Evaluate Division

You are given a list of equations where:

a / b = value

You are also given queries asking for the value of:

c / d

Return the answer for every query.

If the answer cannot be determined, return:

-1.0

Important Idea

Treat the equations as a weighted graph.

For:

a / b = 2

create:

a → b = 2

b → a = 1/2

Then a query can be solved by finding a path between the two variables.

Example Graph

Given:

a / b = 2

b / c = 3

The graph becomes:

a --2--> b --3--> c

a <--1/2-- b <--1/3-- c

Therefore:

a / c = 2 × 3 = 6

and:

c / a = 1/3 × 1/2 = 1/6

Main Logic

Use:

HashMap + DFS

For each equation:

a / b = k

store:

a → b : k

b → a : 1/k

For a query:

a / c

perform DFS from a to c.

Multiply the edge weights along the path.

If no path exists:

return -1.0

If:

a == c

and a exists, the answer is:

1.0