ACM&&OI模板

各种算法的模板整理

蒟蒻的模板 可能不是很好

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基础类

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• 快速排序【2018.3.10】

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const int M=1e6+10;
namespace QSort{
   int size;
template <class T>
  void swap(T &a,T &b){T t=a;a=b;b=t;}
template <class T>
  void Qsort(T a,T b,T *c)
   {
        if(a==b) return;
        T mid=(a+b)/2;
        T val=c[mid];
        T i=a-1,j=b+1;
        while(1)
        {
            do i++;while(c[i]<val);
            do j--;while(c[j]>val);
            if(i>=j) break;
            swap(c[i],c[j]);
        }
        Qsort(a,j,c);
        Qsort(j+1,b,c);
   }
}
using namespace QSort;
int x[M];
void init(){
   scanf("%d",&size);
   for(int i=1;i<=size;i++)scanf("%d",&x[i]);
}
void out(){
   Qsort(1,size,x);
   for(int i=1;i<=size;i++)printf("%d ",x[i]);
}
int main(){
    init();
    out();
    return 0;
}

---

• 归并排序 【2018.3.10】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e6+10;
namespace GSort{
    int size;
template <class T>
  void Gsort(T a,T b,T *c,T *d)
  {
     if(a==b) return;
     T mid=(a+b)/2;
     Gsort(a,mid,c,d);
     Gsort(mid+1,b,c,d);
     int f=a,f1=a,f2=mid+1;
     while(f1<=mid&&f2<=b){
        if(d[f1]<d[f2])c[f++]=d[f1++];
        else           c[f++]=d[f2++];
     }
     for(T i=f1;i<=mid;i++)c[f++]=d[i];
     for(T i=f2;i<=b;i++)  c[f++]=d[i];
     for(T i=a;i<=b;i++)   d[i]  =c[i];
  }
}
using namespace GSort;
int td[M],x[M];
void init(){
   scanf("%d",&size);
   for(int i=1;i<=size;i++)scanf("%d",&x[i]);
}
void out(){
   Gsort(1,size,td,x);
   for(int i=1;i<=size;i++)printf("%d ",x[i]);
}
int main(){
    init();
    out();
    return 0;
}

---

图论

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• 最小生成树-Kruskal【2018.3.12】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=2e5+10,N=5010;
int n,m;
struct ss{
    int from,to,val;
    ss(int a=0,int b=0,int c=0):from(a),to(b),val(c){}
    bool operator <(ss a)const{return val<a.val;}
}g[M];
struct ufs{
    int f[N];
    int find(int a){return f[a]==a?a:f[a]=find(f[a]);}
    void init(){for(int i=1;i<=n;i++)f[i]=i;}
    void uni(int a,int b){f[a]=b;}
}uf;
void readin(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++) scanf("%d%d%d",&g[i].from,&g[i].to,&g[i].val);
}
int Kruskal(){
    sort(g+1,g+m+1);
    uf.init();
    int tot=0,ans=0;
    for(int i=1;i<=m;i++){
        int a=uf.find(g[i].from),b=uf.find(g[i].to);
        if(a==b) continue;
        uf.uni(a,b);
        tot++;ans+=g[i].val;
        if(tot==n-1) break;
    }
    return ans;
}
int main()
{
    readin();
    printf("%d\n",Kruskal());
    return 0;
}

Before 风格

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e5+10;
struct ss{
    int from,to,cap;
    bool operator <(ss a)const{return cap<a.cap;}
}g[M<<1];
int f[M];
int n,m;
int find(int a){return f[a]==a?a:f[a]=find(f[a]);}
void init(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++) f[i]=i;
}
int main()
{
    init();
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&g[i].from,&g[i].to,&g[i].cap);
    }
    sort(g+1,g+m+1);
    int tot=0,ans=0;
    for(int i=1;i<=m;i++){
        int f1=find(g[i].from),f2=find(g[i].to);
        if(f1==f2) continue;
        f[f1]=f2;
        ans+=g[i].cap;tot++;
        if(tot==n-1) break;
    }
    printf("%d\n",ans);
    return 0;
}

---

• 最大流-Dinic 【2018.3.13】
  
  • 前向星存图(链表)

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=1e5+10;
int n,m,s,t;
struct ss{
    int to,last,cap;
    ss(int a=0,int b=0,int c=0):to(a),last(b),cap(c){}
}g[M<<1];
int head[M],cnt=1;
void add(int a,int b,int c){
    g[++cnt]=ss(b,head[a],c);head[a]=cnt;
    g[++cnt]=ss(a,head[b],0);head[b]=cnt;
}
int dep[M],cur[M],que[M],p,q;
int bfs(){
    memset(dep,0,sizeof(dep));
    dep[s]=1;que[p=q=1]=s;
    for(;p<=q;p++){
        int now=que[p];
        for(int i=head[now];i;i=g[i].last){
            if(!dep[g[i].to]&&g[i].cap>0){
                dep[g[i].to]=dep[now]+1;
                que[++q]=g[i].to;
            }
        }
    }
    return dep[t];
}
int dfs(int a,int cap){
    if(a==t||cap<0) return cap;
    int tot=0;
    if(!cur[a]) cur[a]=head[a];
    for(int &i=cur[a];i;i=g[i].last){
        if(g[i].cap>0&&dep[g[i].to]==dep[a]+1){
            int now=dfs(g[i].to,min(g[i].cap,cap));
            tot+=now;cap-=now;
            g[i].cap-=now;g[i^1].cap+=now;
            if(cap<=0) break;
        }
    }
    return tot;
}
const int inf=0x7fffffff;
int maxflow(){
    int ans=0;
    while(bfs()){
        memset(cur,0,sizeof(cur));
        ans+=dfs(s,inf);
    }
    return ans;
}
int a,b,c;
void readin(){
    scanf("%d%d%d%d",&n,&m,&s,&t);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&a,&b,&c);
        add(a,b,c);
    }
}
int main()
{
    readin();
    printf("%d\n",maxflow());
    return 0;
}

