HDU-6393 Traffic Network in Numazu (lca+rmq+ tree-like array)

This problem is equivalent to combining the two questions:

http://poj.org/problem?id=2763

Http://codeforces.com/gym/101808/problem/K

Test instructions: There are n each point n edge of the weighted graph (equivalent to a tree more than one edge), two operations: Modify the weight of an edge; find the shortest path between two points.

Analysis: Take any one edge out, the remaining n-1 can be combined with LCA to solve the shortest path. When asked, compare the size of the path by removing the Bien Hoa only through the edges of the tree, the minimum is the shortest path of two points.

The tree array differential maintains the distance from the root node, and records the range of maintenance required according to the DFS sequence.

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>using namespacestd;#defineMAXN 100005typedefLong LongLL;structedge{intTo,next,id;} EDGE[MAXN<<1]; intn,a[maxn],head[maxn],dep[maxn<<1],cnt,pos[maxn],dfs_seq[maxn<<1],dfn,f[maxn<<1][ -];intL[MAXN],R[MAXN],DFS_CLOCK,G[MAXN]; LL W[maxn],c[maxn];inlinevoidAddintUintVintID) {edge[cnt].to=v; Edge[cnt].next=Head[u]; Edge[cnt].id=ID; Head[u]=cnt++;} InlineintLowbit (intx) {return(x) & (-x);} voidinit () {memset (head,-1,sizeof(head)); memset (POS,-1,sizeof(POS)); memset (C,0,sizeof(C)); CNT=dfn=0; Dfs_clock=0;} voidDfsintUintDeep ) {DFS_SEQ[DFN]=u,dep[dfn]=deep,pos[u]=dfn++; L[u]=++Dfs_clock;  for(intI=head[u];~i;i=Edge[i].next) {        intv=edge[i].to; if(pos[v]==-1) {G[edge[i].id]=v;//ImportantDFS (v,deep+1); DFS_SEQ[DFN]=u,dep[dfn++]=Deep ; }} R[u]=Dfs_clock;} voidINIT_RMQ (intN) {     for(intI=1; i<=n;++i) f[i][0]=i;  for(intj=1;(1&LT;&LT;J) <=n;++j) for(intI=1; i+ (1&LT;&LT;J)-1<=n;++i) {            if(dep[f[i][j-1]]<dep[f[i+ (1<< (J-1))][j-1]]) f[i][j]=f[i][j-1]; Elsef[i][j]=f[i+ (1<< (J-1))][j-1]; }} inlineintRMQ (intLintR) {    intk=0;  while(1<< (k +1) <=r-l+1) ++K; if(Dep[f[l][k]]<dep[f[r-(1&LT;&LT;K) +1][K]])returnF[l][k]; returnf[r-(1&LT;&LT;K) +1][k];} InlineintLcaintUintv) {    if(Pos[u]>pos[v])returnDFS_SEQ[RMQ (Pos[v],pos[u]); returnDFS_SEQ[RMQ (Pos[u],pos[v]);} InlinevoidUpdateinti,ll x) {     for(; I<=n;i+=lowbit (i)) c[i]+=x;} inline LL sum (inti) {LL s=0;  for(;i>0; I-=lowbit (i)) s+=C[i]; returns;} Inline LL Dist (intUintv) {    returnSUM (L[u]) +sum (L[v])-2*sum (L[LCA (U,V)]);} intMain () {#ifndef Online_judge freopen ("In.txt","R", stdin); Freopen ("OUT.txt","W", stdout); #endif    inti,u,v,k,q,s,t;    LL W; scanf ("%d",&T);  while(t--) {scanf ("%d%d",&n,&q);        Init ();  for(i=1; i<=n-1;++i) {scanf ("%d%d%lld",&u,&v,&W);            Add (u,v,i);            Add (v,u,i); W[i]=W; } DFS (1,0); INIT_RMQ (DFN-1); intx, y;        LL Z; scanf ("%d%d%lld", &x,&y,&z);//section n EdgeW[n] =Z;  for(i=1; i<n;++i)            {update (l[g[i]],w[i]); Update (R[g[i]]+1,-W[i]); }                 while(q--) {scanf ("%d",&k); if(k==0) {scanf ("%d%lld",&u,&W); if(u==N) w[n]=W; Else{update (l[g[u]],w-W[u]); Update (R[g[u]]+1,-w+W[u]); W[u]=W; }            }            Else{scanf ("%d%d",&u,&v); LL ans=Dist (U,V); Ans=min (Ans,dist (u,x) +Dist (v,x)); Ans=min (Ans,dist (u,y) +Dist (v,y)); Ans=min (Ans,dist (u,x) +dist (v,y) +Z); Ans=min (Ans,dist (u,y) +dist (v,x) +Z); printf ("%lld\n", ans); }        }    }    return 0;}

HDU-6393 Traffic Network in Numazu (lca+rmq+ tree-like array)