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| struct node{
int from, to, next;
ll w;
}edge[maxn<<1], e[N];
int head[maxn], cnt;
inline void add(int u,int v, ll w){
edge[++cnt].w = w;
edge[cnt].to = v;
edge[cnt].next = head[u];
head[u] = cnt;
}
int cmp(node a, node b){
return a.w < b.w;
}
int id[maxn];
inline void init(void){
for(int i = 0; i < maxn;i++) id[i] = i;
cnt = 0;
}
inline int find(int p){
if(p == id[p]) return p;
return id[p] = find(id[p]);
}
inline int funion(int p, int q){
int fp = find(p);
int fq = find(q);
if(fp == fq) return 0;
id[fp] = fq;
return 1;
}
int n, m;
int flag[N];
inline ll krusral(void){
init();
sort(e, e+m, cmp);
ll ans = 0;
for(int i = 0;i < m;i++){
if(funion(e[i].from, e[i].to)){
flag[i] = 1;
add(e[i].from, e[i].to, e[i].w);
add(e[i].to, e[i].from, e[i].w);
ans += e[i].w;
}
}
return ans;
}
ll mx[maxn][20];
ll smx[maxn][20];
int fa[maxn][20];
int deep[maxn];
inline void dfs(int now, int f){
deep[now] = deep[f]+1;
fa[now][0] = f;
for(int i = 1;i <= (int)log2(deep[now]);i++){
fa[now][i] = fa[fa[now][i-1]][i-1];
mx[now][i] = max(mx[now][i-1], mx[fa[now][i-1]][i-1]);
if(mx[now][i-1] == mx[fa[now][i-1]][i-1])
smx[now][i] = max(smx[now][i-1], smx[fa[now][i-1]][i-1]);
else
smx[now][i] = max(min(mx[now][i-1], mx[fa[now][i-1]][i-1]),
max(smx[now][i-1], smx[fa[now][i-1]][i-1]));
}
for(int i = head[now];i;i = edge[i].next){
if(edge[i].to == f) continue;
mx[edge[i].to][0] = edge[i].w;
smx[edge[i].to][0] = -1;
dfs(edge[i].to, now);
}
}
inline ll lca(int u, int v, ll w){
if(u == v) return (ll)1e9;
ll ans1 = 0, ans2 = 0;
if(deep[u] < deep[v]) swap(u, v);
while(deep[u] > deep[v]){
int mid = (int)log2(deep[u] - deep[v]);
if(mx[u][mid] == ans1){
ans2 = max(ans2, smx[u][mid]);
}else{
ans2 = max(min(ans1, mx[u][mid]),
max(ans2, smx[u][mid]));
}
ans1 = max(ans1, mx[u][mid]);
u = fa[u][mid];
}
if(u == v) return ((w - ans1) == 0) ? (w - ans2) : (w-ans1);
for(int i = (int)log2(deep[u]);i >= 0;i--){
if(fa[u][i] != fa[v][i]){
if(mx[u][i] == ans1)
ans2 = max(ans2, smx[u][i]);
else{
ans2 = max(min(ans1, mx[u][i]),
max(ans2, smx[u][i]));
}
ans1 = max(ans1, mx[u][i]);
if(mx[v][i] == ans1)
ans2 = max(ans2, smx[v][i]);
else{
ans2 = max(min(ans1, mx[v][i]),
max(ans2, smx[v][i]));
}
ans1 = max(ans1, mx[v][i]);
u = fa[u][i];
v = fa[v][i];
}
}
int i = 0;
if(mx[u][i] == ans1)
ans2 = max(ans2, smx[u][i]);
else{
ans2 = max(min(ans1, mx[u][i]),
max(ans2, smx[u][i]));
}
ans1 = max(ans1, mx[u][i]);
if(mx[v][i] == ans1)
ans2 = max(ans2, smx[v][i]);
else{
ans2 = max(min(ans1, mx[v][i]),
max(ans2, smx[v][i]));
}
ans1 = max(ans1, mx[v][i]);
return ((w - ans1) == 0) ? (w - ans2) : (w-ans1);
}
inline void solve(void){
read(n, m);
for(int i = 0;i < m;i++){
read(e[i].from, e[i].to, e[i].w);
}
ll temp = krusral();
dfs(1, 0);
ll ans = 1e9;
for(int i = 0;i < m;i++){
if(!flag[i]){
ll mid = lca(e[i].from, e[i].to, e[i].w);
ans = min(ans, mid);
}
}
write('\n', temp + ans);
}
signed main(void){
#ifdef _DEBUG
freopen("in.in","r",stdin);
freopen("out.out","w",stdout);
#endif
int t = 1;
while(t--){
solve();
}
return 0;
}
|
