# Evaluate Division

Moderate
0/80
Average time to solve is 15m
Contributed by

## Problem statement

You are given an array of pairs of strings 'EQUATIONS', and an array of real numbers 'VALUES'. Each element of the 'EQUATIONS' array denotes a fraction where the first string denotes the numerator variable and the second string denotes the denominator variable, and the corresponding element in 'VALUES' denotes the value this fraction is equal to.

You are given ‘Q’ queries, and each query consists of two strings representing the numerator and the denominator of a fraction. You have to return the value of the given fraction for each query. Return -1 if the value cannot be determined.

Example :
``````'EQUATIONS' = { {“a”, ”s”} , {“s”, “r”} }
'VALUES' = { 1.5, 2 }
queries = { {“a”, “r” } }

For the above example (a / s) = 1.5 and (s / r) = 2 therefore (a / r) = 1.5 * 2 = 3.
``````
Detailed explanation ( Input/output format, Notes, Images )
Constraints :
``````1 <= T <= 50
1 <= N <= 100
1 <= Q <= 100
1 <= |S| <= 10
0.0 < values[i] <= 100.0

Where '|S|' denotes the length of the variables, and 'VALUES[i]' denotes the value of the i’th equation.

Time limit: 1 sec
``````
##### Sample Input 1 :
``````2
2 1
a s
s r
1.5 2
a
r
3 2
a abc ab
x xyz xy
0.5 1 3.4
abc pqr
xyz rew
``````
##### Sample Output 1 :
``````3.00000
1.00000 -1.00000
``````
##### Explanation of Sample Output 1 :
``````In test case 1, (a / s) = 1.5 and (s / r) = 2 therefore (a / r) = 1.5 * 2 = 3.

In test case 2, for the first query, the value of (abc / xyz) is given as 1, and the value of (pqr / rew) cannot be determined.
``````
##### Sample Input 2 :
``````2
4 2
a r w p
r w p e
1.2 2.6 1 0.5
e a
p p
2 1
a x
b y
0.5 0.4
a
y
``````
##### Sample Output 2 :
``````2.00000 3.12000
-1.00000
``````
##### Explanation of Sample Output 2 :
``````In test case 1, for the first query we have p / e = 0.5 ,therefore e / p = 1 / 0.5 = 2, for the second query (a / r) * (r / w) * (w / p) = a / p which is equal to 1.2 * 2.6 * 1 = 3.12.

In test case 2, we can not determine the value of the a / y, by the given set of equations. Thus return -1.
``````
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