Problem:
Diameter of a Tree

Given a tree T with non-negative weight, find the diameter of the tree.

The diameter of a tree is the maximum distance between two nodes in a tree.

Input

n
s1 t1 w1
s2 t2 w2
:
sn-1 tn-1 wn-1

The first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.

In the following n-1 lines, edges of the tree are given.

si and ti represent end-points of the i-th edge (undirected) and wi represents the weight (distance) of the i-th edge.

Output

Print the diameter of the tree in a line.

Constraints

1 ≤ n ≤ 100,000

0 ≤ wi ≤ 1,000

Sample Input 1

4
0 1 2
1 2 1
1 3 3

Sample Output 1

5

Sample Input 2

4
0 1 1
1 2 2
2 3 4

Sample Output 2

7

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;
using System.Security.Cryptography.X509Certificates;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var G = new Graph(N);
			for(int i = 0; i<N-1; i++) {
				var edge = cin.ReadIntArray(3);
				G.AddEdge(edge[0], edge[1], edge[2]);
				G.AddEdge(edge[1], edge[0], edge[2]);
			}
			var L = G.Dijkstra(0);
			var M = L.Max();
			var farest = Enumerable.Range(0, N).First(i => L[i]==M);
			L=G.Dijkstra(farest);
			Console.WriteLine(L.Max());
		}

	}
	static class ExtendClass {
		public static void Swap<T>(this T[] A, int x, int y) {
			var tmp = A[x];
			A[x]=A[y];
			A[y]=tmp;
		}
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
		public static IEnumerable<int> Indices<T>(this T[] X) => Enumerable.Range(0, X.Length);
		public static IEnumerable<int> Indices<T>(this T[,] X, int dim)
			=> Enumerable.Range(0, X.GetLength(dim));
		//public static IEnumerable<(int i1, int i2)> Indices<T>(this T[,] X)
		//	=> X.Indices(0).SelectMany(i => X.Indices(1).Select((i, j) => (i, j)));
		public static string Join<T>(this T[,] X, string separatorD2 = ",", string separatorD1 = "\n")
			=> X.Indices(0).Select(
				i => X.Indices(1).Select(j => X[i, j]).Join(separatorD2)
			).Join(separatorD1);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}

