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 jth 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.
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: [6.0,0.5,-1.0,1.0,-1.0]
Explanation: Given: a / b = 2.0, b / c = 3.0. Queries are: a / c = (a/b) * (b/c) = 6.0, b / a = 1/(a/b) = 0.5, a / e = -1.0 (e is not defined), a / a = 1.0, x / x = -1.0 (x is not defined).
Example 2:
Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
Output: [0.5,2.0,-1.0,-1.0]
Explanation: Given: a / b = 0.5. Queries: a / b = 0.5, b / a = 2.0, a / c = -1.0 (c undefined), x / y = -1.0 (both undefined).
Example 3:
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: [3.75,0.4,5.0,0.2]
Explanation: Given: a / b = 1.5, b / c = 2.5, bc / cd = 5.0. Queries: a / c = (a/b) * (b/c) = 3.75, c / b = 1/(b/c) = 0.4, bc / cd = 5.0, cd / bc = 0.2.
1 <= equations.length <= 20equations[i].length == 21 <= Ai.length, Bi.length <= 5values.length == equations.length0.0 < values[i] <= 20.01 <= queries.length <= 20queries[j].length == 21 <= Cj.length, Dj.length <= 5Ai, Bi, Cj, Dj consist of lower case English letters and digits