algorithms

Evaluate Division

Medium

https://leetcode.com/problems/evaluate-division

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

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

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 <= A_i.length, B_i.length <= 5`

- `values.length == equations.length`

- `0.0 < values[i] <= 20.0`

- `1 <= queries.length <= 20`

- `queries[i].length == 2`

- `1 <= C_j.length, D_j.length <= 5`

- `A_i, B_i, C_j, D_j` consist of lower case English letters and digits.