	class PriorityQueue<T> where T : IComparable<T> {
		protected readonly List<T> body = new List<T>();
		protected Comparer<T> comparer { get; }
		public PriorityQueue(bool maxTop = true) {
			comparer
			=maxTop ? Comparer<T>.Create((T i, T j) => i.CompareTo(j))
			: Comparer<T>.Create((T i, T j) => j.CompareTo(i));
		}
		public PriorityQueue(Comparer<T> mComparer) { comparer=mComparer; }
		//suppose Me>Her if isRootMaximum
		protected int Compare(T Me, T Her) => comparer.Compare(Me, Her);
		protected int Compare(int x, int y) => Compare(body[x], body[y]);
		protected virtual void Swap(int x, int y) { T tmp = body[x]; body[x]=body[y]; body[y]=tmp; }
		public virtual void Push(T elem) {
			body.Add(elem);
			//the parent of n-th element is the ((n+1)>>1)-1-th
			UpHeap(lastIndex);
		}
		public void Push(IEnumerable<T> seq) {
			foreach(var item in seq) {
				Push(item);
			}
		}
		protected int UpHeap(int j) {
			while(j>0) {
				int parent = ((j+1)>>1)-1;
				if(Compare(parent, j)<0) {
					Swap(parent, j);
				} else break;
				j=parent;
			}
			return j;
		}
		public virtual T Pop() {
			T top = body[0];
			Swap(0, lastIndex);
			body.RemoveAt(lastIndex);
			DownHeap(0);
			return top;
		}
		protected int DownHeap(int j) {
			while(j<length) {
				var leftChild = ((j+1)<<1)-1;
				if(leftChild>=length) break;
				var toSwap = leftChild;
				var rightChild = leftChild+1;
				if(rightChild<length&&Compare(leftChild, rightChild)<0)
					toSwap=rightChild;
				if(Compare(j, toSwap)<0) {
					Swap(toSwap, j);
				} else break;
				j=toSwap;
			}
			return j;
		}
		public T Top { get { return body[0]; } }
		public int length { get { return body.Count(); } }
		protected int lastIndex { get { return body.Count()-1; } }
		public bool Any() => body.Any();
		public string Emit() { return body.ToArray().Join(","); }
	}
	class ImmutablePriorityQueue<T>: PriorityQueue<T> where T : IComparable<T> {
		public Dictionary<T, int> map { get; private set; } = new Dictionary<T, int>();
		public ImmutablePriorityQueue(bool maxTop) : base(maxTop) { }
		public ImmutablePriorityQueue(Comparer<T> mComparer) : base(mComparer) { }
		protected override void Swap(int x, int y) {
			map[body[x]]=y;
			map[body[y]]=x;
			base.Swap(x, y);
		}
		public override void Push(T elem) {
			map.Add(elem, length);
			base.Push(elem);
		}
		public override T Pop() {
			var V = base.Pop();
			map.Remove(V);
			return V;
		}
		public void Remove(T X) {
			var x = map[X];
			map.Remove(X);
			Swap(x, lastIndex);
			body.RemoveAt(lastIndex);
			var b = DownHeap(x);
			if(b==x) UpHeap(x);
		}
		public void Update(T X) {
			var x = map[X];
			var b = DownHeap(x);
			if(b==x) UpHeap(x);
		}
		public bool hasKey(T X) { int c; return map.TryGetValue(X, out c); }
	}
	class Edge<V>: IComparable<Edge<V>> where V : IComparable<V> {
		public int In { get; set; }
		public int Out { get; set; }
		public V cost { get; set; }
		public int CompareTo(Edge<V> y) => cost.CompareTo(y.cost);
	}
	class Node<V>: IComparable<Node<V>> where V : IComparable<V> {
		public V Value { get; set; }
		public int index { get; set; }
		public int CompareTo(Node<V> y) => Value.CompareTo(y.Value);
	}
	class Graph: Graph<long> {
		public Graph(int count) : base(count) { }
		public long[] Dijkstra(int start) {
			var PQ = new ImmutablePriorityQueue<Node<long>>(false);
			const long large = 0x3FFFFFFFFFFFFFFF;
			var Nodes = new Node<long>[N];
			var picked = new bool[N];
			var parentIndex = Enumerable.Repeat(-1, N).ToArray();
			var O = Outs;
			for(int i = 0; i<N; i++) {
				Nodes[i]=new Node<long> {
					index=i,
					Value=i==start ? 0 : large
				};
				PQ.Push(Nodes[i]);
			}
			while(PQ.Any()) {
				var nv = PQ.Pop();
				var v = nv.index;
				picked[v]=true;
				foreach(var e in O[v]) {
					var w = e.Out;