• 邻接表存图(vector)

#include<cstdio>
#include<cstring>
#include<iostream>
#include<vector>
using namespace std;
const int M=6e5+10,N=1010,inf=0x7fffffff;
int cal[N],que[N],p,q,dep[N],cnt=1;
int n,m,st,en,ans;
struct ss{
    int to,cap;
    ss(int a=0,int b=0):to(a),cap(b){}
}g[M];
vector <int> vec[N];
void add(int a,int b,int c){
    g[++cnt]=ss(b,c);vec[a].push_back(cnt);
    g[++cnt]=ss(a,0);vec[b].push_back(cnt);
}
int bfs(){
    memset(dep,0,sizeof(dep));
    dep[st]=1;que[p=q=1]=st;
    for(;p<=q;p++){
        int now=que[p];
        for(int i=0;i<(int)vec[now].size();i++){
            int t=vec[now][i];
            if(!dep[g[t].to]&&g[t].cap){
                dep[g[t].to]=dep[now]+1;
                que[++q]=g[t].to;
            }
        }
    }
    return dep[en];
}
int dfs(int a,int cap){
    if(a==en||!cap) return cap;
    int tot=0;
    for(int &i=cal[a];i<vec[a].size();i++){
        int t=vec[a][i];
        if(dep[g[t].to]==dep[a]+1&&g[t].cap){
            int now=dfs(g[t].to,min(cap,g[t].cap));
            g[t].cap-=now;g[t^1].cap+=now;
            tot+=now;
            cap-=now;
            if(!cap) break;
        }
    }
    return tot;
}
int a,b,c;
int read(){
    int x=0;char ch=0;
    while(ch<'0'||ch>'9') ch=getchar();
    while(ch>='0'&&ch<='9') {
        x=(x<<3)+(x<<1)+ch-'0';ch=getchar();
    }
    return x;
}
int main()
{
    scanf("%d%d%d%d",&n,&m,&st,&en);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&a,&b,&c);
        add(a,b,c);
    }
    while(bfs()){
        memset(cal,0,sizeof(cal));
        int now;
        while(now=dfs(st,inf)) ans+=now;
    }
    printf("%d\n",ans);
    return 0;
}

---

• 并查集【2018.3.15】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=2e5+10;
namespace BCJ{
template <class T>
    struct bcj{
        T f[M];
        T find(T a){return f[a]==a?a:f[a]=find(f[a]);}
        T operator [](T a){return find(a);}
        void clear(){memset(f,0,sizeof(f));}
        void init(T a){for(T i=0;i<=a;i++)f[i]=i;}
    };
    void merge(bcj <int> &a,int t1,int t2){
        int f1=a[t1],f2=a[t2];
        if(f1==f2) return;
        a.f[f1]=f2;
    }
}
using namespace BCJ;
bcj <int> f;
int n,m,a,b,c;
int main()
{
    scanf("%d%d",&n,&m);
    f.init(n);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&a,&b,&c);
        switch(a){
            case 1:{
                merge(f,b,c);
                break;
            }
            case 2:{
                if(f[b]==f[c]) printf("Y\n");
                else printf("N\n");
                break;
            }
        }
    }
    return 0;
}

• 并查集【以前的风格】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=2e5+10;
int n,m;
int f[M];
int find(int a){return f[a]==a?a:f[a]=find(f[a]);}
void init(){for(int i=1;i<=n;i++)f[i]=i;}
int cao,a,b;
int main(){
    scanf("%d%d",&n,&m);
    init();
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&cao,&a,&b);
        int p1=find(a),p2=find(b);
        if(cao==2){
            if(p1==p2) printf("Y\n");
            else printf("N\n");
        }else{
            f[p1]=p2;
        }
    }
    return 0;
}

---

• LCA【2018.3.19】

• Tarjan离线算法

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=5e5+10;
struct ss{
    int to,last;
    ss(int a=0,int b=0):to(a),last(b){}
}g[M<<1];
struct que{
    int to,last,lca;
    que(int a=0,int b=0,int c=0):to(a),last(b),lca(c){}
}q[M<<1];
int headg[M],headq[M],n,m,root,a,b;
int cnt,tot=1;
int f[M];
int find(int a){return f[a]==a?a:f[a]=find(f[a]);}
void add1(int a,int b){
    g[++cnt]=ss(b,headg[a]);headg[a]=cnt;
    g[++cnt]=ss(a,headg[b]);headg[b]=cnt;
}
void add2(int a,int b){
    q[++tot]=que(b,headq[a]);headq[a]=tot;
    q[++tot]=que(a,headq[b]);headq[b]=tot;
}
bool vis[M];
void dfs(int a){
    f[a]=a;vis[f[a]]=1;
    for(int i=headg[a];i;i=g[i].last){
        if(vis[g[i].to]) continue;
        dfs(g[i].to);f[g[i].to]=a;
    }
    for(int i=headq[a];i;i=q[i].last){
        if(vis[q[i].to]){
            q[i^1].lca=q[i].lca=find(q[i].to);
        }
    }
}
int main()
{
    scanf("%d%d%d",&n,&m,&root);
    for(int i=1;i<n;i++){
        scanf("%d%d",&a,&b);
        add1(a,b);
    }
    for(int i=1;i<=m;i++){
        scanf("%d%d",&a,&b);
        add2(a,b);
    }
    dfs(root);
    for(int i=1;i<=m;i++)printf("%d\n",q[i<<1].lca);
    return 0;
}

