topic:
analysis:
Conversion issues: first obtaining a minimum spanning tree
for the non-tree edge, the non-attached side of the tree will be a ring, but can be non-tree edge side of the tree that is the ring max-1
for the side of the tree is it can not be infinitely increased, due to the impact of non-tree edges, and the answer is that it can affect non-tree edges min-1
The first requires only a maximum chain, with a doubling solve
the second: For each non-tree edge, we must update a chain, but you can not write a sectional chain
practices: non-tree edge from small to large sorted, apparently a first side is a small update, will not be big update, so open a ff array
represents a depth shallower than it point to point in that path (without root) has been updated when the non-enumeration tree edge to update when the skip has been updated
to ensure that each edge is updated only once
/ * First find a minimum spanning tree for the non-tree edge, the non-attached side of the tree will be a ring, but can be non-tree edge side of the tree that is the ring max-1 for the side of the tree, the it can not be infinitely increased, due to the impact of non-tree edges, and the answer is min-1 it can affect non-tree edges of the first strand just claim maximum doubling solution with the second: for each non-tree edge, it must update a chain, but you can not write a sectional chain practices: non-tree edge from small to large sorted, apparently a first side updates are small, and it will not be a big update, so open a ff array represents a point shallower than the depth to which that path points (without roots) has been updated when the non-tree edge to enumerate the update has been updated skipped ensures that each edge is updated only once * / #include <bits / STDC ++ H.> the using namespace STD; #define INF 1,000,000,001 #define N 100005 int head [N], W [N << . 1 ], to [N << . 1 ], NEX [N << . 1 ], TOT = 0 , FA [N], ANS [N], ID [N << . 1 ]; int F [N] [30],mx[N][30],dep[N],num[N],s[N],ff[N],fl[N],n,m; struct node{ int u,v,w,o,ans; }e[N]; bool cmp1(const node &a,const node &b) { return a.w<b.w; } bool cmp2(const node &a,const node &b) { return a.o<b.o; } void add(int a,int b,int ww,int i) { to[++tot]=b; nex[tot]=head[a]; w[tot]=ww; id[tot]=i; head[a]=tot; } int find(int x) { IF (FA [X] == X) return X; return FA [X] = Find (FA [X]); } void DFS ( int U) { for ( int I = head [U]; I; I = NEX [I]) { int V = to [I]; IF (V == F [U] [ 0 ]) Continue ; F [V] [ 0 ] = U; DEP [V] DEP = [U] + . 1 ; MX [V] [ 0 ] = W [I]; NUM [V] = ID [I]; // ID upward even record the point corresponding to the discharge side of the good sequence number for ( int J = . 1 ; J <= 20;j++) f[v][j]=f[f[v][j-1]][j-1]; for(int j=1;j<=20;j++) mx[v][j]=max(mx[f[v][j-1]][j-1],mx[v][j-1]); dfs(v); } } int lca(int a,int b) { if(dep[a]>dep[b]) swap(a,b); for(int i=20;i>=0;i--) if(dep[f[b][i]]>=dep[a]) b=f[b][i];//=!! if(a==b) return a; for(int i=20;i>=0;i--) if(f[a][i]!=f[b][i]) a=f[a][i],b=f[b][i]; return f[a][0]; } int lca_max(int a,int b,int lc) { int anss=-1; if(dep[a]>dep[b]) swap(a,b); for(int i=20;i>=0;i--) if(dep[f[b][i]]>=dep[a]) anss=max(anss,mx[b][i]),b=f[b][i];//先更新再跳 一定要有dep>=！！ if(a==b) return anss; for(int i=20;i>=0;i--) if(f[a][i]!=f[b][i]) anss=max(anss,max(mx[a][i],mx[b][i])),a=f[a][i],b=f[b][i]; anss=max(anss,max(mx[a][0],mx[b][0])); return anss; } void work(int u,int lc,int ww) { while(dep[u]>dep[lc]){ if(!s[num[u]] || s[num[u]]>ww) s[num[u]]=ww;//更新最小值 FF [u] = LC; u = f [u] [ 0 ]; // record where u been updated a point u must = fa [u] otherwise it will not move in place the while (FF [u] =! U) = U FF [U]; } } int main () { The freopen ( " tree.in " , " R & lt " , stdin); The freopen ( " tree.out " , " W " , stdout); int A, B , WW; Scanf ( " % D% D " , & n-, & m); for ( int I = . 1 ; I <= m;i++ ) { scanf("%d%d%d",&a,&b,&ww); e[i].u=a,e[i].v=b,e[i].w=ww,e[i].o=i; } sort(e+1,e+1+m,cmp1); for(int i=1;i<=n;i++) fa[i]=i; for(int i=1;i<=m;i++){ int f1=find(e[i].u),f2=find(e[i].v); if(f1==f2) continue; fa[f1]=f2; fl[i]=1; add (e [i] .u, e [i] .v, e [i] .w, i); add (e [i] .v, e [i] .u, e [i] .w, i ); } DEP [ . 1 ] = . 1 ; DFS ( . 1 ); for ( int I = . 1 ; I <= n-; I ++) FF [I] = I; // FF record array update each point where a point initially for its own for ( int I = . 1 ; I <= m; I ++ ) { IF (FL [I]) Continue ; int U = E [I] .u, V = E [I] .v, WW = E [I] .W; int LC LCA = (U, V), Maxx = lca_max (U, V, LC); ANS [I] = maxx- . 1 ; // ANS non-tree edge value stored the while (FF [U] ! = U) FF U = [U]; // jump directly to the position has been updated to the while (FF [V] = V!) V = FF [V] ; Work (u, LC, WW); // process a strand of u to v is updated to the minimum value of the non-tree edges Work (v, LC, WW); } for ( int I = . 1 ; I <= m ; I ++ ) { IF ! (FL [I]) E [I] .ans = ANS [I]; the else E [I] .ans = S [I] - . 1 ; } Sort (E + . 1 , E + . 1 + m , CMP2); for ( int I = . 1 ; I <= m; I ++) the printf ( " % D \ n- " , E [I] .ans); / ** / } /* 4 4 2 1 2 3 2 2 4 3 2 1 4 3 7 8 1 2 2 1 4 3 2 3 6 2 5 8 2 7 5 1 7 9 3 6 7 2 4 4 */