DIY: Evaluate Division

Problem statement

You are given equations, an array of variable pairs, and values, an array of real numbers. 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 also have some queries, where queries[j] = [Cj, Dj] represents the jth query, and you must find the answer for Cj / Dj = ?.

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

Input

The following is an example input:

equations = [["a","b"],["b","c"]]
values = [2.0,3.0]
queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]

Output

The following is an example output:

[6.0, 0.5, -1.0, 1.0, -1.0]

Coding exercise

For this coding exercise, you need to implement the evaluate(equations, values, queries) function. The function will return the answers for every variable pair in the queries array.