Evaluate Division

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Problem Statement

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.

Examples

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]
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.

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicString