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  1. /*
  2. * @Author: hungeazy
  3. * @Date:   2025-10-21 09:24:36
  4. * @Last Modified by:   hungeazy
  5. * @Last Modified time: 2025-10-21 14:20:05
  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. bool M1;
  16. #define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
  17. #define int long long
  18. #define ll long long 
  19. #define ull unsigned long long
  20. #define sz(x) x.size()
  21. #define sqr(x) (1LL * (x) * (x))
  22. #define all(x) x.begin(), x.end()
  23. #define fill(f,x) memset(f,x,sizeof(f))
  24. #define FOR(i,l,r) for(int i=l;i<=r;i++)
  25. #define FOD(i,r,l) for(int i=r;i>=l;i--)
  26. #define debug(x) cout << #x << " = " << x << '\n'
  27. #define ii pair<int,int>
  28. #define iii pair<int,ii>
  29. #define di pair<ii,ii>
  30. #define vi vector<int>
  31. #define vii vector<ii>
  32. #define mii map<int,int>
  33. #define fi first
  34. #define se second
  35. #define pb push_back
  36. #define MOD 1000000007
  37. #define __lcm(a,b) (1ll * ((a) / __gcd((a), (b))) * (b))
  38. #define YES cout << "YES\n"
  39. #define NO cout << "NO\n"
  40. #define MASK(i) (1LL << (i))
  41. #define c_bit(i) __builtin_popcountll(i)
  42. #define BIT(x,i) ((x) & MASK(i))
  43. #define SET_ON(x,i) ((x) | MASK(i))
  44. #define SET_OFF(x,i) ((x) & ~MASK(i))
  45. #define oo 1e18
  46. #define name ""
  47. #define endl '\n'
  48. #define memory() cerr << abs(&M2-&M1)/1024.0/1024 << " MB" << endl
  49. #define time() cerr << endl << "-------------Time:" << 1000.0 * clock() / CLOCKS_PER_SEC << "ms." << endl
  50. template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
  51. template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
  52. template <class T> using ordered_set = tree <T, null_type, less_equal <T>, rb_tree_tag,tree_order_statistics_node_update>;
  53. const int N = (int)2e5+10;
  54. int n,m;
  55. vii g[N];
  56. array<int,3> edge[N];
  57. map<ii,int> val;
  58.  
  59. namespace sub1 {
  60.  
  61. 	int par[N][20],h[N],lo[N];
  62.  
  63. 	bool approved() {
  64. 		return m == n-1;
  65. 	}
  66.  
  67. 	void DFS(int u, int p)
  68. 	{
  69. 		for (auto [v,w] : g[u])
  70. 			if (v != p)
  71. 			{
  72. 				par[v][0] = u;
  73. 				h[v] = h[u]+1;
  74. 				DFS(v,u);
  75. 			}
  76. 	}
  77.  
  78. 	void init() 
  79. 	{
  80. 		lo[1] = 0;
  81. 		FOR(i,2,N-10) lo[i] = lo[i/2]+1;
  82. 		FOR(j,1,lo[n])
  83. 			FOR(i,1,n) 
  84. 				par[i][j] = par[par[i][j-1]][j-1];
  85. 	}
  86.  
  87. 	int LCA(int x, int y)
  88. 	{
  89. 		if (h[x] < h[y]) swap(x,y);
  90. 		int z = lo[n];
  91. 		FOD(i,z,0)
  92. 			if (h[x]-h[y] >= MASK(i)) x = par[x][i];
  93. 		if (x == y) return x;
  94. 		FOD(i,z,0)
  95. 			if (par[x][i] != par[y][i])
  96. 			{
  97. 				x = par[x][i];
  98. 				y = par[y][i];
  99. 			}
  100. 		return par[x][0];
  101. 	}
  102.  
