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
Taking the worst case scenario, the minimum number of
iterations required is 20. Here is why:
For N drops you can cover a range of the sum(1,..N), which
is n*(n+1) / 2.
If we have 200 potential heights to test, we solve n*(n+1) =
400, and using the quadratic equation gives us
19.5062490237426, rounding up to 20.
The sequence of tests would be drop at heights of:
20
39
57
74
90
105
119
132
144
155
165
174
182
189
195
200
(Notice, the distance between each level decreases by 1 to
account for the extra drop it took to get there.)
If the bulb does not break on a level, try the next higher
number in the above sequence. If it does break, then do a
linear search starting at the previous "level", plus 1.
Any answer that partitions segments into equal lengths will
be suboptimal.
| Is This Answer Correct ? | 3 Yes | 0 No |
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