# https://leetcode.com/problems/satisfiability-of-equality-equations/
"""
Given an array equations of strings that represent relationships between variables, each string equations[i] has length 4 and takes one of two different forms: "a==b" or "a!=b".  Here, a and b are lowercase letters (not necessarily different) that represent one-letter variable names.

Return true if and only if it is possible to assign integers to variable names so as to satisfy all the given equations.

Example 1:
Input: ["a==b","b!=a"]
Output: false
Explanation: If we assign say, a = 1 and b = 1, then the first equation is satisfied, but not the second.  There is no way to assign the variables to satisfy both equations.

Example 2:
Input: ["b==a","a==b"]
Output: true
Explanation: We could assign a = 1 and b = 1 to satisfy both equations.

Example 3:
Input: ["a==b","b==c","a==c"]
Output: true

Example 4:
Input: ["a==b","b!=c","c==a"]
Output: false

Example 5:
Input: ["c==c","b==d","x!=z"]
Output: true


Note:
1 <= equations.length <= 500
equations[i].length == 4
equations[i][0] and equations[i][3] are lowercase letters
equations[i][1] is either '=' or '!'
equations[i][2] is '='
"""
from typing import List

from puzzles.union_find import UF


def equations_possible(equations: List[str]) -> bool:
    uf = UF(26)

    for eq in equations:
        if eq[1] == "=":
            x, y = eq[0], eq[3]
            uf.union(ord(x) - ord("a"), ord(y) - ord("a"))

    for eq in equations:
        if eq[1] == "!":
            x, y = eq[0], eq[3]
            if uf.connected(ord(x) - ord("a"), ord(y) - ord("a")):
                return False
    return True
