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.
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 ]
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.

