P4180 "Template" strictly sub-niche into a tree [BJWC2010]

Small C recently learned a lot of the minimum spanning tree algorithm, Prim algorithm, Kurskal algorithm, elimination loop algorithm and so on. Just as small c complacent, small P again to pour small c cold water. Small P said, let small C to find a non-map of the sub-niche into a tree, and this sub-niche into a tree still have to be strict small, that is to say: if the minimum spanning tree selection of the edge set is EM, the strict sub-niche into a tree selected edge set is ES, then need to meet: (Value (e) indicates the weight of the edge e) This little C-blindfolded, he looked for To you, I hope you help him solve the problem.

Input

The first line contains two integers, N and m, representing the number of points and sides of the graph without a direction. Next m lines, 3 x y Z for each line, have an edge between point x and Point y, and the weight of the Edge is Z.

Output

Contains a row, only a number, indicating the strict sub-niche into the tree Benquan and. (Data assurance must exist strictly sub-niche into a tree)

Sample Input5 6 1 2 1 1 3 2 2 4 3 3 5 4 3 4 3 4 5 6

Sample Outputone Hint

There is no self-loop in the data, 50% of data N≤2 M≤3 000; 80% of data N≤50 m≤100 000; 100% of data N≤100 m≤300 000, margin value is non-negative and does not exceed 10^9.

Ask yourself, What is the essence of Kruskal?

Greedy

The Kruskal algorithm has been shown for any u,v

Benquan with edge weights between U and v less than equals U to V not selected

So, not strictly the sub-niche into a tree as long as

Iterate through each of the selected edges (u,v,d), replacing the largest edge between U and V

Now, our mission is to keep the non-strict

Why is it not strict?

Because

Benquan of edge weights between U and v less than equals U to V not selected

#include <cstdio>#include<algorithm>#include<cstring>using namespacestd;#definell Long LongConst intM =100000+5;Const intME = 6e5 +Ten, P = -;Long LongINF =1e14;ll mx[m][p+1], mi[m][p+1];intDep[m], anc[m][p+1], fa[m], tot, h[m]; BOOLBan[me], vis[m];structedge{intV, W, NXT;} g[m<<1];structnode{intu, V, W, id;} G[me];voidAddintUintVintW) {g[++TOT].V =v, g[tot].nxt = H[u], G[TOT].W = W, h[u] =tot;}BOOLCMP (node A, node B) {returnA.W <B.W;}intFindintu) {returnU = = fa[u]? U:fa[u] =find (Fa[u]);}voidDfsintUintFintW) {Vis[u]=1; Dep[u]= Dep[f] +1; anc[u][0] = f, mx[u][0] = W, mi[u][0] = -inf;  for(intp =1; P <= p; p++) {Anc[u][p]= anc[anc[u][p-1]][p-1]; MX[U][P]= Max (mx[u][p-1], mx[anc[u][p-1]][p-1]); MI[U][P]= Max (mi[u][p-1], mi[anc[u][p-1]][p-1]); if(mx[u][p-1] > mx[anc[u][p-1]][p-1]) Mi[u][p]= Max (Mi[u][p], mx[anc[u][p-1]][p-1]); Else if(mx[u][p-1] < mx[anc[u][p-1]][p-1]) Mi[u][p]= Max (Mi[u][p], mx[u][p-1]); }     for(inti = H[u]; I i =g[i].nxt) {        intv =g[i].v; if(v = = f)Continue;    DFS (V, u, G[I].W); }}intGetlca (intUintv) {    if(Dep[u] <Dep[v]) Swap (U, v); intt = Dep[u]-Dep[v];  for(intp =0; T t>>=1, p++)        if(t&1) U =Anc[u][p]; if(U = = v)returnu;  for(intp = p; P >=0; p--)        if(Anc[u][p]! =anc[v][p]) u= Anc[u][p], V =Anc[v][p]; returnanc[u][0];} llGet(intUintVintW) {LL ret= -inf;  for(intp = p; P >=0; p--)        if(Dep[anc[u][p]] >=Dep[v]) {            if(w = = Mx[u][p]) ret =Max (ret, mi[u][p]); ElseRET =Max (ret, mx[u][p]); U=Anc[u][p]; }    returnret;}intMain () {Long LongAns =0, ret =inf; intN, M, U, V, W; scanf ("%d%d", &n,&m);  for(inti =1; I <= m; i++) {scanf ("%d%d%d", &u, &v, &W); G[i]=(node) {u, V, W, i}; } memset (mx[1],0x8f,sizeof(mx[1])); memset (mi[1],0x8f,sizeof(mi[1])); Sort (g+1, g+1+m, CMP);  for(inti =1; I <= N; i++) Fa[i] =i;  for(inti =1; I <= m; i++){        intU = g[i].u, v =g[i].v; if(Find (u) = = Find (v))Continue; Fa[find (u)]=Find (v); Ans+ = 1ll*G[I].W;        Add (U, V, G[I].W), add (V, U, G[I].W); Ban[i]=1; } DFS (1,0,0);  for(inti =1; I <= N; i++)if(!vis[i])return!puts ("Orz");  for(inti =1; I <= m; i++){        if(Ban[i])Continue; intU = g[i].u, v =g[i].v; intLCA =Getlca (U, v); ll S=Get(U, LCA, G[I].W); LL P=Get(V, LCA, G[I].W); RET= Min (ret, 1LL*G[I].W-Max (S, p)); } printf ("%lld\n", ans+ret); }

P4180 "Template" strictly sub-niche into a tree [BJWC2010]