# [990. Satisfiability of Equality Equations](https://leetcode.com/problems/satisfiability-of-equality-equations/)


## 题目

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. `1 <= equations.length <= 500`
2. `equations[i].length == 4`
3. `equations[i][0]` and `equations[i][3]` are lowercase letters
4. `equations[i][1]` is either `'='` or `'!'`
5. `equations[i][2]` is `'='`



## 题目大意

给定一个由表示变量之间关系的字符串方程组成的数组，每个字符串方程 equations[i] 的长度为 4，并采用两种不同的形式之一："a==b" 或 "a!=b"。在这里，a 和 b 是小写字母（不一定不同），表示单字母变量名。只有当可以将整数分配给变量名，以便满足所有给定的方程时才返回 true，否则返回 false。 

提示：

1. 1 <= equations.length <= 500
2. equations[i].length == 4
3. equations[i][0] 和 equations[i][3] 是小写字母
4. equations[i][1] 要么是 '='，要么是 '!'
5. equations[i][2] 是 '='



## 解题思路


- 给出一个字符串数组，数组里面给出的是一些字母的关系，只有 `'=='` 和 `'! ='` 两种关系。问给出的这些关系中是否存在悖论？
- 这一题是简单的并查集的问题。先将所有 `'=='` 关系的字母 `union()` 起来，然后再一一查看 `'! ='` 关系中是否有 `'=='` 关系的组合，如果有，就返回 `false`，如果遍历完都没有找到，则返回 `true`。