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[POJ3678] Katu Puzzle | 2-SAT 入门

2022-06-14 164

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简介： Description Katu Puzzle is presented as a directed graph G ( V , E ) with each edge e ( a , b ) labeled by a boolean operator op (oneofAND,OR,XOR) and an integer c ( 0 ≤ c ≤ 1 ) . One Katu is solvable if one can find each vertex Vi a value X i ( 0 ≤ X i ≤ 1 )

Description
Katu Puzzle is presented as a directed graph G ( V , E ) with each edge e ( a , b ) labeled by a boolean operator op (oneofAND,OR,XOR) and an integer c ( 0 ≤ c ≤ 1 ) . One Katu is solvable if one can find each vertex Vi a value X i ( 0 ≤ X i ≤ 1 ) such that for each edge e(a, b) labeled by op and c, the following formula holds:
Xa op Xb = c
The calculating rules are:
AND 0 1
0 0 0
1 0 1
OR 0 1
0 0 1
1 1 1
XOR 0 1
0 0 1
1 1 0
Given a Katu Puzzle, your task is to determine whether it is solvable.
Input
The first line contains two integers N ( 1 ≤ N ≤ 1000 )and M,( 0 ≤ M ≤ 1 , 000 , 000 ) (0 ≤ M ≤ 1,000,000) indicating the number of vertices and edges.
The following M lines contain three integers a ( 0 ≤ a < N ) , b ( 0 ≤ b < N ), c and an operator op each, describing the edges.
Output
Output a line containing “YES” or “NO”.
Sample Input