#41 Shortest Path (division + linear basis)

Source: Internet
Author: User

Consider how the different or shortest circuits should be asked. So this is a WC problem, and DFS finds all the useful rings in the linear basis again, because the weights of each ring can be taken and not affected by other parts.

Now for a tree, think of him as the original Dfs tree. Each additional edge is added with a ring. After calculating the weights, the problem now becomes the maximum difference or value for a number and a number in the interval of any selection.

The way to compare violence is to build a line tree directly, each time logn*log2v out the interval linear basis. This will take 50 points.

The merging of linear radicals is too slow. Consider whether you can do it offline. Each time a query is taken out of the midpoint of the interval, the suffix prefix linear base around the midpoint is processed, and the linear base is merged on the query. So it became LOGV (LOGN+LOGV).

Half a day to find M and N was reversed.

Sure enough it was noip simulation.

`#include <iostream>#include<cstdio>#include<cmath>#include<cstdlib>#include<cstring>#include<algorithm>#include<cassert>using namespacestd;intRead () {intx=0, f=1;CharC=GetChar ();  while(c<'0'|| C>'9') {if(c=='-') f=-1; c=GetChar ();}  while(c>='0'&&c<='9') x= (x<<1) + (x<<3) + (c^ -), c=GetChar (); returnx*F;}#defineN 300010intn,m,q,p[n],deep[n],value[n],ans[n],t=0;struct Base{    intsize,a[ to]; voidInsintx) { for(RegisterintI= -; ~i;i--)        {            if(!x) Break; if(x& (1<<i))if(!a[i]) {a[i]=x;size++; Break;} Elsex^=A[i]; }    }    Base operator+(Const Base&AMP;B)Const    {        BaseC; if(size>b.size) {c.size=size; for(intI=0;i< to; i++) c.a[i]=A[i]; if(size== to)returnC;  for(RegisterintI= -; ~i;i--) C.ins (B.a[i]); }        Else{c.size=b.size; for(intI=0;i< to; i++) c.a[i]=B.a[i]; if(b.size== to)returnC;  for(RegisterintI= -; ~i;i--) C.ins (A[i]); }        returnC; }}pre[n],suf[n];structdata{intTo,nxt,len;} Edge[n<<1];structdata2{inti,l,r,x;} Q[n],u[n];voidAddedge (intXintYintZ) {t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,p[x]=t;}voidDfsintKint  from){     for(intI=p[k];i;i=edge[i].nxt)if(edge[i].to!= from) {deep[edge[i].to]=deep[k]^Edge[i].len;    DFS (EDGE[I].TO,K); }}intWorkintXBasep) {     for(intI= -; ~i;i--) x=min (x,x^P.a[i]); returnx;}voidSolveintLintRintLowintHigh ) {    if(l>r| | Low>high)return; if(low==High ) {         for(inti=l;i<=r;i++) Ans[q[i].i]=min (q[i].x,q[i].x^Value[low]); return; }    intMid=low+high>>1;  for(inti=mid;i>=low;i--)    {        if(I==mid) pre[i]= (Base){0,{0}}; Elsepre[i]=pre[i+1];    Pre[i].ins (Value[i]); }     for(intI=mid+1; i<=high;i++)    {        if(i==mid+1) suf[i]= (Base){0,{0}}; Elsesuf[i]=suf[i-1];    Suf[i].ins (Value[i]); }    inthead=l-1, tail=r+1;  for(inti=l;i<=r;i++)    if(Q[i].l<=mid&&q[i].r>mid) Ans[q[i].i]=work (q[i].x,pre[q[i].l]+SUF[Q[I].R]); Else if(Q[i].r<=mid) u[++head]=Q[i]; Elseu[--tail]=Q[i];  for(inti=l;i<=r;i++) q[i]=U[i];    Solve (L,head,low,mid); Solve (Tail,r,mid+1, high);}intMain () {#ifndef Online_judge freopen ("c.in","R", stdin); Freopen ("C.out","W", stdout); Const Charll[]="%i64d\n";#else    Const Charll[]="%lld\n";#endifN=read (), M=read (), q=read ();  for(intI=1; i<n;i++)    {        intX=read (), Y=read (), z=read ();    Addedge (x, Y, z), Addedge (y,x,z); } DFS (1,1);  for(intI=1; i<=m;i++)    {        intX=read (), Y=read (), z=read (); Value[i]=deep[x]^deep[y]^Z; }     for(intI=1; i<=q;i++)    {        intS=read (), T=read (), L=read (), r=read (); Q[I].I=i,q[i].x=deep[s]^deep[t],q[i].l=l,q[i].r=R; } Solve (1Q1, M);  for(intI=1; i<=q;i++) printf ("%d\n", Ans[i]); return 0;}`

#41 Shortest Path (division + linear basis)

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