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| #include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
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 << 1) + (x << 3) + 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('0' + x % 10);
}
template <class Type>
void chkmax (Type &x, Type k)
{
k > x && (x = k);
}
typedef long long LL;
const int N = 2e5 + 10, M = 4e5 + 10;
bool vis[N];
int n, w[N];
LL d[N];
int idx, hd[N], nxt[M], edg[M], wt[M];
namespace DSU
{
int p[N];
int fa (int x)
{
return p[x] == x ? x : p[x] = fa(p[x]);
}
void init()
{
for (int i = 1; i <= n; i++)
p[i] = i;
}
bool check (int a, int b)
{
return fa(a) ^ fa(b);
}
void merge (int a, int b)
{
p[fa(a)] = fa(b);
}
}
struct Edge
{
int u, v;
LL w;
bool operator < (const Edge &_) const
{
return w < _.w;
}
};
vector <Edge> e;
void add (int a, int b, int c)
{
nxt[++idx] = hd[a];
hd[a] = idx;
edg[idx] = b;
wt[idx] =c;
}
int Size (int x, int fa)
{
if (vis[x])
return 0;
int res = 1;
for (int i = hd[x]; ~i; i = nxt[i])
edg[i] ^ fa && (res += Size(edg[i], x));
return res;
}
int WeightCentre (int x, int fa, int tot, int &wc)
{
if (vis[x])
return 0;
int sum = 1, mx = 0;
for (int i = hd[x]; ~i; i = nxt[i])
if (edg[i] ^ fa)
{
int t = WeightCentre(edg[i], x, tot, wc);
chkmax(mx, t), sum += t;
}
chkmax(mx, tot - sum);
if (mx <= tot / 2)
wc = x;
return sum;
}
void Dist (int x, int fa, LL s, vector <int> &p)
{
if (vis[x])
return;
d[x] = s + w[x];
p.push_back(x);
for (int i = hd[x]; ~i; i = nxt[i])
edg[i] ^ fa && (Dist(edg[i], x, s + wt[i], p), 0);
}
void calc (int x)
{
if (vis[x])
return;
WeightCentre(x, -1, Size(x, 0), x);
vis[x] = true;
vector <int> p;
for (int i = hd[x]; ~i; i = nxt[i])
Dist(edg[i], x, wt[i], p);
d[x] = w[x];
p.push_back(x);
int t = -1;
for (int i : p)
(t == -1 || d[i] < d[t]) && (t = i);
e.push_back((Edge){t, x, d[t] + w[x]});
for (int i : p)
e.push_back((Edge){t, i, d[t] + d[i]});
for (int i = hd[x]; ~i; i = nxt[i])
calc(edg[i]);
}
int main ()
{
read(n);
for (int i = 1; i <= n; i++)
hd[i] = -1;
for (int i = 1; i <= n; i++)
read(w[i]);
for (int i = 1, a, b, c; i < n; i++)
{
read(a), read(b), read(c);
add(a, b, c), add(b, a, c);
}
calc(1);
sort(e.begin(), e.end());
LL res = 0;
DSU::init();
for (Edge i : e)
if (DSU::check(i.u, i.v))
{
res += i.w;
DSU::merge(i.u, i.v);
}
write(res);
return 0;
}
|