#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2> istream &operator>>(istream &is, const pair<T1, T2> &pa) { is >> pa.first >> pa.second; return is; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << "(" << pa.first << "," << pa.second << ")"; return os; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template <typename T> void resize_array(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args> void resize_array(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) resize_array(v, args...); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
mt19937 mrand(random_device{}());
int rnd(int x) { return mrand() % x; }
template <unsigned int MOD>
class ModInt {
public:
ModInt(unsigned long long _v = 0) { set_v((_v % MOD + MOD)); }
explicit operator bool() const { return val != 0; }
ModInt operator-() const { return ModInt() - *this; }
ModInt operator+(const ModInt &r) const { return ModInt().set_v(val + r.val); }
ModInt operator-(const ModInt &r) const { return ModInt().set_v(val + MOD - r.val); }
ModInt operator*(const ModInt &r) const { return ModInt().set_v((unsigned int)((unsigned long long)(val)*r.val % MOD)); }
ModInt operator/(const ModInt &r) const { return *this * r.inv(); }
ModInt &operator+=(const ModInt &r) { return *this = *this + r; }
ModInt &operator-=(const ModInt &r) { return *this = *this - r; }
ModInt &operator*=(const ModInt &r) { return *this = *this * r; }
ModInt &operator/=(const ModInt &r) { return *this = *this / r; }
// ModInt &operator=(unsigned long long _v) { set_v((_v % MOD + MOD)); return *this; }
unsigned int operator=(unsigned long long _v) { set_v((_v % MOD + MOD)); return val; }
bool operator==(const ModInt &r) const { return val == r.val; }
bool operator!=(const ModInt &r) const { return val != r.val; }
ModInt pow(long long n) const {
ModInt x = *this, r = 1;
while (n) {
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
ModInt inv() const { return pow(MOD - 2); }
unsigned int get_val() { return val; }
friend ostream &operator<<(ostream &os, const ModInt &r) { return os << r.val; }
friend istream &operator>>(istream &is, ModInt &r) { return is >> r.val; }
private:
unsigned int val;
ModInt &set_v(unsigned int _v) {
val = (_v < MOD) ? _v : _v - MOD;
return *this;
}
};
constexpr unsigned int mod = 1e9+7;
using Mint = ModInt<mod>;
#define rep(i, a, n) for (int i = a; i < (n); i++)
#define per(i, a, n) for (int i = (n)-1; i >= a; i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define sz(x) ((int)(x).size())
typedef vector<int> vi;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef double db;
#if DEBUG
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
#else
#define dbg(x)
#endif
using Mint2 = ModInt<mod-1>;
class Solution {
struct Edge {
int u,v;
int cost;
friend ostream &operator<<(ostream &os, const Edge &r) {
return os << r.u << "-->" << r.v << ":" << r.cost;
}
};
struct LCA {
int node;
int son1=-1, son2=-1;
friend ostream &operator<<(ostream &os, const LCA &r) {
return os << r.node << "(" << r.son1 << ", " << r.son2 << ")";
}
};
public:
void Solve() {
int n,m;
// n<=1000, m<=5000
while(cin>>n>>m) {
dbg("===================");
int total_cost = 0;
vi degree(n);
vector<vi> tree_edges(n);
vector<Edge> edges;
int u,v,c;
rep(i,0,m) {
cin>>u>>v>>c;
u--; v--;
degree[u]++; degree[v]++;
if (c == 0) {
tree_edges[u].emplace_back(v);
