Xor && 线性基练习

 #include <cstdio>
 #include <cstring>
 const int Len=;
 const int Maxn=;
 int cnt,Ans,b,x,n;
 inline int Max(int x,int y) {return x>y?x:y;}
 struct Node {int next[];}Tree[Maxn*Len];
 void Insert(int x)
 {
     int Now=; bool k;
     for (int i=Len;i>=;i--)
     {
         k=x&(<<i);
         if (Tree[Now].next[k]==-) Tree[Now].next[k]=++cnt;
         Now=Tree[Now].next[k];
     }
 }
 int Query(int x)
 {
     int Now=,v=; bool k;
     for (int i=Len;i>=;i--)
     {
         k=x&(<<i);
         if (Tree[Now].next[!k]!=-) k=!k;
         v=v|(k<<i);
         Now=Tree[Now].next[k];
     }
     return v;
 }
 int main()
 {
     // freopen("c.in","r",stdin);
     while (scanf("%d",&n)!=EOF)
     {
         Ans=cnt=; memset(Tree,-,sizeof(Tree));
         for (int i=;i<=n;i++)
         {
             scanf("%d",&x);
             Insert(x);
             Ans=Max(Ans,x^Query(x));
         }
         printf("%d\n",Ans);
     }
     return ;
 }

CSU1216

在n个数取两个Xor最大。用0-1Trie.

 #include <cstdio>
 #include <algorithm>
 #define LL long long
 using namespace std;
 LL n,Ans,Base[];
 struct Node{LL a,b;}A[];
 inline bool cmp(Node A,Node B) {return A.b>B.b;}
 
 int main()
 {
     scanf("%lld",&n);
     for (LL i=;i<=n;i++) scanf("%lld%lld",&A[i].a,&A[i].b);
     sort(A+,A+n+,cmp); Ans=;
     for (LL i=;i<=n;i++)
     {
         for (LL j=;j>=;j--)
             if (A[i].a>>j&)
             {
                 if (!Base[j])
                 {
                     Base[j]=A[i].a;
                     break;
                 }
                 A[i].a^=Base[j];
             }
         if (A[i].a) Ans+=A[i].b;
     }
     printf("%lld\n",Ans);
     return ;
 }

BZOJ2460

若子集异或为0，则集合一定不为线性基。从大到小排序，贪心即可。

 #include <cstdio>
 #include <iostream>
 using namespace std;
 #define LL long long
 const LL Maxn=;
 LL a[Maxn],Kase,n,Ans,k,q,Bin[];
 inline void Swap(LL &x,LL &y) {LL t=x;x=y;y=t;}
 inline LL Get(LL Row,LL k)
 {
     if (Row<n)
     {if (k==) return ; else k--;}
     if (k>=Bin[Row]) return -;
     LL Ret=;
     for (int i=;i<=Row;i++)
         if (k&Bin[Row-i]) Ret^=a[i];
     return Ret;
 }
 int main()
 {
     scanf("%I64d",&Kase);
     Bin[]=; for (int i=;i<=;i++) Bin[i]=Bin[i-]<<;
     for (LL kase=;kase<=Kase;kase++)
     {
         printf("Case #%I64d:\n",kase);
         scanf("%I64d",&n);
         for (LL i=;i<=n;i++) scanf("%I64d",&a[i]);
         LL Now=;
         for (LL i=Bin[];i;i>>=)
         {
             LL j=Now+;
             while (!(i&a[j])&&j<=n) j++;
             if (j==n+) continue;
             ++Now; Swap(a[Now],a[j]);
             for (j=;j<=n;j++)
             {
                 if (j==Now) continue;
                 if (a[j]&i) a[j]=a[j]^a[Now];
             }
         }
         scanf("%I64d",&q);
         for (LL i=;i<=q;i++)
         {
             scanf("%I64d",&k);
             printf("%I64d\n",Get(Now,k));
         }
     }
     return ;
 }

HDU3949

求第K大的Xor和，求出线性基，把K转为二进制在Xor就可以了

 #include <cstdio>
 #include <algorithm>
 #define LL long long
 using namespace std;
 const LL Mod=;
 const LL Maxn=;
 struct Node{LL b[Maxn],c;}a[Maxn];
 LL Base[Maxn],cnt,Ans,n,m;
 inline LL Pow(LL x,LL y)
 {
     LL Ret=;
     while (true)
     {
         if (y&) Ret=(Ret*x)%Mod;
         x=(x*x)%Mod; y>>=;
         if (y==) break;
     }
     return Ret;
 }
 inline bool cmp(Node A,Node B) {return A.c<B.c;}
 int main()
 {
     scanf("%lld%lld",&n,&m);
     for (LL i=;i<=n;i++)
         for (LL j=;j<=m;j++) scanf("%lld",&a[i].b[j]);
     for (LL i=;i<=n;i++) scanf("%lld",&a[i].c);
     sort(a+,a+n+,cmp);
     for (LL i=;i<=n;i++)
     {
         bool flag=false;
         for (LL j=;j<=m;j++)
             if (a[i].b[j])
             {
                 if (!Base[j])
                 {
                     Base[j]=i; flag=true;
                     break;
                 }
                 LL t=Mod-(a[i].b[j]*Pow(a[Base[j]].b[j],Mod-))%Mod;
                 for (LL k=j;k<=m;k++)
                     a[i].b[k]=(a[i].b[k]+(t*a[Base[j]].b[k])%Mod)%Mod;
             }
         if (flag) Ans+=a[i].c,cnt++;
     }
     printf("%lld %lld\n",cnt,Ans);
     return ;
 }