					if(picked[w]) continue;
					var c = e.cost;
					if(Nodes[v].Value+c<Nodes[w].Value) {
						Nodes[w].Value=Nodes[v].Value+c;
						PQ.Update(Nodes[w]);
						parentIndex[w]=v;
					}
				}
			}
			return Nodes.Select(n => n.Value).ToArray();
		}
		public long Prim(out Graph tree, int start = 0) {
			tree=new Graph(N);
			var res = 0L;
			var PQ = new PriorityQueue<Edge<long>>(false);
			var O = Outs;
			PQ.Push(O[start]);
			var picked = new bool[N];
			picked[start]=true;
			while(PQ.Any()) {
				var e = PQ.Pop();
				var w = e.Out;
				if(picked[w]) continue;
				else picked[w]=true;
				res+=e.cost;
				tree.Edges.Add(e);
				PQ.Push(O[w]);
			}
			return res;
		}
	}
	class Graph<V> where V : IComparable<V> {
		public int N { get; }
		public Graph(int count) {
			N=count;
			Edges=new List<Edge<V>>();
		}
		public List<Edge<V>> Edges { get; }
		public void AddEdge(int In, int Out, V Value) {
			var e = new Edge<V> { In=In, Out=Out, cost=Value };
			Edges.Add(e);
		}
		protected List<Edge<V>>[] Outs {
			get {
				var Res = new List<Edge<V>>[N];
				for(int i = 0; i<N; i++)
					Res[i]=new List<Edge<V>>();
				foreach(var e in Edges)
					Res[e.In].Add(e);
				return Res;
			}
		}
		protected List<Edge<V>>[] Ins {
			get {
				var Res = new List<Edge<V>>[N];
				for(int i = 0; i<N; i++)
					Res[i]=new List<Edge<V>>();
				foreach(var e in Edges)
					Res[e.Out].Add(e);
				return Res;
			}
		}
		public bool DepthFirstSearch(int start, Action<int> OnEnter, Action<int> OnLeave)
			=> DepthFirstSearch(start, i => { OnEnter?.Invoke(i); return false; }, i => { OnLeave?.Invoke(i); return false; });
		public bool DepthFirstSearch(int start, Func<int, bool> OnEnter, Func<int, bool> OnLeave) {
			var Next = Outs;
			var visited = new bool[N];
			visited[start]=true;
			var S = new Stack<int>();
			S.Push(start);
			while(S.Any()) {
				var v = S.Peek();
				if(OnEnter?.Invoke(v)??false)
					return true;
				var E = Next[v].FirstOrDefault(e => !visited[e.Out]);
				if(E!=default(Edge<V>)) {
					var o = E.Out;
					S.Push(o);
					visited[o]=true;
				} else {
					S.Pop();
					if(OnLeave?.Invoke(v)??false)
						return true;
				}
			}
			return false;
		}
		public void BreadthFirstSearch(int start, Action<int> F) {
			var Q = new Queue<int>();
			var Labeled = new bool[N];
			var G = Outs;
			Q.Enqueue(start);
			Labeled[start]=true;
			F(start);
			while(Q.Any()) {
				var v = Q.Dequeue();
				F(v);
				foreach(var e in G[v]) {
					var w = e.Out;
					if(Labeled[w]) continue;
					Q.Enqueue(w);
					Labeled[w]=true;
				}
			}
		}
		public bool hasPath(int from, int to) {
			if(from==to) return true;
			return DepthFirstSearch(from, i => i==to, null);
		}
		public bool MakePath(int from, int to, Stack<int> Path) {
			if(from==to) return true;
			Path=new Stack<int>();
			return DepthFirstSearch(from,
			i => { Path.Push(i); return i==to; },
			j => { Path.Pop(); return false; });
		}
		public bool hasCircuit(int start) {
			var X = PreLabel(start);
			Func<int, int, bool> isBackward = (i, j) => X[i]!=-1&&X[j]!=-1&&X[i]>X[j];
			return Edges.Any(e => isBackward(e.In, e.Out));
		}
		public List<int> PreOrder(int start) {
			var Res = new List<int>();
			DepthFirstSearch(start, v => Res.Add(v), null);
			return Res;
		}
		public List<int> PostOrder(int start) {
			var Res = new List<int>();
			DepthFirstSearch(start, null, v => Res.Add(v));
			return Res;
		}
		public int[] PreLabel(int start) {
			var Res = Enumerable.Repeat(-1, N).ToArray();
			var count = 0;
			DepthFirstSearch(start, v => Res[v]=count++, null);
			return Res;
		}
		public int[] PostLabel(int start) {
			var Res = Enumerable.Repeat(-1, N).ToArray();
			var count = 0;
			DepthFirstSearch(start, null, v => Res[v]=count++);
			return Res;
		}
	}
}