tree_edges[v].emplace_back(u);
} else {
edges.emplace_back(Edge{u,v,c});
total_cost += c;
}
}
dbg(total_cost);
int max_edge_num = 1;
rep(i,0,n) {
max_edge_num = max(max_edge_num, degree[i]);
}
dbg(max_edge_num);
vector<vi> tree_path_len(n, vi(n));
int root = 0;
function<void(int,int,int)> dfs1 = [&] (int u, int p, int d) {
tree_path_len[root][u] = d;
for (int v : tree_edges[u]) {
if (v != p) dfs1(v, u, d+1);
}
};
// O(n*m)
for (root = 0; root < n; root++) {
dfs1(root, -1, 0);
}
// dbg(tree_path_len);
vector<Edge> even_edges;
for (auto edge : edges) {
if (tree_path_len[edge.u][edge.v] % 2 == 0) {
even_edges.emplace_back(edge);
}
}
dbg(even_edges);
int max_d = 1;
while ((1<<max_d) <= n) {
max_d++;
}
vector<vi> parent(n, vi(max_d));
vi nth_son(n);
function<void(int,int)> dfs2 = [&] (int u, int p) {
// for (int v : tree_edges[u]) {
rep(i,0,sz(tree_edges[u])) {
int v = tree_edges[u][i];
if (v != p) {
parent[v][0] = u;
nth_son[v] = i;
dfs2(v, u);
}
}
};
parent[0][0] = -1;
nth_son[0] = -1;
dfs2(0, -1);
// O(nlogn)
rep(d,1,max_d) {
rep(u, 0, n) {
if (parent[u][d-1] == -1) parent[u][d] = -1;
else parent[u][d] = parent[parent[u][d-1]][d-1];
}
}
dbg(parent);
dbg(nth_son);
auto get_depth = [&] (int idx) {
int depth = 0;
int d = sz(parent[0]) - 1;
while(idx != 0) {
// dbg(mp(idx, d));
if (parent[idx][d] != -1) {
depth |= (1<<d);
idx = parent[idx][d];
}
d--;
}
return depth;
};
// least common ancestor
auto get_lca = [&] (int u, int v) {
int d1 = get_depth(u);
int d2 = get_depth(v);
// dbg(mp(d1,d2));
if (d1 < d2) {
swap(u, v);
}
LCA lca;
int t = abs(d1 - d2);
if (t>0) {
t--;
rep(i,0,sz(parent[0])) {
if (t & (1<<i)) u = parent[u][i];
}
lca.son1 = nth_son[u];
u = parent[u][0];
}
if (u == v) {
lca.node = u;
return lca;
}
int d = sz(parent[0]) - 1;
// dbg(d);
// dbg(mp(u,v))
while(d >= 0) {
// dbg(mp(parent[u][d], parent[v][d]));
if (parent[u][d] != parent[v][d]) {
u = parent[u][d];
v = parent[v][d];
}
// dbg(d);
// dbg(mp(u,v));
d--;
}
lca.son1 = nth_son[u];
lca.son2 = nth_son[v];
lca.node = parent[u][0];
return lca;
};
// O(mlogn)
vector<vi> node_to_even_edges(n);
vector<vector<pii>> node_to_direct_sons(n);
rep(i,0,sz(even_edges)) {
// dbg(mp(even_edges[i].u, even_edges[i].v));
LCA lca = get_lca(even_edges[i].u, even_edges[i].v);
// dbg(lca);
node_to_even_edges[lca.node].emplace_back(i);
node_to_direct_sons[lca.node].emplace_back(mp(lca.son1, lca.son2));
}
// O(m*2^k)
vector<vi> dp(n, vi(1<<max_edge_num, -1));
vector<vi> cache(n, vi(n, -1));
rep(i,0,n) cache[i][i] = 0;
rep(u,0,n) {
for(int v : tree_edges[u]) {
cache[u][v] = cache[v][u] = 0;
}
}
function<int(int,int)> get_most_cost = [&] (int node, int mask) {
// dbg(mp(node, mask));
if (dp[node][mask] != -1) return dp[node][mask];
int cost = 0;
rep(i,0,sz(tree_edges[node])) {
if ((1<<i) & mask) continue;
if (tree_edges[node][i] == parent[node][0]) continue;
cost += get_most_cost(tree_edges[node][i], 0);
}
dp[node][mask] = max(dp[node][mask], cost);
if (node == 0 && mask == 0) {
dbg("+++++++++");
dbg(cost);
}
rep(idx,0,sz(node_to_even_edges[node])) {
int i = node_to_even_edges[node][idx];
if (node_to_direct_sons[node][idx].first != -1
&& (mask & (1<<node_to_direct_sons[node][idx].first))) continue;
if (node_to_direct_sons[node][idx].second != -1
&& (mask & (1<<node_to_direct_sons[node][idx].second))) continue;
cost = even_edges[i].cost;
