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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.util.AbstractMap;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

     static Scanner scanner;

     public static void main(String[] args) {
         scanner = new Scanner(System.in);

         int N=gi();
         int M=gi();
         long[] R=new long[M];
         long[] L=new long[M];
         long[] D=new long[M];
         Map<Pair<Long,Long>, Long> tm=new HashMap<Pair<Long,Long>, Long>();
         long[] x=new long[N];
         Pair<Long,Long>[] pa=new Pair[M];

         for (int i=0; i<N;i++) {
             x[i]=Long.MAX_VALUE;
         }
         for (int i=0; i<M;i++) {
             long l=gl()-1;
             long r=gl()-1;
             long d=gl();
             if(l>r) {
            	 l^=r;
            	 r^=l;
            	 l^=r;
            	 d=-d;
             }
             Pair<Long,Long> p=new Pair<Long,Long>(l,r);
             tm.put(p, d);
             pa[i]=p;
         }

         Arrays.parallelSort(pa);

         boolean f=true;
         for (int i=0; i<M;i++) {

        	 Pair<Long,Long> p=pa[i];
        	 long l=p.getKey();
        	 long r=p.getValue();
        	 long d=tm.get(p);
        	 if(x[(int)l]!=Long.MAX_VALUE) {
        		 if(x[(int)r]!=Long.MAX_VALUE) {
        			 if(x[(int)r] - x[(int)l] != d) {
        				 f=false;
        				 break;
        			 }
        		 } else {
        			 x[(int)r]=x[(int)l]+d;
        		 }
        	 } else {
        		 if(x[(int)r]!=Long.MAX_VALUE) {
        			 x[(int)l]=x[(int)r]-d;
        		 } else {
        			 x[(int)l]=0;
        			 x[(int)r]=d;
        		 }
        	 }
         }


         if(f) {
        	 System.out.println("Yes");
         }else {
        	 System.out.println("No");
         }
         //System.out.println(ans);
     }

     public static class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> implements Comparable<Pair<K, V>> {
    		/** serialVersionUID. */
    	    private static final long serialVersionUID = 6411527075103472113L;

    	    public Pair(final K key, final V value) {
    	        super(key, value);
    	    }

    		@Override
    		public int compareTo(Pair<K, V> o) {

    			Comparable key = (Comparable)this.getKey();
    			Comparable key2 = (Comparable)o.getKey();

    			return key.compareTo(key2);
    		}

    	}

     // 文字列として入力を取得
     public static String gs() {
          return scanner.next();
     }

     // intとして入力を取得
     public static int gi() {
          return Integer.parseInt(scanner.next());
     }

     // longとして入力を取得
     public static long gl() {
          return Long.parseLong(scanner.next());
     }

     // doubleとして入力を取得
     public static double gd() {
          return Double.parseDouble(scanner.next());
     }
}