CODEWITHSUNDEEP
algorithmdata-structures
maz
maz

Reputation: 523

Find second minimum - algorithm

I want to find the second minimum for three numbers.

I have a blackbox that gets two input numbers, the blackbox returns the max between numbers.

Additionally, I have a blackbox that returns the min.

Now I have a box that gets 3 numbers as input and it needs to return the second min.

Can you help me to solve this? How can I solve this by only using the two blackboxes?

Thanks!

Upvotes: 2

Views: 116

Answers (2)

maraca
maraca

Reputation: 8743

Inputs: a, b, c

Level 1 (filtering out the biggest value):
min(a,b) -> min_ab
min(a,c) -> min_ac
min(b,c) -> min_bc

Level 2 (selecting the highest remaining value, step 1):
max(min_ab, min_bc) -> m*

Level 3 (step 2):
max(m*, min_ac) -> solution

Gives a total of 5 boxes.

a --+--\
    |   min --\
b -----<       max --\
    |   min --/       max --
c -----<             /
    |   min --------/
    \--/

Alternatively you can do 3 maxes first and then 2 mins.

Upvotes: 1

Smith
Smith

Reputation: 21

I can see of a way to to this with 3 uses of the blackbox. Let's pretend each element is a,b,c. Find the min of a with b and b with c. You then find the max of those 2 answers and you have the second min. If only b was returned, you find the min of a and c.

Upvotes: 1

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