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OI-codes/BZOJ/1977/1977.cpp

263 lines
5.8 KiB
C++

#include <iostream>
#include <algorithm>
#include <limits>
#include <numeric>
#include <queue>
#include <stack>
#include <tuple>
#include <utility>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e5 + 5,
M = 3e5 + 5;
int n, m, a[N + M];
long long res, ans = std::numeric_limits<long long>::max();
std::tuple<int, int, int> edges[M];
bool vis[M];
class LinkCutTree {
private:
struct node {
size_t lchild, rchild, father;
int max1, max2;
bool reversed;
node()
: lchild(0),
rchild(0),
father(0),
max1(0),
max2(0),
reversed(false) {}
size_t& child(const unsigned& x) {
return !x ? lchild : rchild;
}
} tr[N + M];
void pushup(const size_t& u) {
tr[u].max1 = a[u];
if (tr[u].max1 < tr[tr[u].lchild].max1) {
tr[u].max2 = tr[u].max1;
tr[u].max1 = tr[tr[u].lchild].max1;
} else if (tr[u].max1 > tr[tr[u].lchild].max1) {
tr[u].max2 = std::max(tr[u].max2, tr[tr[u].lchild].max1);
}
if (tr[u].max1 < tr[tr[u].rchild].max1) {
tr[u].max2 = tr[u].max1;
tr[u].max1 = tr[tr[u].rchild].max1;
} else if (tr[u].max1 > tr[tr[u].rchild].max1) {
tr[u].max2 = std::max(tr[u].max2, tr[tr[u].rchild].max1);
}
tr[u].max2 = std::max({tr[u].max2, tr[tr[u].lchild].max2, tr[tr[u].rchild].max2});
}
void pushdown(const size_t& u) {
if (!tr[u].reversed) return;
std::swap(tr[u].lchild, tr[u].rchild);
tr[tr[u].lchild].reversed = !tr[tr[u].lchild].reversed;
tr[tr[u].rchild].reversed = !tr[tr[u].rchild].reversed;
tr[u].reversed = false;
}
bool relation(const size_t& u) {
return u == tr[tr[u].father].lchild ? 0 : 1;
}
bool is_root(const size_t& u) {
return tr[tr[u].father].lchild != u && tr[tr[u].father].rchild != u;
}
void rotate(const size_t& u) {
size_t p = tr[u].father;
bool x = relation(u);
if (!is_root(p)) tr[tr[p].father].child(relation(p)) = u;
tr[u].father = tr[p].father;
if (tr[u].child(x ^ 1)) tr[tr[u].child(x ^ 1)].father = p;
tr[p].child(x) = tr[u].child(x ^ 1);
tr[u].child(x ^ 1) = p;
tr[p].father = u;
pushup(p);
pushup(u);
}
void splay(size_t u) {
std::stack<size_t> st;
size_t cur = u;
st.emplace(cur);
while (!is_root(cur)) {
st.emplace(tr[cur].father);
cur = tr[cur].father;
}
while (!st.empty()) {
pushdown(st.top());
st.pop();
}
while (!is_root(u)) {
if (is_root(tr[u].father)) {
rotate(u);
} else if (relation(u) == relation(tr[u].father)) {
rotate(tr[u].father);
rotate(u);
} else {
rotate(u);
rotate(u);
}
}
}
void access(size_t u) {
for (size_t f = 0; u; u = tr[f = u].father) {
splay(u);
tr[u].rchild = f;
pushup(u);
}
}
void make_root(const size_t& u) {
access(u);
splay(u);
tr[u].reversed = !tr[u].reversed;
}
size_t find_root(size_t u) {
access(u);
splay(u);
while (tr[u].lchild) {
u = tr[u].lchild;
}
return u;
}
void split(const size_t& x, const size_t& y) {
make_root(x);
access(y);
splay(y);
}
public:
bool check(const int& x, const int& y) {
return find_root(x) == find_root(y);
}
std::pair<int, int> query(const int& x, const int& y) {
split(x, y);
return {tr[y].max1, tr[y].max2};
}
void link(const int& x, const int& y) {
make_root(x);
if (find_root(y) != x) {
tr[x].father = y;
}
}
void cut(const int& x, const int& y) {
split(x, y);
if (tr[y].lchild == x) {
tr[y].lchild = tr[x].father = 0;
}
}
} lct;
struct DSU : private std::vector<int> {
DSU(const int& _n)
: std::vector<int>(_n + 1) {
std::iota(begin(), end(), 0);
}
int find(const int& x) {
return x == at(x) ? x : at(x) = find(at(x));
}
bool check(const int& x, const int& y) {
return find(x) == find(y);
}
void merge(int x, int y) {
x = find(x);
y = find(y);
if (x != y) at(x) = y;
}
};
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m;
for (int i = 1; i <= m; ++i) {
int u, v, w;
cin >> u >> v >> w;
edges[i] = {u, v, w};
}
std::sort(edges + 1, edges + m + 1, [](const std::tuple<int, int, int>& a, const std::tuple<int, int, int>& b) {
return std::get<2>(a) < std::get<2>(b);
});
DSU dsu(n);
for (int i = 1; i <= m; i++) {
int u = std::get<0>(edges[i]),
v = std::get<1>(edges[i]),
x = dsu.find(u),
y = dsu.find(v),
w = std::get<2>(edges[i]);
a[n + i] = w;
if (x != y) {
dsu.merge(x, y);
lct.link(u, i + n);
lct.link(i + n, v);
res += w;
vis[i] = true;
}
}
for (int i = 1; i <= m; i++) {
if (vis[i]) continue;
int u, v, w;
std::tie(u, v, w) = edges[i];
auto max = lct.query(u, v);
if (w > max.first) {
ans = std::min(ans, static_cast<long long>(w) - max.first);
} else {
ans = std::min(ans, static_cast<long long>(w) - max.second);
}
}
cout << res + ans << endl;
return 0;
}