]!=rad[i]-k;k++) 
            rad[i+k]=min(rad[i-k],rad[i]-k);
        i+=k;
        j=max(j-k,0);
    }
}

void init() {
    a[tot++]='&';
    a[tot++]='#';
    char ch=getchar();
    while(ch<'a'||ch>'z') ch=getchar();
    for(;ch>='a'&&ch<='z';ch=getchar()) {
        a[tot++]=ch;
        a[tot++]='#';
    }
    a[tot++]='*';
    manacher();
    printf("%d\n",ans);
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    return 0;
}

 

 20.AC自动机

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
typedef long long LL;
using namespace std;
const int maxn=1e6+7;
int ch[maxn][26],w[maxn],fail[maxn],tot,rt,n,ans;
char a[maxn];

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

void insert() {
    int now=rt;
    for(int i=0;a[i]!='\0';i++) {
        int c=a[i]-'a';
        if(!ch[now][c]) ch[now][c]=++tot;
        now=ch[now][c];
    }
    w[now]++;
}

queue<int>que;
void get_fail() {
    que.push(rt);
    while(!que.empty()) {
        int x=que.front();
        que.pop();
        for(int i=0;i<26;i++) if(ch[x][i]){
            int y=ch[x][i];
            if(x==rt) fail[y]=rt;
            else {
                int tp=fail[x];
                while(fail[tp]&&!ch[tp][i]) tp=fail[tp];
                if(ch[tp][i]) fail[y]=ch[tp][i]; else fail[y]=rt;
            }    
            que.push(y); 
        }
    }  
}

void qry() {
    int now=rt;
    for(int i=0;a[i]!='\0';i++) {
        int c=a[i]-'a';
        while(!ch[now][c]&&fail[now]) now=fail[now];
        if(ch[now][c]) {
            now=ch[now][c];
            ans+=w[now];
            w[now]=0;
            int tp=fail[now];
            while(tp&&w[tp]) {
                ans+=w[tp];
                w[tp]=0;
                tp=fail[tp];
            }
        }
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    read(n);
    for(int i=1;i<=n;i++) {
        scanf("%s",a);
        insert();
    }
    get_fail();
    scanf("%s",a);
    qry();
    printf("%d\n",ans);    
    return 0;
}

 

 21.lucas定理

//Twenty
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<vector>
#include<cmath>
#include<ctime>
#include<queue>
const int maxn=1e5+7;
typedef long long LL;
using namespace std;
int T,p;
LL n,m,power[maxn]; 

template<typename T> void read(T &x) {
    char ch=getchar(); T f=1; x=0;
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') f=-1,ch=getchar();
    for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}

LL ksm(LL a,LL b,int p) {
    LL base=a,res=1;
    while(b) {
        if(b&1) (res*=base)%=p;
        (base*=base)%=p; 
        b>>=1;
    }
    return res;
} 

LL cal(LL n,LL m,int p) {
    if(m>n) return 0;
    return power[n]*ksm(power[m]*power[n-m]%p,p-2,p)%p;
} 

LL lucas(LL n,LL m,int p) {
    if(!m) return 1;
    return cal(n%p,m%p,p)*lucas(n/p,m/p,p)%p;
}

void init() {
    read(T);
    while(T--) {
        read(n);
        read(m);
        read(p);    
        power[0]=1;
        for(int i=1;i<=p;i++) power[i]=power[i-1]*i%p;
        printf("%lld\n",lucas(n+m,m,p));
    }
}

int main() {
#ifdef DEBUG
    freopen(".in","r",stdin);
    freopen(".out","w",stdout);
#endif
    init();
    return 0;
}