• 倍增的在线算法

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=5e5+10;
int n,m,root;
int f[M][22];
struct ss{
    int to,last;
    ss(int a=0,int b=0):to(a),last(b){}
}g[M<<1];
int head[M],cnt;
void add(int a,int b){
    g[++cnt]=ss(b,head[a]);head[a]=cnt;
    g[++cnt]=ss(a,head[b]);head[b]=cnt;
}
int dep[M];
void dfs(int a,int fa,int dp){
    dep[a]=dp;
    f[a][0]=fa;
    for(int i=1;i<=21;i++){f[a][i]=f[f[a][i-1]][i-1];}
    for(int i=head[a];i;i=g[i].last){
        if(g[i].to==fa) continue;
        dfs(g[i].to,a,dp+1);
    }
}
void swap(int &a,int &b){a^=b^=a^=b;}
int lca(int a,int b){
    if(dep[a]<dep[b]) swap(a,b);
    for(int i=21;i>=0;i--){
        if(dep[f[a][i]]>=dep[b]){
            a=f[a][i];
        }
    }
    if(a==b) return a;
    for(int i=21;i>=0;i--){
        if(f[a][i]!=f[b][i]){
            a=f[a][i];
            b=f[b][i];
        }
    }
    return f[a][0];
}
int a,b;
int main()
{
    scanf("%d%d%d",&n,&m,&root);
    for(int i=1;i<n;i++){
        scanf("%d%d",&a,&b);
        add(a,b);
    }
    dfs(root,0,1);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&a,&b);
        printf("%d\n",lca(a,b));
    }
    return 0;
}

---

• 最小费用最大流SPFA【2018.3.31】

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=1e5+10;
const int inf=0x7fffffff;
int n,m,s,t;

struct ss{
    int to,last,cap,cost;
    ss(int a=0,int b=0,int c=0,int d=0):to(a),last(b),cap(c),cost(d){}
}g[M<<1];
int head[M],cnt=1;
void add(int a,int b,int c,int d){
    g[++cnt]=ss(b,head[a],c,d);head[a]=cnt;
    g[++cnt]=ss(a,head[b],0,-d);head[b]=cnt;
}
int dis[M],que[M],p,q,flow[M],from[M],pos[M];
bool used[M];
bool bfs(){
    for(int i=1;i<=n;i++){
        used[i]=flow[i]=from[i]=0;
        dis[i]=inf;
    }
    used[s]=1;flow[s]=inf;dis[s]=0;
    que[p=q=1]=s;
    for(;p<=q;p++){
        int now=que[p];
        used[now]=0;
        for(int i=head[now];i;i=g[i].last){
            if(dis[g[i].to]>dis[now]+g[i].cost&&g[i].cap>0){
                dis[g[i].to]=dis[now]+g[i].cost;
                from[g[i].to]=now;pos[g[i].to]=i;
                flow[g[i].to]=min(flow[now],g[i].cap);
                if(!used[g[i].to]){
                    used[g[i].to]=1;
                    que[++q]=g[i].to;
                    if(dis[que[(p+1)]]>dis[que[q]])
                    swap(que[(p+1)],que[q]);
                }
            }
        }
    }
    if(dis[t]==inf) return 0;return 1;
}
void work(){
    int mc=0,mf=0;
    while(bfs()){
        mc+=flow[t]*dis[t];
        mf+=flow[t];
        for(int i=t;i;i=from[i]){
            g[pos[i]].cap-=flow[t];
            g[pos[i]^1].cap+=flow[t];
        }
    }
    printf("%d %d\n",mf,mc);
}
int a,b,c,d;
int main()
{
    scanf("%d%d%d%d",&n,&m,&s,&t);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d%d",&a,&b,&c,&d);
        add(a,b,c,d);
    }
    work();
    return 0;
}

---

数据结构

---

• 堆（大根和小根）【2018.3.13】

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=1e6+10;
#define MIN
/*
  MIN 从小到大：小根堆
  MAX 从大到小：大根堆
*/
#include<iostream>
namespace Heap{
template <class T>
struct HEAP{
     T heap[M];int sze;
#ifdef MIN
/*Min*/
    void insert(T a){
        heap[++sze]=a;
        int fa=sze>>1,now=sze;
        while(fa){
            if(heap[fa]>heap[now]) swap(heap[fa],heap[now]);
            now=fa;fa=now>>1;
        }
    }
    void pop(){
        heap[1]=heap[sze];sze--;
        int son=2,now=1;
        while(son<=sze){
            if(son+1<=sze&&heap[son+1]<heap[son]) son++;
            if(heap[now]<heap[son]) break;
            else swap(heap[now],heap[son]);
            now=son,son=now<<1;
        }
    }
#endif

#ifndef MIN
#ifdef MAX
/*Max*/
    void insert(T a){
        heap[++sze]=a;
        int fa=sze>>1,now=sze;
        while(fa){
            if(heap[fa]<heap[now]) swap(heap[fa],heap[now]);
            now=fa;fa=now>>1;
          }
    }
    void pop(){
        heap[1]=heap[sze];sze--;
        int son=2,now=1;
        while(son<=sze){
            if(son+1<=sze&&heap[son+1]>heap[son]) son++;
            if(heap[now]>heap[son]) break;
            else swap(heap[now],heap[son]);
            now=son,son=now<<1;
        }
    }

#endif
#endif
    T top(){return heap[1];}
    void out(T *a,int begin,int end){for(int i=begin;i<=end;i++) a[i]=top(),pop();}
    int size(){return sze;}
    void sort(T *a,int begin,int end){
        for(int i=begin;i<=end;i++){insert(a[i]);}
        out(a,begin,end);
    }
    void clear(){memset(heap,0,sizeof(heap));sze=0;}
};
}
using namespace Heap;
HEAP <int> hp;
/*Luogu P1177排序*/
int n,x[M];
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++){scanf("%d",&x[i]);}
    hp.sort(x,1,n);
    for(int i=1;i<=n;i++) printf("%d ",x[i]);
    return 0;
}
/*Luogu P3378 堆*/
int n,cao,b;
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&cao);
        switch(cao){
            case 1:{
                scanf("%d",&b);
                hp.insert(b);
                break;
            }
            case 2:{
                printf("%d\n",hp.top());
                break;
            }
            case 3:{
                hp.pop();
                break;
            }
        }
    }
    return 0;
}

---

• 树状数组(全)【2018.3.16】

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=5e5+10;
namespace BITTREE{
    int lowbit(int a){return (a&(-a));}
/*普通的树状数组*/
template <class T>
struct bit_tree{
    T f[M];
    int sze;
    int size(){return sze;}
    void add_pos(int p,T a){
        for(int i=p;i<=sze;i+=lowbit(i))f[i]+=a;
    }
    void add_area(int l,int r,T a){
        add_pos(l,a);add_pos(r+1,-a);
    }
    T query_pos(int p){
        T ans=0;
        for(int i=p;i;i-=lowbit(i)) ans+=f[i];
        return ans;
    }
    T query_area(int l,int r){
        T ans=query_pos(r)-query_pos(l-1);
        return ans;
    }
    void clear(){memset(f,0,sizeof(f));}
    bit_tree(int a=1){if(!a)clear();}
    T operator [](int a){return query_pos(a);sze=0;}
};
/*树组树组维护区间最大值*/
template <class T>
struct max_tree{
    T maxv[M],v[M];
    int sze;
    int size(){return sze;}
    T max_area(int l,int r){
        T ans=0;
        while(l<=r){
            ans=max(ans,v[r]);r--;
            for(;r-lowbit(r)>=l;r-=lowbit(r)) ans=max(ans,maxv[r]);
        }
        return ans;
    }
    T change_pos(int p,T a){
        v[p]=a;
        for(int i=p;i<=sze;i+=lowbit(i)){
            maxv[i]=v[i];
            for(int j=1;j<lowbit(i);j<<=1) maxv[i]=max(maxv[i],maxv[i-j]);
        }
    }
    T operator [](int a){return v[a];}
    T operator ()(int a,int b){return max_area(a,b);}
    void init(int p){
        for(int i=p;i<=sze;i+=lowbit(i)) maxv[i]=max(maxv[i],v[p]);
    }
    void clear(){memset(maxv,0,sizeof(maxv));memset(v,0,sizeof(v));sze=0;}
};
/*二维树状数组*/
template <class T>
struct two_bit{
    T f[2000][2000];
    int sze1,sze2;
    void add_pos(int a,int b,T v){
        for(int i=a;i<=sze1;i+=lowbit(i))
        for(int j=b;j<=sze2;j+=lowbit(j))
        f[i][j]+=v;
    }
    T query_pos(int a,int b){
        T ans=0;
        for(int i=a;i;i-=lowbit(i))
        for(int j=b;j;j-=lowbit(j))
        ans+=f[i][j];
        return ans;
    }
    void add_area(int x1,int y1,int x2,int y2){
        add_pos(x1,y1,1);
        add_pos(x1,y2+1,-1);
        add_pos(x2+1,y1,-1);
        add_pos(x2+1,y2+1,1);
    }
    T operator ()(int a,int b){return query_pos(a,b);}
    void clear(){memset(f,0,sizeof(f));sze1=sze2=0;}
};
}
using namespace BITTREE;


/*Luogu P3368*/
//bit_tree <int> tr;
//int m,a,b,c,d;
//int main()
//{
//  scanf("%d%d",&tr.sze,&m);
//  for(int i=1;i<=tr.sze;i++){
//      scanf("%d",&a);
//      tr.add_area(i,i,a);
//  }
//  for(int i=1;i<=m;i++){
//      scanf("%d%d",&a,&b);
//      if(a==1){
//          scanf("%d%d",&c,&d);
//          tr.add_area(b,c,d);
//      }else{
//          printf("%d\n",tr[b]);
//      }
//  }
//  return 0;
//}

/*Luogu P3374*/
//bit_tree <int> tr;
//int m,a,b,c,d;
//int main()
//{
//  scanf("%d%d",&tr.sze,&m);
//  for(int i=1;i<=tr.sze;i++){
//      scanf("%d",&a);
//      tr.add_pos(i,a);
//  }
//  for(int i=1;i<=m;i++){
//      scanf("%d%d%d",&a,&b,&c);
//      if(a==1){
//          tr.add_pos(b,c);
//      }else{
//          printf("%d\n",tr.query_area(b,c));
//      }
//  }
//  return 0;
//}

