This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <cmath>
#include <functional>
#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <list>
#include <time.h>
#include <math.h>
#include <random>
#include <deque>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <sstream>
#include <chrono>
#include <cstring>
#include <numeric>
using namespace std;
#define int long long
void maxup(int& a, int b)
{
a = max(a, b);
}
const int N = 200000 + 7;
const int INF = (int)1e18 + 7;
int n;
int par[N];
int parval[N];
vector<pair<int, int>> ginit[N];
vector<int> g[N];
int dp[N][2][2]; // dp[a][taken up][has bb]
void build(int a, int p = 0)
{
vector<int> kids;
for (auto& it : ginit[a])
{
int b = it.first, c = it.second;
if (b == p)
{
continue;
}
build(b, a);
par[b] = a;
parval[b] = c;
kids.push_back(b);
}
g[a] = kids;
}
int get(int a, bool okup, bool okhas)
{
int sol = 0;
maxup(sol, dp[a][0][0]);
if (okup) maxup(sol, dp[a][1][0]);
if (okhas) maxup(sol, dp[a][0][1]);
if (okup && okhas) maxup(sol, dp[a][1][1]);
return sol;
}
int best[5][5][5]; // how many legs and how many downs and how many downs from legs
int newbest[5][5][5]; // how many legs and how many downs and how many downs from legs
void clr()
{
for (int i = 0; i < 3; i++) for (int j = 0; j < 2; j++)for (int k = 0; k < 2; k++) best[i][j][k] = newbest[i][j][k] = -INF;
best[0][0][0] = 0;
}
void swp()
{
for (int i = 0; i < 3; i++) for (int j = 0; j < 2; j++) for (int k = 0; k < 2; k++) best[i][j][k] = newbest[i][j][k], newbest[i][j][k] = -INF;
}
void solve(int a)
{
for (auto& b : g[a])
{
solve(b);
}
clr();
for (auto& b : g[a])
{
for (int leg = 0; leg < 3; leg++)
{
for (int dw = 0; dw < 2; dw++)
{
for (int dwl = 0; dwl < 2; dwl++)
{
for (int l2 = 0; l2 <= 1; l2++)
{
for (int d2 = 0; d2 <= 1; d2++)
{
int val = best[leg][dw][dwl] + get(b, !l2, d2) + l2 * parval[b];
//if (leg == 0 && dw == 0 && dwl == 0 && l2 == 1 && d2 == 0 && val == 50)
//{
// cout << best[leg][dw][dwl] << "\n";
// cout << " : " << val << "\n";
// cout << leg + l2 << " " << dw + d2 * (l2 == 0) << " " << dwl + d2 * (l2 == 1) << "\n";
// exit(0);
//}
if (leg + l2 == 0 && dw + d2 * (l2 == 0) == 0 && dwl + d2 * (l2 == 1) == 0 && val == 10)
{
cout << leg << " " << dw << " " << dwl << "\n";
cout << best[leg][dw][dwl] << "\n";
cout << get(b, !l2, d2) << "\n";
cout << l2 * parval[b] << "\n";
cout << "aici!\n";
exit(0);
}
maxup(newbest[leg + l2][dw + d2 * (l2 == 0)][dwl + d2 * (l2 == 1)], val);
}
}
}
}
}
swp();
}
{
// nu am nimic
maxup(dp[a][0][0], best[0][0][0]);
maxup(dp[a][0][1], best[0][1][0]);
}
{
// am doua picioare
maxup(dp[a][0][1], best[2][0][0]);
maxup(dp[a][0][1], best[2][0][1]);
}
if (par[a])
{
// am un picior
maxup(dp[a][1][0], best[1][0][0] + parval[a]);
maxup(dp[a][1][1], best[1][0][1] + parval[a]);
}
}
signed main()
{
#ifdef ONPC
FILE* stream;
freopen_s(&stream, "input.txt", "r", stdin);
#else
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#endif
cin >> n;
for (int i = 1; i < n; i++)
{
int a, b, c;
cin >> a >> b >> c;
ginit[a].push_back({ b, c });
ginit[b].push_back({ a, c });
}
build(1);
solve(1);
cout << get(1, 1, 1) << "\n";
return 0;
}
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