evaluate-division

Evaluate Division

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calcEquation

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

You are also given some <code>queries</code>, where <code>queries[j] = [Cj, Dj]</code> represents the <code>jth</code> query where you must find the answer for <code>Cj / Dj = ?</code>.

Return the answers to all queries. If a single answer cannot be determined, return <code>-1.0</code>.

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.

&nbsp;
Example 1:

<pre>
Input: equations = [[&quot;a&quot;,&quot;b&quot;],[&quot;b&quot;,&quot;c&quot;]], values = [2.0,3.0], queries = [[&quot;a&quot;,&quot;c&quot;],[&quot;b&quot;,&quot;a&quot;],[&quot;a&quot;,&quot;e&quot;],[&quot;a&quot;,&quot;a&quot;],[&quot;x&quot;,&quot;x&quot;]]
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 ]
</pre>

Example 2:

<pre>
Input: equations = [[&quot;a&quot;,&quot;b&quot;],[&quot;b&quot;,&quot;c&quot;],[&quot;bc&quot;,&quot;cd&quot;]], values = [1.5,2.5,5.0], queries = [[&quot;a&quot;,&quot;c&quot;],[&quot;c&quot;,&quot;b&quot;],[&quot;bc&quot;,&quot;cd&quot;],[&quot;cd&quot;,&quot;bc&quot;]]
Output: [3.75000,0.40000,5.00000,0.20000]
</pre>

Example 3:

<pre>
Input: equations = [[&quot;a&quot;,&quot;b&quot;]], values = [0.5], queries = [[&quot;a&quot;,&quot;b&quot;],[&quot;b&quot;,&quot;a&quot;],[&quot;a&quot;,&quot;c&quot;],[&quot;x&quot;,&quot;y&quot;]]
Output: [0.50000,2.00000,-1.00000,-1.00000]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= equations.length &lt;= 20</code></li>
	<li><code>equations[i].length == 2</code></li>
	<li><code>1 &lt;= Ai.length, Bi.length &lt;= 5</code></li>
	<li><code>values.length == equations.length</code></li>
	<li><code>0.0 &lt; values[i] &lt;= 20.0</code></li>
	<li><code>1 &lt;= queries.length &lt;= 20</code></li>
	<li><code>queries[i].length == 2</code></li>
	<li><code>1 &lt;= Cj.length, Dj.length &lt;= 5</code></li>
	<li><code>Ai, Bi, Cj, Dj</code> consist of lower case English letters and digits.</li>
</ul>

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