/*HDU1754*/
//max_tree <int> tr2;
//int n,m,a,b;
//char cao[2];
//int main(){
//  while(scanf("%d%d",&n,&m)==2){
//      tr2.sze=n;
//      for(int i=1;i<=n;i++){
//          scanf("%d",&a);
//          tr2.v[i]=a;
//          tr2.init(i);
//      }
//      for(int i=1;i<=m;i++){
//          scanf("%s%d%d",cao,&a,&b);
//          if(cao[0]=='Q'){
//              printf("%d\n",tr2(a,b));
//          }else{
//              tr2.change_pos(a,b);
//          }
//      }
//      tr2.clear();
//  }
//  return 0;
//}

/*POJ2155*/
//int T,t1,t2,t3,t4,n,m;
//char cao[5];
//two_bit <int> tr;
//int main()
//{
//  scanf("%d",&T);
//  while(T--){
//      tr.clear();
//      scanf("%d%d",&n,&m);
//      tr.sze1=tr.sze2=n;
//      for(int i=1;i<=m;i++){
//          scanf("%s",cao);
//          if(cao[0]=='C'){
//              scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
//              tr.add_area(t1,t2,t3,t4);
//          }else{
//              scanf("%d%d",&t1,&t2);
//              printf("%d\n",tr(t1,t2)&1);
//          }
//      }
//      printf("\n");
//  }
//  return 0;
//}

---

• 线段树1【2018.3.16】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e5+10;
namespace Segment_tree{
template <class T>
   struct segment_tree{
        int sze;
        T sumv[M<<2],v[M],lazy[M<<2];
        void pushup(int o){sumv[o]=sumv[o<<1]+sumv[o<<1|1];}
        void pushdown(int o,int l,int r){
            if(!lazy[o]) return;
            int mid=l+r>>1;
            lazy[o<<1]+=lazy[o];lazy[o<<1|1]+=lazy[o];
            sumv[o<<1]+=lazy[o]*(mid-l+1);
            sumv[o<<1|1]+=lazy[o]*(r-mid);
            lazy[o]=0;
        }
        void build(int o,int l,int r){
            lazy[o]=0;
            if(l==r){sumv[o]=v[l];return;}
            int mid=l+r>>1;
            build(o<<1,l,mid);
            build(o<<1|1,mid+1,r);
            pushup(o);
        }
        void init(){build(1,1,sze);}
        void add_area(int o,int l,int r,int L,int R,T val){
            if(L<=l&&r<=R){
                lazy[o]+=val;sumv[o]+=(r-l+1)*val;
                return;
            }
            pushdown(o,l,r);
            int mid=l+r>>1;
            if(L<=mid) add_area(o<<1,l,mid,L,R,val);
            if(R>mid)  add_area(o<<1|1,mid+1,r,L,R,val);
            pushup(o);
        }
        T query_area(int o,int l,int r,int L,int R){
            if(L<=l&&r<=R){return sumv[o];}
            pushdown(o,l,r);
            int mid=l+r>>1;
            T ans=0;
            if(L<=mid) ans+=query_area(o<<1,l,mid,L,R);
            if(R>mid)  ans+=query_area(o<<1|1,mid+1,r,L,R);
            pushup(o);
            return ans;
        }
        void add_pos(int o,int l,int r,int pos,T val){
            if(l==r){sumv[o]+=val;return;}
            pushdown(o,l,r);
            int mid=l+r>>1;
            if(pos<=mid) add_pos(o<<1,l,mid,pos,val);
            else       add_pos(o<<1|1,mid+1,r,pos,val);
            pushup(o);
        }
        T query_pos(int o,int l,int r,int pos){
            if(l==r){return sumv[o];}
            pushdown(o,l,r);
            int mid=l+r>>1;
            T ans=0;
            if(pos<=mid) ans=query_pos(o<<1,l,mid,pos);
            else     ans=query_pos(o<<1|1,mid+1,r,pos);
            pushup(o);
            return ans;
        }
        void clear(){
            memset(v,0,sizeof(v));
            memset(sumv,0,sizeof(sumv));
        }
        T get_area(int a,int b){return query_area(1,1,sze,a,b);}
        void up_area(int a,int b,T c){add_area(1,1,sze,a,b,c);}
        T get_pos (int a){return query_pos(1,1,sze,a);}
        void up_pos (int a,T b){add_pos(1,1,sze,a,b);}
        T operator ()(int a,int b){return get_area(a,b);}
        T operator ()(int a){return get_pos(a);}
   };
}
#define ll long long
using namespace Segment_tree;
segment_tree <ll> tr;
int m,cao,x,y;
ll k;
/*Luogu P3372*/
int main()
{
    scanf("%d%d",&tr.sze,&m);
    for(int i=1;i<=tr.sze;i++) scanf("%d",&tr.v[i]);
    tr.init();
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&cao,&x,&y);
        if(cao==1){
            scanf("%lld",&k);
            tr.up_area(x,y,k);
        }else{
            printf("%lld\n",tr(x,y));
        }
    }
    return 0;
}

