Evaluate Division

Medium

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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.

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"],["ab","bc"]], values = [4.0,1.0,3.25], queries = [["a","c"],["b","a"],["c","c"],["ab","a"],["d","d"]]

Output: [4.00000,0.25000,1.00000,-1.00000,-1.00000]

Example 2:

Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"]]

Output: [0.50000,2.00000]

Constraints:

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


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equations =

values =

queries =