  103. 	void solve(void)
  104. 	{
  105. 		DFS(1,-1);
  106. 		init();
  107. 		vi vec,vec2;
  108. 		int u = 1, v = n, lca = LCA(u,v);
  109. 		while (u != lca)
  110. 		{
  111. 			vec.pb(u);
  112. 			u = par[u][0];
  113. 		}
  114. 		while (v != lca)
  115. 		{
  116. 			vec2.pb(v);
  117. 			v = par[v][0];
  118. 		}
  119. 		vec2.pb(lca);
  120. 		reverse(all(vec2));
  121. 		for (int x : vec2) vec.pb(x);
  122. 		int pre = 0, ans = 0;
  123. 		FOR(i,0,sz(vec)-2) 
  124. 		{
  125. 			ans += abs(val[{vec[i],vec[i+1]}]-pre);
  126. 			pre = val[{vec[i],vec[i+1]}];
  127. 		}
  128. 		cout << ans;
  129. 	}
  130.  
  131. }
  132.  
  133. namespace sub2 {
  134.  
  135. 	int d[N][11];
  136.  
  137. 	bool approved() {
  138. 		FOR(i,1,m)
  139. 			if (edge[i][2] > 10) return false;
  140. 		return true;
  141. 	}
  142.  
  143. 	void Dijkstra(int p)
  144. 	{
  145. 		FOR(i,1,n) 
  146. 			FOR(j,1,10) d[i][j] = oo;
  147. 		d[p][0] = 0;
  148. 		priority_queue<array<int,3>,vector<array<int,3>>,greater<array<int,3>>> q;
  149. 		q.push({0,p,0});
  150. 		while (!q.empty())
  151. 		{
  152. 			auto [cost,u,W] = q.top();
  153. 			q.pop();
  154. 			if (cost > d[u][W]) continue;
  155. 			for (auto [v,w] : g[u])
  156. 				if (minimize(d[v][w],d[u][W]+abs(w-W)))
  157. 					q.push({d[v][w],v,w});
  158. 		}
  159. 	}
  160.  
  161. 	void solve(void)
  162. 	{
  163. 		Dijkstra(1);
  164. 		int ans = oo;
  165. 		FOR(i,1,10) minimize(ans,d[n][i]);
  166. 		cout << ans;
  167. 	}
  168.  
  169. }
  170.  
  171. namespace sub3 {
  172.  
  173. 	unordered_map<int,int> d;
  174.  
  175. 	bool approved() {
  176. 		FOR(i,1,m)
  177. 			if (edge[i][2] > 10) return false;
  178. 		return true;
  179. 	}
  180.  
  181. 	int convert(int x, int y) {
  182. 		return (x<<31LL)+y;
  183. 	}
  184.  
  185. 	void Dijkstra(int p)
  186. 	{
  187. 		d[convert(p,0)] = 0;
  188. 		priority_queue<array<int,3>,vector<array<int,3>>,greater<array<int,3>>> q;
  189. 		q.push({0,p,0});
  190. 		while (!q.empty())
  191. 		{
  192. 			auto [cost,u,W] = q.top();
  193. 			q.pop();
  194. 			if (u == n) 
  195. 			{
  196. 				cout << cost;
  197. 				return;
  198. 			}
  199. 			if (cost > d[convert(u,W)]) continue;
  200. 			for (auto [v,w] : g[u])
  201. 				if (!d.count(convert(v,w)) or minimize(d[convert(v,w)],d[convert(u,W)]+abs(w-W)))
  202. 				{
  203. 					d[convert(v,w)] = d[convert(u,W)]+abs(w-W);
  204. 					q.push({d[convert(v,w)],v,w});
  205. 				}
  206. 		}
  207. 	}
  208.  
  209. 	void solve(void)
  210. 	{
  211. 		Dijkstra(1);
  212. 	}
  213.  
  214. }
  215.  
  216. namespace sub4 {
  217.  
  218. 	vii G[N];
  219. 	vi adj[N];
  220. 	int d[N];
  221.  