---

• RMQ算法【2018.3.20】

//#include<cstdio>
//#include<cstring>
//#include<algorithm>
//
//using namespace std;
//const int M=1e5+10,Log=17;
//#define MIN
//namespace RMQ{
//#ifdef MIN
//template <class T>
//  T ck(T a,T b){return a<b?a:b;}
//#endif
//#ifndef MIN
//#ifdef MAX
//template <class T>
//  T ck(T a,T b){return a<b?b:a;}
//#endif
//#endif
//template <class T>
//   struct rmq{
//          T rmq[M][Log];
//          int sze;
//          int &size(){return sze;}
//          T &operator [](int a){return rmq[a][0];}
//          void init(){
//              for(int i=1;(1<<i)<=sze;i++){
//                  for(int j=1;j+(1<<i)-1<=sze;j++){
//                      rmq[j][i]=ck(rmq[j][i-1],rmq[j+(1<<(i-1))][i-1]);
//              }
//          }
//      }
//      T query(int l,int r){
//          if(l>r) swap(l,r);
//          int k=0;
//          while(1<<(k+1)<=r-l+1) k++;
//          return ck(rmq[l][k],rmq[r-(1<<k)+1][k]);
//      }
//      T operator ()(int l,int r){return query(l,r);}
//   };
//}
//using namespace RMQ;
//rmq <int> sta;
//int main()
//{
//  scanf("%d",&sta.size());
//  for(int i=1;i<=sta.size();i++){scanf("%d",&sta[i]);}
//  sta.init();
//  int m,l,r;
//  scanf("%d",&m);
//  for(int i=1;i<=m;i++){
//      scanf("%d%d",&l,&r);
//      printf("%d\n",sta(l,r));
//  }
//  return 0;
//}
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e5+10,Log=17;
namespace RMQ{
template <class T>
//class==typename
   struct rmq{
        T rmq[M][Log];
        int sze;
        int &size(){return sze;}
        T &operator [](int a){return rmq[a][0];}
        template <typename Comp>
        void init(Comp ck){
            for(int i=1;(1<<i)<=sze;i++){
                for(int j=1;j+(1<<i)-1<=sze;j++){
                    rmq[j][i]=ck(rmq[j][i-1],rmq[j+(1<<(i-1))][i-1]);
                }
            }
        }
        template <typename Comp>
        T query(int l,int r,Comp ck){
            if(l>r) swap(l,r);
            int k=0;
            while(1<<(k+1)<=r-l+1) k++;
            return ck(rmq[l][k],rmq[r-(1<<k)+1][k]);
        }
        template <typename Comp>
        T operator ()(int l,int r,Comp ck){return query(l,r,ck);}
   };
}
using namespace RMQ;
int mi(int a,int b){return a<b?a:b;}
rmq <int> sta;
int main()
{
    scanf("%d",&sta.size());
    for(int i=1;i<=sta.size();i++){scanf("%d",&sta[i]);}
    sta.init(mi);
    int m,l,r;
    scanf("%d",&m);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&l,&r);
        printf("%d\n",sta(l,r,mi));
    }
    return 0;
}

---

• 树链剖分【2018.3.31】

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;
const int M=1e5+10;
int n,m,root,p;

struct ss{
    int to,last;
    ss(int a=0,int b=0):to(a),last(b){}
}g[M<<1];
int head[M],cnt;
void add(int a,int b){
    g[++cnt]=ss(b,head[a]);head[a]=cnt;
    g[++cnt]=ss(a,head[b]);head[b]=cnt;
}
int dep[M],f[M],son[M],sze[M],num[M],top[M],rf[M],val[M],tim;
void dfs1(int a,int fa,int dp){
    f[a]=fa;dep[a]=dp;sze[a]=1;
    for(int i=head[a];i;i=g[i].last){
        if(g[i].to==fa) continue;
        dfs1(g[i].to,a,dp+1);
        sze[a]+=sze[g[i].to];
        if(!son[a]||sze[g[i].to]>sze[son[a]]) son[a]=g[i].to;
    }
}
void dfs2(int a,int b){
    num[a]=++tim;rf[tim]=a;top[a]=b;
    if(!son[a]) return;
    dfs2(son[a],b);
    for(int i=head[a];i;i=g[i].last){
        if(g[i].to==f[a]||g[i].to==son[a]) continue;
        dfs2(g[i].to,g[i].to);
    }
}

