Evaluate Division
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 = [2,3], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]Output
[6,0.5,-1,1,-1]Given
a / b = 2.0 and b / c = 3.0, the queries evaluate to 6.0, 0.5, -1.0, 1.0, and -1.0 because e and x are undefined.Example 2
Input
equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]Output
[3.75,0.4,5,0.2]The known equations imply
a / c = 3.75, c / b = 0.4, bc / cd = 5.0, and cd / bc = 0.2.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.