Evaluate Division

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Description

You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [Ai, Bi] and values[i] represent the equation Ai / Bi = values[i]. Each Ai or Bi is a string that represents a single variable.

You are also given some queries, where queries[j] = [Cj, Dj] represents the j-th query where you must find the answer for Cj / Dj = ?.

Return the answers to all queries. If a single answer cannot be determined, return -1.0.

Note: The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.

Note: The variables that do not occur in the list of equations are undefined, so the answer cannot be determined for them.

Example 1:

• Input: equations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
• Output: [6.00000,0.50000,-1.00000,1.00000,-1.00000]
• Explanation:

Given: a / b = 2.0, b / c = 3.0
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? 
return: [6.0, 0.5, -1.0, 1.0, -1.0 ]
note: x is undefined => -1.0

Example 2:

• Input: equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]
• Output: [3.75000,0.40000,5.00000,0.20000]

Example 3:

• Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
• Output: [0.50000,2.00000,-1.00000,-1.00000]

Constraints:

• 1 <= equations.length <= 20
• equations[i].length == 2
• 1 <= Ai.length, Bi.length <= 5
• values.length == equations.length
• 0.0 < values[i] <= 20.0
• 1 <= queries.length <= 20
• queries[i].length == 2
• 1 <= Cj.length, Dj.length <= 5
• Ai, Bi, Cj, Dj consist of lower case English letters and digits.

Solution

class Solution {
public:
    vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
        unordered_set<string> vertices;
        unordered_map<string, unordered_map<string, double>> edges;

        for (int i = 0; i < equations.size(); i++) {
            string a = equations[i][0], b = equations[i][1];
            double var = values[i];
            edges[a][b] = var, edges[b][a] = 1 / var;
            vertices.insert(a), vertices.insert(b);
        }

        for (const string& k : vertices) {
            for (const string& i : vertices) {
                for (const string& j : vertices) {
                    if (edges[i][k] && edges[j][k])
                        edges[i][j] = edges[i][k] * edges[k][j];
                }
            }
        }

        vector<double> res;
        for (vector<string>& q : queries) {
            string a = q[0], b = q[1];
            if (edges[a][b]) res.push_back(edges[a][b]);
            else res.push_back(-1);
        }

        return res;
    }
};