  222. 	void Dijkstra(int p)
  223. 	{
  224. 		FOR(i,0,m) d[i] = oo;
  225. 		d[p] = 0;
  226. 		priority_queue<ii,vii,greater<ii>> q;
  227. 		q.push({0,p});
  228. 		while (!q.empty())
  229. 		{
  230. 			auto [cost,u] = q.top();
  231. 			q.pop();
  232. 			if (cost > d[u]) continue;
  233. 			for (auto [v,w] : G[u])
  234. 				if (minimize(d[v],d[u]+w))
  235. 					q.push({d[v],v});
  236. 		}
  237. 	}
  238.  
  239. 	void solve(void)
  240. 	{
  241. 		FOR(i,1,m)
  242. 		{
  243. 			auto [u,v,w] = edge[i];
  244. 			adj[u].pb(i); adj[v].pb(i);
  245. 		}
  246. 		FOR(i,1,n)
  247. 		{
  248. 			if (sz(adj[i]) <= 1) continue;
  249. 			sort(all(adj[i]),[&](int x, int y) {
  250. 				return edge[x][2] < edge[y][2];
  251. 			});
  252. 			FOR(j,1,sz(adj[i])-1)
  253. 			{
  254. 				int u = adj[i][j-1], v = adj[i][j];
  255. 				int w = abs(edge[u][2]-edge[v][2]);
  256. 				G[u].pb({v,w}); G[v].pb({u,w});
  257. 			}
  258. 		}
  259. 		FOR(i,1,m)
  260. 			if (edge[i][0] == 1 or edge[i][1] == 1)
  261. 				G[0].pb({i,edge[i][2]});
  262. 		Dijkstra(0);
  263. 		int ans = oo;
  264. 		FOR(i,1,m)
  265. 			if (edge[i][0] == n or edge[i][1] == n)
  266. 				minimize(ans,d[i]);
  267. 		cout << ans;
  268. 	}
  269.  
  270. }
  271.  
  272. bool M2;
  273. signed main()
  274. {
  275.     fast;
  276.     if (fopen(name".inp","r"))
  277.     {
  278.     	freopen(name".inp","r",stdin);
  279.     	freopen(name".out","w",stdout);
  280.     }
  281.     cin >> n >> m;
  282.     FOR(i,1,m)
  283.     {
  284.     	int u,v,w;
  285.     	cin >> u >> v >> w;
  286.     	g[u].pb({v,w}); g[v].pb({u,w});
  287.     	edge[i] = {u,v,w};
  288.     	val[{u,v}] = val[{v,u}] = w;
  289.     }
  290.     if (sub1::approved()) return sub1::solve(), time(), memory(), 0;
  291.     if (sub2::approved()) return sub2::solve(), time(), memory(), 0;
  292.     if (sub3::approved()) return sub3::solve(), time(), memory(), 0;
  293.     sub4::solve();
  294.     time();
  295.     memory();
  296.     return 0;
  297. }
  298. // ██░ ██  █    ██  ███▄    █   ▄████
  299. //▓██░ ██▒ ██  ▓██▒ ██ ▀█   █  ██▒ ▀█▒
  300. //▒██▀▀██░▓██  ▒██░▓██  ▀█ ██▒▒██░▄▄▄░
  301. //░▓█ ░██ ▓▓█  ░██░▓██▒  ▐▌██▒░▓█  ██▓
  302. //░▓█▒░██▓▒▒█████▓ ▒██░   ▓██░░▒▓███▀▒
  303. // ▒ ░░▒░▒░▒▓▒ ▒ ▒ ░ ▒░   ▒ ▒  ░▒   ▒
  304. // ▒ ░▒░ ░░░▒░ ░ ░ ░ ░░   ░ ▒░  ░   ░
  305. // ░  ░░ ░ ░░░ ░ ░    ░   ░ ░ ░ ░   ░
  306. // ░  ░  ░   ░              ░       ░
Success #stdin #stdout #stderr 0.01s 24476KB
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-------------Time:9.005ms.
70.1942 MB
https://ideone.com/1kyoh8
language:
C++14 (gcc 8.3)
created:
9 days ago
visibility:
public

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