990. Satisfiability of Equality Equations. 并查集

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: ["ba","ab"]
Output: true
Explanation: We could assign a = 1 and b = 1 to satisfy both equations.
Example 3:

Input: ["ab","bc","a==c"]
Output: true
Example 4:

Input: ["ab","b!=c","ca"]
Output: false
Example 5:

Input: ["cc","bd","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 '='

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/satisfiability-of-equality-equations

直接并查集

class Solution {
public:
    vector <int> fa;

    int find(int x){
        return x == fa[x] ? x : fa[x] = find(fa[x]);
    }

    void unite(int x,int y){
        int xx = find(x);
        int yy = find(y);

        fa[xx] = yy;
    }

    bool same(int x,int y){
        return find(x) == find(y);
    }


    bool equationsPossible(vector<string>& equations) {
        
        fa.resize(26);
        iota(fa.begin(), fa.end(), 0);

        for (auto str : equations){
            if (str[1] == '='){
                int x = str[0] - 'a';
                int y = str[3] - 'a';
                unite(x,y);
            }
        }

        for (auto str : equations){
            if (str[1] == '!'){
                int x = str[0] - 'a';
                int y = str[3] - 'a';
                if (same(x,y)){
                    return false;
                }
            }
        }

        return true;
    }
};