BZOJ4004

即求出线性基，然后贪心取即可。

 #include <cstdio>
 #include <cstring>
 #define LL long long
 inline void Get_Int(LL & x)
 {
     char ch=getchar(); x=;
     while (ch<'' || ch>'') ch=getchar();
     while (ch>='' && ch<='') {x=x*+ch-'';ch=getchar();}
 }
 inline void Swap(LL &x,LL &y) {LL t=x;x=y;y=t;}
 inline LL Max(LL x,LL y) {return x>y?x:y;}
 inline LL Min(LL x,LL y) {return x>y?y:x;}
 //==================================================
 const LL Maxn=;
 LL head[Maxn],father[Maxn][],Dep[Maxn],n,m,Bin[],x,u,v,cnt,Sum;
 bool vis[Maxn];
 struct Edge{LL to,next;}edge[Maxn<<];
 struct Base
 {
     LL a[];
     inline void Clr() {memset(a,,sizeof(a));}
     inline void Insert(LL x)
     {
         for (LL i=;i>=;i--)
             if (Bin[i]&x)
             {
                 if (!a[i]) {a[i]=x; return;}
                 x^=a[i];
             }
     }
 };
 Base f[Maxn][],Ans;
 inline void Add(LL u,LL v) {edge[cnt].to=v;edge[cnt].next=head[u];head[u]=cnt++;}
 void Dfs(LL u)
 {
     vis[u]=true;
     for (LL i=head[u];i!=-;i=edge[i].next)
         if (!vis[edge[i].to])
         {
             father[edge[i].to][]=u;
             Dep[edge[i].to]=Dep[u]+;
             Dfs(edge[i].to);
         }
 }
 inline void Init()
 {
     for (LL j=;j<=;j++)
         for (LL i=;i<=n;i++)
         {
             father[i][j]=father[father[i][j-]][j-];
             for (LL k=;k>=;k--) if (f[i][j-].a[k])f[i][j].Insert(f[i][j-].a[k]);
             for (LL k=;k>=;k--) if (f[father[i][j-]][j-].a[k])f[i][j].Insert(f[father[i][j-]][j-].a[k]);
         }
 }
 void Solve(LL u,LL v)
 {
     if (Dep[u]<Dep[v]) Swap(u,v);
     for (LL i=;i>=;i--)
         if (Dep[father[u][i]]>=Dep[v])
         {
             for (LL k=;k>=;k--) if (f[u][i].a[k]) Ans.Insert(f[u][i].a[k]);
             u=father[u][i];
         }
     if (u==v)
     {
         for (LL k=;k>=;k--) if (f[u][].a[k]) Ans.Insert(f[u][].a[k]);
         return;
     }
 
     for (LL i=;i>=;i--)
         if (father[u][i]!=father[v][i])
         {
             for (LL k=;k>=;k--) if (f[u][i].a[k]) Ans.Insert(f[u][i].a[k]);
             for (LL k=;k>=;k--) if (f[v][i].a[k]) Ans.Insert(f[v][i].a[k]);
             u=father[u][i],v=father[v][i];
         }
     for (LL k=;k>=;k--) if (f[u][].a[k])Ans.Insert(f[u][].a[k]);
     for (LL k=;k>=;k--) if (f[v][].a[k])Ans.Insert(f[v][].a[k]);
     for (LL k=;k>=;k--) if (f[father[u][]][].a[k])Ans.Insert(f[father[u][]][].a[k]);
 }
 
 int main()
 {
     Bin[]=; for (LL i=;i<=;i++) Bin[i]=Bin[i-]<<;
     Get_Int(n),Get_Int(m);
     for (LL i=;i<=n;i++)
     {
         Get_Int(x);
         f[i][].Insert(x);
     }
     memset(head,-,sizeof(head));
     for (LL i=;i<n;i++)
     {
         Get_Int(u),Get_Int(v);
         Add(u,v),Add(v,u);
     }
     father[][]=; Dep[]=;
     memset(vis,false,sizeof(vis)); Dfs();
     Init();
     for (LL i=;i<=m;i++)
     {
         Get_Int(u),Get_Int(v);
         Ans.Clr();
         Solve(u,v); Sum=;
         for (LL j=;j>=;j--) Sum=Max(Sum,Sum^Ans.a[j]);
         printf("%lld\n",Sum);
     }
     return ;
 }

BZOJ4568

倍增合并线性基，贪心求最大值即可