int sumv[M<<2],lazy[M<<2];
void pushup(int o){sumv[o]=(sumv[o<<1]+sumv[o<<1|1])%p;}
int pushdown(int o,int l,int r){
    if(!lazy[o]) return (l+r)>>1;
    lazy[o<<1]+=lazy[o];lazy[o<<1|1]+=lazy[o];
    lazy[o<<1]%=p;lazy[o<<1|1]%=p;
    int mid=l+r>>1;
    sumv[o<<1]+=lazy[o]*(mid-l+1);sumv[o<<1]%=p;
    sumv[o<<1|1]+=lazy[o]*(r-mid);sumv[o<<1|1]%=p;
    lazy[o]=0;
    return mid;
}
void build(int o,int l,int r){
    if(l==r){sumv[o]=val[rf[l]]%p;return;}
    int mid=l+r>>1;
    build(o<<1,l,mid);
    build(o<<1|1,mid+1,r);
    pushup(o);
}
int query(int o,int l,int r,int L,int R){
    if(L<=l&&r<=R) return sumv[o]%p;
    int mid=pushdown(o,l,r),ans=0;
    if(L<=mid) ans=query(o<<1,l,mid,L,R);
    if(R> mid) ans=(ans+query(o<<1|1,mid+1,r,L,R))%p;
    pushup(o);
    return ans;
}
void update(int o,int l,int r,int L,int R,int v){
    if(L<=l&&r<=R){
        sumv[o]=(sumv[o]+v*(r-l+1)%p)%p;
        lazy[o]=(lazy[o]+v)%p;
        return;
    }
    int mid=pushdown(o,l,r);
    if(L<=mid) update(o<<1,l,mid,L,R,v);
    if(R> mid) update(o<<1|1,mid+1,r,L,R,v);
    pushup(o);
}
void add1(int a,int v){update(1,1,tim,num[a],num[a]+sze[a]-1,v);}
int  ask1(int a){return query(1,1,tim,num[a],num[a]+sze[a]-1);}
void add2(int a,int b,int v){
    while(top[a]!=top[b]){
        if(dep[top[a]]<dep[top[b]]) swap(a,b);
        update(1,1,tim,num[top[a]],num[a],v);
        a=f[top[a]];
    }
    if(dep[a]>dep[b]) swap(a,b);
    update(1,1,tim,num[a],num[b],v);
}
int ask2(int a,int b){
    int ans=0;
    while(top[a]!=top[b]){
        if(dep[top[a]]<dep[top[b]]) swap(a,b);
        ans=(ans+query(1,1,tim,num[top[a]],num[a]))%p;
        a=f[top[a]];
    }
    if(dep[a]>dep[b]) swap(a,b);
    return (ans+query(1,1,tim,num[a],num[b]))%p;
}
int cao,a,b,c;
int main()
{
    scanf("%d%d%d%d",&n,&m,&root,&p);
    for(int i=1;i<=n;i++) scanf("%d",&val[i]);
    for(int i=1;i<n;i++){scanf("%d%d",&a,&b);add(a,b);}
    dfs1(root,0,1);dfs2(root,root);
    build(1,1,tim);
    for(int i=1;i<=m;i++){
        scanf("%d",&cao);
        switch(cao){
            case 1:{
                scanf("%d%d%d",&a,&b,&c);c%=p;
                add2(a,b,c);
                break;
            }
            case 2:{
                scanf("%d%d",&a,&b);
                printf("%d\n",ask2(a,b));
                break;
            }
            case 3:{
                scanf("%d%d",&a,&b);b%=p;
                add1(a,b);
                break;
            }
            case 4:{
                scanf("%d",&a);
                printf("%d\n",ask1(a));
                break;
            }
        }
    }
    return 0;
}

---

字符串

---

• 后缀数组【2018.3.16】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e6+500;
int cnt[M],y[M<<1],sa[M<<1],rak[M<<1],A=256;
char str[M<<1];
int main()
{
    scanf("%s",str);
    int len=strlen(str);
    for(int i=0;i<len;i++) cnt[rak[i]=str[i]]++;
    for(int i=1;i<255;i++) cnt[i]+=cnt[i-1];
    for(int i=len-1;i>=0;i--) sa[--cnt[rak[i]]]=i;
    for(int w=1;w<=len;w<<=1){
        memset(cnt,0,sizeof(cnt));int p=0;
        for(int i=len-w;i<len;i++) y[p++]=i;
        for(int i=0;i<len;i++) if(sa[i]>=w) y[p++]=sa[i]-w;
        for(int i=0;i<len;i++) cnt[rak[y[i]]]++;
        for(int i=1;i<A;i++) cnt[i]+=cnt[i-1];
        for(int i=len-1;i>=0;i--) sa[--cnt[rak[y[i]]]]=y[i];
        swap(y,rak);p=1;
        for(int i=0;i<len;i++){
            if(y[sa[i-1]]==y[sa[i]]&&y[sa[i-1]+w]==y[sa[i]+w]) rak[sa[i]]=p-1;
            else rak[sa[i]]=p++;
        }
        if(p>len) break;A=p;
    }
    for(int i=0;i<len;i++){rak[sa[i]]=i;printf("%d ",sa[i]+1);}
    return 0;
}

---

• kmp算法【2018.3.29】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int M=1e6+10;
struct kmp{
    bool flag;
    int fail[M];
    char s1[M],s2[M];
    void getfail(char *str,int *f){
        int len=strlen(str);
        f[0]=f[1]=0;
        for(int i=1;i<=len;i++){
            int j=f[i];
            while(j&&str[i]!=str[j])j=f[j];
            if(str[i]==str[j]) f[i+1]=j+1;
            else f[i+1]=0;
        }
    }
    void find(char *a,char *b,int *f){
        int l1=strlen(a),l2=strlen(b);
        getfail(b,f);int j=0;
        for(int i=0;i<l1;i++){
            while(j&&a[i]!=b[j])j=f[j];
            if(a[i]==b[j])j++;
            if(j==l2){printf("%d\n",i-l2+2);}
        }
        if(flag)for(int i=1;i<=l2;i++){printf("%d ",f[i]);}
    }
    void init(){if(!flag)scanf("%*d%*d");scanf("%s%s",s1,s2);}
    void work(){find(s1,s2,fail);}
}K;

