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  1. /*
  2. * @Author: hungeazy
  3. * @Date:   2025-04-17 17:52:51
  4. * @Last Modified by:   hungeazy
  5. * @Last Modified time: 2025-04-17 17:57:18
  6. */
  7. #include <bits/stdc++.h>
  8. #include <ext/pb_ds/assoc_container.hpp> 
  9. #include <ext/pb_ds/tree_policy.hpp> 
  10. // #pragma GCC optimize("O3")  
  11. // #pragma GCC optimize("unroll-loops")  
  12. // #pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")  
  13. using namespace std;
  14. using namespace __gnu_pbds; 
  15. #define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
  16. #define int long long
  17. #define ll long long 
  18. #define ull unsigned long long
  19. #define sz(x) x.size()
  20. #define sqr(x) (1LL * (x) * (x))
  21. #define all(x) x.begin(), x.end()
  22. #define fill(f,x) memset(f,x,sizeof(f))
  23. #define FOR(i,l,r) for(int i=l;i<=r;i++)
  24. #define FOD(i,r,l) for(int i=r;i>=l;i--)
  25. #define debug(x) cout << #x << " = " << x << '\n'
  26. #define ii pair<int,int>
  27. #define iii pair<int,ii>
  28. #define di pair<ii,ii>
  29. #define vi vector<int>
  30. #define vii vector<ii>
  31. #define mii map<int,int>
  32. #define fi first
  33. #define se second
  34. #define pb push_back
  35. #define MOD 1000000007
  36. #define __lcm(a,b) (1ll * ((a) / __gcd((a), (b))) * (b))
  37. #define YES cout << "YES\n"
  38. #define NO cout << "NO\n"
  39. #define MASK(i) (1LL << (i))
  40. #define c_bit(i) __builtin_popcountll(i)
  41. #define BIT(x,i) ((x) & MASK(i))
  42. #define SET_ON(x,i) ((x) | MASK(i))
  43. #define SET_OFF(x,i) ((x) & ~MASK(i))
  44. #define oo 1e18
  45. #define name "DULICH"
  46. #define endl '\n'
  47. #define time() cerr << endl << "-------------Time:" << 1000.0 * clock() / CLOCKS_PER_SEC << "ms.";
  48. template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
  49. template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
  50. template <class T> using ordered_set = tree <T, null_type, less_equal <T>, rb_tree_tag,tree_order_statistics_node_update>;
  51. const int N = (int)1e6+10;
  52. int n,A,B;
  53. vii g[N];
  54.  
  55. namespace hungeazy {
  56.  
  57. 	int dp[N][3];
  58.  
  59. 	void DFS(int u, int p)
  60. 	{
  61. 		dp[u][0] = 0;
  62. 		dp[u][1] = dp[u][2] = oo;
  63. 		for (auto [v,w] : g[u])
  64. 			if (v != p)
  65. 			{
  66. 				DFS(v,u);
  67. 				//Co 2 nhanh voi u 
  68. 				dp[u][2] = min(dp[u][1]+min(dp[v][0],dp[v][1])+min(w*A,B), // noi toi v
  69. 							   dp[u][2]+min({dp[v][0],dp[v][1],dp[v][2]})+B); // khong noi toi v
  70. 				//Co 1 nhanh voi u
  71. 				dp[u][1] = min(dp[u][0]+min(dp[v][0],dp[v][1])+min(w*A,B), // noi toi v
  72. 							   dp[u][1]+min({dp[v][0],dp[v][1],dp[v][2]})+B); // khong noi toi v
  73. 				//Khong co duong di toi u
  74. 				dp[u][0] += min({dp[v][0],dp[v][1],dp[v][2]})+B;
  75. 			}
  76. 	}
  77.  
  78. 	void solve(void)
  79. 	{
  80. 		if (n == 2) return cout << 2*min(B,A*g[1][0].se), void();
  81. 		DFS(1,-1);
  82. 		cout << min({dp[1][0],dp[1][1],dp[1][2]})+B;
  83. 	}
  84.  
  85. }
  86.  
  87. signed main()
  88. {
  89.     fast;
  90.     if (fopen(name".inp","r"))
  91.     {
  92.     	freopen(name".inp","r",stdin);
  93.     	freopen(name".out","w",stdout);
  94.     }
  95.     cin >> n >> A >> B;
  96.     FOR(i,1,n-1)
  97.     {
  98.     	int u,v,w;
  99.     	cin >> u >> v >> w;
  100.     	g[u].pb({v,w}); g[v].pb({u,w});
  101.     }
  102.     hungeazy::solve();
  103.     time();
  104.     return 0;
  105. }
  106. // ██░ ██  █    ██  ███▄    █   ▄████
  107. //▓██░ ██▒ ██  ▓██▒ ██ ▀█   █  ██▒ ▀█▒
  108. //▒██▀▀██░▓██  ▒██░▓██  ▀█ ██▒▒██░▄▄▄░
  109. //░▓█ ░██ ▓▓█  ░██░▓██▒  ▐▌██▒░▓█  ██▓
  110. //░▓█▒░██▓▒▒█████▓ ▒██░   ▓██░░▒▓███▀▒
  111. // ▒ ░░▒░▒░▒▓▒ ▒ ▒ ░ ▒░   ▒ ▒  ░▒   ▒
  112. // ▒ ░▒░ ░░░▒░ ░ ░ ░ ░░   ░ ▒░  ░   ░
  113. // ░  ░░ ░ ░░░ ░ ░    ░   ░ ░ ░ ░   ░
  114. // ░  ░  ░   ░              ░       ░
Success #stdin #stdout #stderr 0.01s 28600KB
comments (?)
stdin 
Standard input is empty
stdout 
Standard output is empty
stderr 
-------------Time:11.416ms.
https://ideone.com/D9cHgP
language:
C++14 (gcc 8.3)
created:
11 days ago
visibility:
public

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