[Leedcode][JAVA][第990题][等式方程的可满足性][并查集]

怼烎@ 2023-02-17 02:53 89阅读 0赞

#### 【问题描述】\[中等\] ####

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。

#### 【解答思路】 ####

![在这里插入图片描述][20200611151539945.png]

###### 并查集 ######

**时间复杂度：O(N^2) 空间复杂度：O(1)**

public class Solution { 
    
        public boolean equationsPossible(String[] equations) { 
            UnionFind unionFind = new UnionFind(26);
    
            for (String equation : equations) { 
                char[] charArray = equation.toCharArray();
                if (charArray[1] == '=') { 
                    int index1 = charArray[0] - 'a';
                    int index2 = charArray[3] - 'a';
                    unionFind.union(index1, index2);
                }
            }
    
            for (String equation : equations) { 
                char[] charArray = equation.toCharArray();
                if (charArray[1] == '!') { 
                    int index1 = charArray[0] - 'a';
                    int index2 = charArray[3] - 'a';
    
                    if (unionFind.isConnected(index1, index2)) { 
                        // 如果合并失败，表示等式有矛盾，根据题意，返回 false
                        return false;
                    }
                }
            }
    
            // 如果检查了所有不等式，都没有发现矛盾，返回 true
            return true;
        }
    
        private class UnionFind { 
            
            private int[] parent;
    
            public UnionFind(int n) { 
                parent = new int[n];
                for (int i = 0; i < n; i++) { 
                    parent[i] = i;
                }
            }
    
            public int find(int x) { 
                while (x != parent[x]) { 
                    parent[x] = parent[parent[x]];
                    x = parent[x];
                }
                return x;
            }
    
            /** * @param x * @param y * @return 如果合并成功，返回 true */
            public void union(int x, int y) { 
                int rootX = find(x);
                int rootY = find(y);
                parent[rootX] = rootY;
            }
    
            public boolean isConnected(int x, int y) { 
                return find(x) == find(y);
            }
        }
    
    
        public static void main(String[] args) { 
            // String[] equations = new String[]{"b==a", "a==b"};
            // String[] equations = new String[]{"a==b","b==c","a==c"};
            // String[] equations = new String[]{"a==b","b!=c","c==a"};
            String[] equations = new String[]{ "c==c", "b==d", "x!=z"};
    
            Solution solution = new Solution();
            boolean res = solution.equationsPossible(equations);
            System.out.println(res);
        }
    }

#### 【总结】 ####

###### 1.并查集知识小结 ######

面试较少出现 酌情掌握  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70]  
![在这里插入图片描述][20200611151615695.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 1]  
![在这里插入图片描述][20200611151909590.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 2]

###### 2.并查集时间复杂度分析 ######

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 3]  
时间复杂度知乎链接：https://www.zhihu.com/question/35090745

###### 3.并查集练习题 ######

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 4]  
转载链接：https://leetcode-cn.com/problems/satisfiability-of-equality-equations/solution/shi-yong-bing-cha-ji-chu-li-bu-xiang-jiao-ji-he-we/

[20200611151539945.png]: https://img-blog.csdnimg.cn/20200611151539945.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20200611154408455.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[20200611151615695.png]: https://img-blog.csdnimg.cn/20200611151615695.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20200611151833594.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[20200611151909590.png]: https://img-blog.csdnimg.cn/20200611151909590.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/20200611151946638.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 3]: https://img-blog.csdnimg.cn/20200611152020427.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 4]: https://img-blog.csdnimg.cn/20200611153035921.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70