int main()
{
    K.flag=1;
    K.init();
    K.work();
    return 0;
}

---

数论

---

• 卢卡斯定理(求组合数&&阶乘取模)【2018.3.16】

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int M=1e5+10;
ll ny[M],pow[M];//ny为预处理逆元
int n,m,p,T;
ll lucas(int a,int b){
    if(a<b) return 0;
    if(a<p) return pow[a]*ny[b]*ny[a-b]%p;
    return lucas(a/p,b/p)*lucas(a%p,b%p)%p;
}
int main()
{
    scanf("%d",&T);
    while(T--){
        scanf("%d%d%d",&n,&m,&p);
        ny[0]=ny[1]=pow[0]=pow[1]=1ll;
        for(int i=2;i<=n+m;i++) pow[i]=1ll*pow[i-1]*i%p;
        for(int i=2;i<=n+m;i++) ny[i]=1ll*(p-p/i)*ny[p%i]%p;
        for(int i=2;i<=n+m;i++) ny[i]=1ll*ny[i-1]*ny[i]%p;
        printf("%lld\n",lucas(n+m,m));
    }
    return 0;
}

---

• 线性基【2018.3.16】

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int M=60;
ll a,p[M];
void insert(ll a){
    for(int i=55;i>=0;i--){
        if(!((a>>i)&1ll)) continue;
        if(!p[i]){p[i]=a;return;}
        a^=p[i];
    }
}
int n;
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%lld",&a);
        insert(a);
    }
    ll ans=0;
    for(int i=55;i>=0;i--){
        ans=max(ans,ans^p[i]);
    }
    printf("%lld\n",ans);
    return 0;
}

---

• FFT快速傅里叶变换【2018.3.31】

#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>

#define db double
#define com Complex

using namespace std;
int n,m;

const int M=3e6+10;
const db  pi=acos(-1);

struct Complex{
    db x,y;
    com(db a=0,db b=0):x(a),y(b){}
    com operator +(com a){return com(x+a.x,y+a.y);}
    com operator -(com a){return com(x-a.x,y-a.y);}
    com operator /(db  a){return com(x/a  ,y/a  );}
    com operator !(     ){return com(x    ,-y   );}
    com operator *(com a){return com(x*a.x-y*a.y,x*a.y+y*a.x);}
}a[M],b[M];
void swap(com &a,com &b){com t=a;a=b;b=t;}

void FFT(com *a,int tot,int f){
    int mid=tot>>1,i,j,k;
    for(i=1,j=mid;i<tot-1;i++){
        if(i<j) swap(a[i],a[j]);
        for(k=mid;j>=k;j-=k,k>>=1);
        if(j<k) j+=k;
    }
    for(i=2;i<=tot;i<<=1){
        mid=i>>1;
        com wn=com(cos(2*pi/i),f*sin(2*pi/i));
        for(j=0;j<tot;j+=i){
            com w=com(1,0),x,y;
            for(k=j;k<j+mid;k++,w=w*wn){
                x=a[k],y=w*a[k+mid];
                a[k]=x+y;a[k+mid]=x-y;
            }
        }
    }
}

void work(){
    int k=1;for(;k<=n+m;k<<=1);
    FFT(a,k,1);FFT(b,k,1);
    for(int i=0;i<=k;i++) a[i]=a[i]*b[i];
    FFT(a,k,-1);
    for(int i=0;i<=n+m;i++)
    printf("%d ",int(a[i].x/k+0.5));
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=0;i<=n;i++) scanf("%lf",&a[i].x);
    for(int i=0;i<=m;i++) scanf("%lf",&b[i].x);
    work();
    return 0;
}

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计算几何

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模板【2018.3.26】 传送门

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• 旋转卡(qia3)壳(ke2) + 凸包 POJ2079 【2018.3.26】

#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define db double
using namespace std;
const int M=1e5+1;
int n,m;
struct point{
    db x,y;
    point(db a=0,db b=0):x(a),y(b){}
    void in(){scanf("%lf%lf",&x,&y);}
    bool operator <(point a)const{return x<a.x||(x==a.x&&y<a.y);}
}pp[M],ans[M];

point operator -(point a,point b){return point(a.x-b.x,a.y-b.y);}

bool cmp(point a,point b){return (a.y<b.y)||(a.y==b.y&&a.x<b.x);}
db cross(point a,point b){return a.x*b.y-a.y*b.x;}

void convexhull(){
    sort(pp,pp+n);
    m=0;
    for(int i=0;i<n;i++){
        while(m>1&&cross(ans[m-1]-ans[m-2],pp[i]-ans[m-2])<=0) m--;
        ans[m++]=pp[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--){
        while(m>k&&cross(ans[m-1]-ans[m-2],pp[i]-ans[m-2])<=0) m--;
        ans[m++]=pp[i];
    }
    if(n>1)m--;
}

db area(point a,point b,point c){return cross(b-a,c-a);}

db rotcap(){
    db zans=0;
    int p=1,q=2;
    for(int i=0;i<m;i++){
        while(fabs(area(ans[(q+1)%m],ans[i],ans[p]))>fabs(area(ans[q],ans[i],ans[p]))) q=(q+1)%m;
        zans=max(zans,fabs(area(ans[q],ans[i],ans[p])));
        while(fabs(area(ans[(p+1)%m],ans[i],ans[q]))>fabs(area(ans[p],ans[i],ans[q]))) p=(p+1)%m;
        zans=max(zans,fabs(area(ans[p],ans[i],ans[q])));
    }
    return zans/2;
}

int main()
{
    while(scanf("%d",&n)==1&&n>0){
        for(int i=0;i<n;i++) pp[i].in();
        convexhull();
        printf("%.2lf\n",rotcap());
    }
    return 0;
}