AtCoder Beginner Contest 087 D - People on a Line 并查集（区间和问题）
Problem Statement
There are N people standing on the x-axis. Let the coordinate of Person i be xi. For every i, xi is an integer between 0 and 109 (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 (Li,Ri,Di). This means that Person Ri is to the right of Person Li by Di units of distance, that is, xRi−xLi=Di holds.
It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x1,x2,…,xN) that is consistent with the given pieces of information.
Constraints
1≤N≤100 000
0≤M≤200 000
1≤Li,Ri≤N (1≤i≤M)
0≤Di≤10 000 (1≤i≤M)
Li≠Ri (1≤i≤M)
If i≠j, then (Li,Ri)≠(Lj,Rj) and (Li,Ri)≠(Rj,Lj).
Di are integers.
Input
Input is given from Standard Input in the following format:
N M
L1 R1 D1
L2 R2 D2
:
LM RM DM
Output
If there exists a set of values (x1,x2,…,xN) 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 (x1,x2,x3) 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, x3−x1=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
There are N people standing on the x-axis. Let the coordinate of Person i be xi. For every i, xi is an integer between 0 and 109 (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 (Li,Ri,Di). This means that Person Ri is to the right of Person Li by Di units of distance, that is, xRi−xLi=Di holds.
It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x1,x2,…,xN) that is consistent with the given pieces of information.
Constraints
1≤N≤100 000
0≤M≤200 000
1≤Li,Ri≤N (1≤i≤M)
0≤Di≤10 000 (1≤i≤M)
Li≠Ri (1≤i≤M)
If i≠j, then (Li,Ri)≠(Lj,Rj) and (Li,Ri)≠(Rj,Lj).
Di are integers.
Input
Input is given from Standard Input in the following format:
N M
L1 R1 D1
L2 R2 D2
:
LM RM DM
Output
If there exists a set of values (x1,x2,…,xN) 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 (x1,x2,x3) 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, x3−x1=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
题意：给出n个数字，m个区间和，判断是否存在那样的区间数字满足m个区间和
思路：并查集区间判断
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