Problem:
Score : 400 points

Problem Statement

There are N people standing on the x-axis.
Let the coordinate of Person i be x_i.
For every i, x_i is an integer between 0 and 10^9 (inclusive).
It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people.
The i-th piece of information has the form (L_i, R_i, D_i).
This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

1 \leq N \leq 100 000

0 \leq M \leq 200 000

1 \leq L_i, R_i \leq N (1 \leq i \leq M)

0 \leq D_i \leq 10 000 (1 \leq i \leq M)

L_i \neq R_i (1 \leq i \leq M)

If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).

D_i are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
class Main
{
	static int noofnodes , noofqueries;
	static int[] arr = new int[100100];
	static Stack<Integer>[] lstk,rstk ;
	// static Stack<Integer> queries ;  
	static HashMap<String,Integer> hmap = new HashMap<>();
	static int[] visit ;
	static int flag =0 ;
	static Queue<Integer> queries = new LinkedList<>();
	public static void dfs()
	{
		// Collection.sort(queries);
		abc:while(!queries.isEmpty())
		{
			int ele = queries.remove();
			// System.out.println("eleemnt poped by queries(ele) "+ele);
			if(visit[ele]==0)
			{
				visit[ele]=1;
				while(!lstk[ele].isEmpty())
				{
					int newele = lstk[ele].pop();
					// System.out.println("element pop by lstk(newele) "+newele);
					
					int sum = hmap.get(ele+" "+newele);
					// System.out.println("sum of ele + newele "+sum);


					if(visit[newele]==0)
					{
						visit[newele] = 1;
						while(!lstk[newele].isEmpty())
						{
							int extra = lstk[newele].pop();
							sum+= hmap.get(newele+" "+extra);
							// System.out.println("extra ele poped  = "+extra);
							// System.out.println("sum of newele and extra = "+hmap.get(newele+" "+extra));
							// System.out.println("and actual sum = "+sum);
							if(hmap.containsKey(ele+" "+extra))
							{
								// System.out.println("ele and extra sum = "+hmap.get(ele+" "+extra));
								if((hmap.get(ele+" "+extra))!= sum )
								{
									flag =1;
									break abc;
								}
							}
							else
							{
								hmap.put(ele+" "+extra , sum);
							}
						}
						
					}

				}
			}
		}

		// System.out.println("flag = "+flag);
		if(flag == 0)
			System.out.println("Yes");
		else
			System.out.println("No");










	}


	public static void main(String[] args)
	{
		Scanner s= new Scanner(System.in);
		noofnodes = s.nextInt();
		noofqueries = s.nextInt();
		visit = new int[noofnodes+1];

		lstk = new Stack[noofnodes+1];
		rstk = new Stack[noofnodes+1];
		// queries = new Stack<Integer>();
		for(int i =0;i<noofnodes+1;i++ )
		{
			lstk[i] = new Stack<Integer>();
			rstk[i] = new Stack<Integer>();
		}

		//storing 
		for(int i=0;i<noofqueries;i++)
		{
			int l = s.nextInt();
			int r = s.nextInt();
			int d = s.nextInt();
			lstk[l].push(r);
			rstk[r].push(l);
			if(arr[l] == 0)
				queries.add(l);
			arr[l] = 1;
			hmap.put(l+" "+r,d);
			hmap.put(r+" "+l,-d);

		}

		for(int i=0;i<=noofnodes;i++)
		{
			int[] temp = new int[lstk[i].size()];
			int indx = 0 ;
			while(!lstk[i].isEmpty())
			{
				temp[indx] = lstk[i].pop();
				indx++;
			}
			Arrays.sort(temp);
			for(int j=indx-1;j>=0;j--)
				lstk[i].push(temp[j]);


		}

		for(int i=0;i<queries.size();i++)
		{
			int[] temp = new int[queries.size()];
			int indx = 0 ;
			while(!queries.isEmpty())
			{
				temp[indx] = queries.remove();
				indx++;
			}

			Arrays.sort(temp);
			for(int j=0;j<temp.length;j++)
				queries.add(temp[j]);
		}



		dfs();

			// System.out.println(queries);
			// for(int i=0;i<noofnodes+1;i++)
			{
				// System.out.println("lstk = "+lstk[i]);
			 
			}

			// for(int i=0;i<noofnodes+1;i++)
			{
				// System.out.println("rstk = "+rstk[i]);
			 
			}
		


		}


}