You have 2 identical glass bulbs with you. Bulb
manufacturer has mentioned that each bulb might withstand a
drop of 200 Feet at maximum. Your task is to find the
height at which the bulb breaks ofcourse with minimum
number of iterations.
Assume that you have 200 blocks of 1 foot each which can be
stacked one by one to create a 200 Feet structure to carry
out the test.
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Answer Posted / chris uzdavinis
Minor typo in previous answer (#7): it should say ... we
solve n*(n+1) = 200
To help get the mindset of the answer, think of the question
differently at first. Rather than solve for the fewest
number of drops to cover a range, think about a twisted
version of that question: "given a fixed number of drops,
what range can be completely covered?"
Our constraints are we have two bulbs, and we're done once
the 2nd breaks, but if it doesn't break we can use it again.
Given only 1 drop, we can only cover a range of 1. Either
it breaks or it doesn't. (If we go higher than the first
level, we don't know if it would have broken at a lower level.)
Given 2 drops, we can cover a range of 3: first drop on 2,
if it breaks, try 1, if not, try 3.
Given 3 drops, we cover a range 1..6: First drop on 3, if
it breaks, try 1, then 2. If it doesn't break, drop #2 is
on 5. If breaks, try 4. If not, try 6.
Given 4 drops, we cover a range of 1..10:
Start on 4, if breaks, try 1,2,3. If not, try 7. If
breaks, try 5,6. If not, try 9. If breaks, try 8. If not
try 10.
And so on. Thus, for N drops, we start on level N. If it
breaks, start a linear search using the remaining bulb, from
1..N-1. Thus, it took a max of 20 drops. But if it doesn't
break, we try level N+(N-1). If it breaks, start a linear
search from N+1. Otherwise try N+(N-1)+(N-2). etc.
This series is clearly the sum from 1 to N drops.
So now that we know how big of a range we can cover given a
fixed number of drops. But the original question asks us to
cover a range of 200, and find the number of drops required.
We just find the smallest integral value for N such that
sum of 1..N >= 200, which is 20.
I gave the sequence of tests in the previous post.
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