HDU-6393 Traffic Network in Numazu (tree chain + base ring tree)

http://acm.hdu.edu.cn/showproblem.php?pid=6393

Test instructions

To the N-point and N-side graphs, there are two operations, one to modify the edge, and the other to query the shortest path from u to v.

Analysis

n points and n edges, is actually a tree + a ring, if it is just a tree, then this problem is the tree chain of the template problem is split.

For the ring, it is possible to consider extracting one edge of the ring first, then the tree chain, modified with a segment tree, single-point modification and interval summation.

When querying, consider three cases, you walk the tree to V, from the edge of the extracted from U and then to V (two kinds), take the minimum value.

As for removing the ring on an edge, use and check the set to engage in.

#include <bits/stdc++.h>#defineMem (A, B) memset (A,b,sizeof (a))using namespaceStd;typedefLong Longll;Const intINF =0x3f3f3f3f;Const intMAXN = 2e5+5;structSide {intu,v,w; intNE;} S[MAXN];structEdge {intL,r; ll v;} E[MAXN<<2];intn,q;intHead[maxn],len;intVAL[MAXN],HOLD[MAXN],PRE[MAXN];intDeep[maxn],fa[maxn],ve[maxn],son[maxn],top[maxn],p[maxn],fp[maxn],sz;voidAddintUintVintW) {s[len].u=u; S[LEN].V=v; S[LEN].W=W; S[len].ne=Head[u]; Head[u]= len++;}intFindintx) {returnPRE[X] = = X?x:pre[x] =find (Pre[x]);}voidDFS1 (intUintPintd) {Deep[u]=D; Fa[u]=p; Ve[u]=1; Son[u]= -1;  for(inti = Head[u]; I!=-1; i =s[i].ne) {        if(s[i].v = = p)Continue; VAL[S[I].V]= S[I].W;//assigning edge weights to connected pointsHold[i>>1] = S[I].V;//at which point the weight of the edge is held .DFS1 (s[i].v,u,d+1); Ve[u]+=VE[S[I].V]; if(Son[u] = =-1|| Ve[s[i].v]>Ve[son[u]]) Son[u]=s[i].v; }    return ;}voidDFS2 (intUintsp) {Top[u]=sp; P[u]= ++sz; Fp[p[u]]=u; if(Son[u] = =-1)return ;    DFS2 (SON[U],SP);  for(inti = Head[u]; I!=-1; i =s[i].ne) {        if(s[i].v = = son[u]| | S[I].V = = Fa[u])Continue;    DFS2 (S[I].V,S[I].V); }    return ;}voidBuildintIintLintr) {E[I].L=l; E[I].R=R; if(L = =r) {e[i].v=Val[fp[l]]; return ; }    intMid = (l+r) >>1; Build (I<<1, L,mid); Build (I<<1|1, mid+1, R); E[I].V= e[i<<1].v+e[i<<1|1].v;}voidModifyintIintPosintv) {if(Pos> e[i].r| | pos< E[I].L)return ; if(E[I].L = =E[I].R) {E[I].V=v; return ; } Modify (I<<1, pos,v); Modify (I<<1|1, pos,v); E[I].V= e[i<<1].v+e[i<<1|1].V;} ll query (intIintLintr) {if(e[i].r< l| | E[i].l> R)return 0; if(e[i].l>= l&&e[i].r<= R)returne[i].v; returnQuery (i<<1, L,r) +query (i<<1|1, l,r);} ll demand (intXinty) {intFX =Top[x]; intFY =Top[y]; ll ans=0;  while(fx!=FY) {        if(deep[fx]<Deep[fy])            {swap (FX,FY);        Swap (x, y); } ans+ = Query (1, p[fx],p[x]); X=FA[FX]; FX=Top[x]; }    if(x = = y)returnans; if(deep[x]>Deep[y]) swap (x, y); Ans+ = Query (1, P[son[x]],p[y]); returnans;}voidinit () {sz= Len =0; Mem (Head,-1);  for(inti =0; i<= N; i++) Pre[i] =i;}intMain () {intT; CIN>>T;  while(t--) {        intSu,sv,sc,ss; scanf ("%d%d",&n,&q);        Init ();  for(inti =1; i<= N; i++) {            intu,v,w; scanf (" %d%d%d",&u,&v,&W); intFX =find (U); intFY =Find (v); if(FX = =FY) {Len+=2; SS=i; Su=u; SV=v; SC=W; Continue; } ElsePre[fy]=FX;            Add (U,V,W);        Add (V,U,W); } DFS1 (1,-1,1); DFS2 (1,1); Build (1,1, N);  while(q--) {            intO,x,y; scanf (" %d%d%d",&o,&x,&y); if(O = =0) {x--; if(x = =SS) {SC=y; Continue; } Modify (1, P[hold[x]],y); } Else{ll ans; Ans= Sc+min (Demand (X,SU) +demand (Y,SV), demand (X,SV) +demand (Y,SU)); Ans=min (Ans,demand (x, y)); printf ("%lld\n", ans); }        }    }    return 0;}

HDU-6393 Traffic Network in Numazu (tree chain + base ring tree)