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| #include<cstdio>
#include<algorithm>
using namespace std;
#define re register
#define int long long
const int MAXn = 1e5;
const int MAXm = 3e5;
const int INF = 0x3f3f3f3f3f3f3f3f;
template <class T>
inline void read(T &a) {
register char c;while (c = getchar(), (c < '0' || c > '9') && c != '-');register bool f = c == '-';register T x = f ? 0 : c - '0';while (c = getchar(), c >= '0' && c <= '9') {x = (x << 3) + (x << 1) + (c ^ 48);}a = f ? -x : x;
}
int n, m, root = 1;
int head[MAXn + 10], cntnex, nex[MAXm * 2 + 10], to[MAXm * 2 + 10], wei[MAXm * 2 + 10];
void Insert(int u, int v, int w) {
nex[++cntnex] = head[u];
head[u] = cntnex;
to[cntnex] = v;
wei[cntnex] = w;
}
int fat[MAXn + 10];
int anc(int x) {
return fat[x] = fat[x] == x ? x : anc(fat[x]);
}
void Merge(int x, int y) {
if (anc(x) != anc(y)) {
fat[anc(x)] = y;
}
}
bool SameAnc(int x, int y) {
return anc(x) == anc(y);
}
void Init(int top) {
for (re int i = 1; i <= top; ++i) {
fat[i] = i;
}
}
struct Edge {
int u, v, w;
Edge():u(0), v(0), w(0){}
Edge(int u_, int v_, int w_):u(u_), v(v_), w(w_){}
inline bool operator<(Edge x) {
return this->w < x.w;
}
}edge[MAXm + 10];
bool intree[MAXm + 10];
int Kruskal() {
int ans = 0;
sort(edge + 1, edge + 1 + m);
Init(n);
for (re int i = 1; i <= m; ++i) {
if (!SameAnc(edge[i].u, edge[i].v)) {
ans += edge[i].w;
Merge(edge[i].u, edge[i].v);
intree[i] = 1;
}
}
return ans;
}
void mergemax(int &ansmax, int &anscmx, int max1, int cmx1, int max2, int cmx2) {
if (max1 > max2) {
ansmax = max1;
anscmx = max(max2, cmx1);
} else if (max1 < max2) {
ansmax = max2;
anscmx = max(max1, cmx2);
} else {
ansmax = max1;
anscmx = max(cmx1, cmx2);
}
}
int le[MAXn * 4 + 10], ri[MAXn * 4 + 10], maxx[MAXn * 4 + 10], cmax[MAXn * 4 + 10];
void pushup(int id) {
mergemax(maxx[id], cmax[id], maxx[id << 1], cmax[id << 1], maxx[(id << 1) + 1], cmax[(id << 1) + 1]);
}
void BuildUseArr(int id, int l, int r, int *a) {
le[id] = l;
ri[id] = r;
if (l == r) {
maxx[id] = a[l];
cmax[id] = -INF;
} else {
int mid = (l + r) >> 1;
BuildUseArr(id << 1, l, mid, a);
BuildUseArr((id << 1) + 1, mid + 1, r, a);
pushup(id);
}
}
pair<int, int> Eva(int id, int l, int r) {
if (le[id] >= l && ri[id] <= r) {
return make_pair(maxx[id], cmax[id]);
} else {
int mid = (le[id] + ri[id]) >> 1;
if (l <= mid && r > mid) {
int ansmax, anscmx;
pair<int, int> left, right;
left = Eva(id << 1, l, r);
right = Eva((id << 1) + 1, l, r);
mergemax(ansmax, anscmx, left.first, left.second, right.first, right.second);
return make_pair(ansmax, anscmx);
} else if (l <= mid) {
return Eva(id << 1, l, r);
} else {
return Eva((id << 1) + 1, l, r);
}
}
}
int ndwei[MAXn + 10], idxwei[MAXn + 10];
int fa[MAXn + 10], dep[MAXn + 10], siz[MAXn + 10], hson[MAXn + 10];
void Dfs1(int cur) {
dep[cur] = dep[fa[cur]] + 1;
siz[cur] = 1;
int mx = -INF;
for (re int i = head[cur]; i; i = nex[i]) {
if (!intree[i >> 1]) continue;
if (to[i] == fa[cur]) continue;
fa[to[i]] = cur;
ndwei[to[i]] = wei[i];
Dfs1(to[i]);
siz[cur] += siz[to[i]];
if (siz[to[i]] > mx) {
mx = siz[to[i]];
hson[cur] = to[i];
}
}
}
int cntdfs, nddfs[MAXn + 10], idxdfs[MAXn + 10], top[MAXn + 10];
void Dfs2(int cur) {
nddfs[cur] = ++cntdfs;
idxdfs[cntdfs] = cur;
if (hson[cur]) {
top[hson[cur]] = top[cur];
Dfs2(hson[cur]);
}
for (re int i = head[cur]; i; i = nex[i]) {
if (!intree[i >> 1]) continue;
if (to[i] == hson[cur] || to[i] == fa[cur]) continue;
top[to[i]] = to[i];
Dfs2(to[i]);
}
}
pair<int, int> TreePathEva(int x, int y) {
int ansmax = -INF, anscmx = -INF;
int tmpansmax, tmpanscmx;
pair<int, int> tmp;
while (top[x] != top[y]) {
if (dep[top[x]] > dep[top[y]]) {
swap(x, y);
}
tmp = Eva(1, nddfs[top[y]], nddfs[y]);
mergemax(tmpansmax, tmpanscmx, ansmax, anscmx, tmp.first, tmp.second);
ansmax = tmpansmax;
anscmx = tmpanscmx;
y = fa[top[y]];
}
if (dep[x] > dep[y]) {
swap(x, y);
}
if (x == y) {
return make_pair(ansmax, anscmx);
} else {
tmp = Eva(1, nddfs[x] + 1, nddfs[y]);
mergemax(tmpansmax, tmpanscmx, ansmax, anscmx, tmp.first, tmp.second);
ansmax = tmpansmax;
anscmx = tmpanscmx;
return make_pair(ansmax, anscmx);
}
}
int ans, diff = INF;
signed main() {
cntnex = 1;
read(n), read(m);
int tmp = 0;
for (re int i = 1, u, v, w; i <= m; ++i) {
read(u), read(v), read(w);
if (u == v) {
++tmp;
continue;
}
edge[i - tmp] = Edge(u, v, w);
}
m -= tmp;
ans = Kruskal();
for (re int i = 1; i <= m; ++i) {
Insert(edge[i].u, edge[i].v, edge[i].w);
Insert(edge[i].v, edge[i].u, edge[i].w);
}
Dfs1(root);
Dfs2(root);
for (re int i = 1; i <= n; ++i) {
idxwei[i] = ndwei[idxdfs[i]];
}
BuildUseArr(1, 1, n, idxwei);
for (re int i = 1; i <= m; ++i) {
if (!intree[i]) {
pair<int, int> tmp = TreePathEva(edge[i].u, edge[i].v);
if (tmp.first == edge[i].w) {
diff = min(diff, edge[i].w - tmp.second);
} else {
diff = min(diff, edge[i].w - tmp.first);
}
}
}
printf("%lld\n", ans + diff);
}
|