if (node == 0 && mask == 0) {
dbg("---------");
dbg(cost);
}
int u = even_edges[i].u, v= even_edges[i].v;
if (u != node) cost += get_most_cost(u, 0);
if (node == 0 && mask == 0) dbg(cost);
if (v != node) cost += get_most_cost(v, 0);
if (node == 0 && mask == 0) dbg(cost);
vi nodes, subtree_cost;
while (true) {
if (cache[node][u] != -1) {
if (sz(nodes) > 0) {
cache[node][nodes.back()] = subtree_cost.back() + cache[node][u];
per(i,0,sz(nodes)-1) {
cache[node][nodes[i]] = subtree_cost[i] + cache[node][nodes[i+1]];
}
}
break;
}
int p = parent[u][0];
nodes.emplace_back(u);
subtree_cost.emplace_back(get_most_cost(p, (1<<nth_son[u])));
u = p;
}
cost += cache[node][even_edges[i].u];
if (node == 0 && mask == 0) {
dbg(subtree_cost);
dbg(cost);
}
nodes.clear(), subtree_cost.clear();
while (true) {
if (cache[node][v] != -1) {
if (sz(nodes) > 0) {
cache[node][nodes.back()] = subtree_cost.back() + cache[node][v];
per(i,0,sz(nodes)-1) {
cache[node][nodes[i]] = subtree_cost[i] + cache[node][nodes[i+1]];
}
}
break;
}
int p = parent[v][0];
nodes.emplace_back(v);
subtree_cost.emplace_back(get_most_cost(p, (1<<nth_son[v])));
v = p;
}
cost += cache[node][even_edges[i].v];
if (node == 0 && mask == 0) {
dbg(subtree_cost);
dbg(cost);
}
int mask2 = mask;
if (node_to_direct_sons[node][idx].first != -1)
mask2 |= (1<<node_to_direct_sons[node][idx].first);
if (node_to_direct_sons[node][idx].second != -1)
mask2 |= (1<<node_to_direct_sons[node][idx].second);
if (node == 0 && mask == 0) dbg(mask2);
cost += get_most_cost(node, mask2);
if (node == 0 && mask == 0) dbg(cost);
dp[node][mask] = max(dp[node][mask], cost);
}
// dbg(mp(node, mask));
// dbg(dp[node][mask]);
return dp[node][mask];
};
cout << total_cost - get_most_cost(0, 0) << endl;
}
}
private:
};
// #define USACO 1
void set_io(const string &name = "") {
ios::sync_with_stdio(false);
cin.tie(nullptr);
#if FILE_IO || USACO
if (!name.empty()) {
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
}
#endif
}
int main() {
#if USACO
set_io("time");
#else
set_io("input");
#endif
Solution().Solve();
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
600 KB |
Output is correct |
| 2 |
Correct |
1 ms |
604 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
19 ms |
12636 KB |
Output is correct |
| 2 |
Correct |
22 ms |
12892 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
344 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
1 ms |
856 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
2396 KB |
Output is correct |
| 2 |
Correct |
2 ms |
2396 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
4444 KB |
Output is correct |
| 2 |
Correct |
5 ms |
4456 KB |
Output is correct |
| 3 |
Correct |
13 ms |
4600 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
17 ms |
12636 KB |
Output is correct |
| 2 |
Correct |
23 ms |
12736 KB |
Output is correct |
| 3 |
Correct |
18 ms |
12636 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
11 ms |
4444 KB |
Output is correct |
| 2 |
Correct |
8 ms |
4696 KB |
Output is correct |
| 3 |
Correct |
29 ms |
12636 KB |
Output is correct |
| 4 |
Correct |
5 ms |
4700 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
15 ms |
12760 KB |
Output is correct |
| 2 |
Correct |
31 ms |
12892 KB |
Output is correct |
| 3 |
Correct |
16 ms |
12796 KB |
Output is correct |
| 4 |
Correct |
22 ms |
12832 KB |
Output is correct |
