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| #include <cstdio>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;
typedef pair<int, int> PII;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
flag && (x = ~x + 1);
}
template <class Type>
void write(Type x)
{
x < 0 && (putchar('-'), x = ~x + 1);
x > 9 && (write(x / 10), 0);
putchar(x % 10 + '0');
}
const int N = 210, inf = 1e5;
int n, m;
namespace NetFlow
{
const int M = 2e3 + 10;
int st, ed, d[N], cur[N];
int idx, hd[N], nxt[M], edg[M], wt[M];
bool bfs()
{
for (int i = 1; i <= n; i++)
d[i] = -1;
d[st] = 0;
cur[st] = hd[st];
queue<int> q;
q.push(st);
while (!q.empty())
{
int t = q.front();
q.pop();
for (int i = hd[t]; ~i; i = nxt[i])
if (d[edg[i]] == -1 && wt[i])
{
cur[edg[i]] = hd[edg[i]];
d[edg[i]] = d[t] + 1;
if (edg[i] == ed)
return true;
q.push(edg[i]);
}
}
return false;
}
int exploit(int x, int limit)
{
if (x == ed)
return limit;
int res = 0;
for (int i = cur[x]; ~i && res < limit; i = nxt[i])
{
cur[x] = i;
if (d[edg[i]] == d[x] + 1 && wt[i])
{
int t = exploit(edg[i], min(wt[i], limit - res));
if (!t)
d[edg[i]] = -1;
wt[i] -= t;
wt[i ^ 1] += t;
res += t;
}
}
return res;
}
int dinic()
{
int res = 0, flow;
while (bfs())
while (flow = exploit(st, inf))
res += flow;
for (int i = 0; i <= idx; i += 2)
wt[i] = wt[i + 1] = wt[i] + wt[i + 1] >> 1;
return res;
}
void add(int a, int b, int c)
{
nxt[++idx] = hd[a];
hd[a] = idx;
edg[idx] = b;
wt[idx] = c;
}
void init()
{
idx = -1;
for (int i = 1; i <= n; i++)
hd[i] = -1;
}
}
namespace Tree
{
const int M = 410, K = 10;
bool vis[N];
int ans, lg[N], d[N], fa[N][K], mn[N][K];
int idx, hd[N], nxt[M], edg[M], wt[M];
void add(int a, int b, int c)
{
nxt[++idx] = hd[a];
hd[a] = idx;
edg[idx] = b;
wt[idx] = c;
}
void build(vector<int> &p)
{
if (p.size() == 1)
return;
int s = p.front(), t = p.back();
NetFlow::st = s, NetFlow::ed = t;
int cut = NetFlow::dinic();
ans += cut;
add(s, t, cut), add(t, s, cut);
vector<int> L, R;
for (int i : p)
~NetFlow::d[i] ? L.push_back(i) : R.push_back(i);
build(L), build(R);
}
void dfs(int x)
{
for (int i = hd[x]; ~i; i = nxt[i])
{
if (edg[i] == fa[x][0])
continue;
d[edg[i]] = d[x] + 1;
fa[edg[i]][0] = x;
mn[edg[i]][0] = wt[i];
for (int k = 1; (1 << k) <= d[edg[i]]; k++)
{
fa[edg[i]][k] = fa[fa[edg[i]][k - 1]][k - 1];
mn[edg[i]][k] = min(mn[edg[i]][k - 1], mn[fa[edg[i]][k - 1]][k - 1]);
}
dfs(edg[i]);
}
}
int query(int x, int y)
{
int res = inf;
d[x] < d[y] && (swap(x, y), 0);
while (d[x] > d[y])
{
int k = lg[d[x] - d[y]];
res = min(res, mn[x][k]);
x = fa[x][k];
}
if (x == y)
return res;
for (int k = lg[d[x]]; ~k; k--)
if (fa[x][k] != fa[y][k])
{
res = min(res, min(mn[x][k], mn[y][k]));
x = fa[x][k], y = fa[y][k];
}
return min(res, min(mn[x][0], mn[y][0]));
}
void init()
{
lg[1] = 0;
for (int i = 2; i <= n; i++)
lg[i] = lg[i >> 1] + 1;
vector<int> p;
for (int i = 1; i <= n; i++)
p.push_back(i);
idx = -1;
for (int i = 1; i <= n; i++)
hd[i] = -1;
build(p);
dfs(1);
}
int main()
{
write(ans), puts("");
priority_queue<PII> q;
q.push(make_pair(0, 1));
while (!q.empty())
{
int t = q.top().second;
printf("%d ", t);
q.pop();
vis[t] = true;
for (int i = hd[t]; ~i; i = nxt[i])
!vis[edg[i]] && (q.push(make_pair(wt[i], edg[i])), 0);
}
return 0;
}
}
int main()
{
read(n), read(m);
NetFlow::init();
for (int a, b, c; m; m--)
{
read(a), read(b), read(c);
NetFlow::add(a, b, c);
NetFlow::add(b, a, c);
}
Tree::init();
return Tree::main();
}
|