How should I practice Revolver: Will the Next Shot Fire??

Start by reading the full statement, solve the visible examples, then compare the pattern against related Tower Research Capital phone screen problems in FastPrep.

Is Revolver: Will the Next Shot Fire? associated with Tower Research Capital?

FastPrep tags this as a Tower Research Capital phone screen coding practice problem when the problem catalog has that company and stage context.

Revolver: Will the Next Shot Fire?

Tower Research Capital● EasyINTERNPHONE SCREEN

Problem statement

Source note: An interview question asked how likely the next shot is to fire after one empty shot from a 6-chamber revolver holding 2 bullets. It covered three cases: bullets placed at random, known not to be next to each other, and known to be next to each other.

The report does not say whether the cylinder is spun again before the second shot. This version does not spin it again, because only then does the answer depend on where the bullets are. With a new spin, every answer would be 2/6. The report also has only 6 chambers. Here, the number of chambers is from 4 to 1000, the last chamber and the first count as neighbors, and every allowed placement is equally likely. Answers are accepted within 10^-9. The three interview cases are the examples.

The judged task matches the report at about 85%.

A revolver has chambers chambers arranged in a ring. Two bullets are loaded into two different chambers, the cylinder is spun once, and the trigger is pulled. The gun does not fire, so the fired chamber was empty. The cylinder is not spun again: the next pull fires the next chamber in the ring.

bulletLayout says what you know about where the two bullets are:

"unknown": nothing. Every pair of chambers was equally likely.
"nonadjacent": the bullets are not in neighboring chambers. Every such pair was equally likely.
"adjacent": the bullets are in neighboring chambers. Every such pair was equally likely.

Two chambers are neighbors when they are next to each other in the ring, so the last chamber and the first one are neighbors too.

Return the probability that the next pull fires. Answers within 10^-9 of the exact value are accepted.

Function

nextShotProbability(chambers: int, bulletLayout: String) → double

Examples

Example 1

chambers = 6bulletLayout = "unknown"return = 0.4

This is the revolver question from the interview. The two bullets can sit in 15 pairs of chambers. The empty first shot rules out the 5 pairs that use the fired chamber, leaving 10. In 4 of them a bullet sits in the next chamber, so the probability is 4/10 = 0.4.

Example 2

chambers = 6bulletLayout = "nonadjacent"return = 0.5

Only 9 pairs keep the bullets apart. 3 of them use the fired chamber, leaving 6. The next chamber holds a bullet in 3 of those, the ones where the other bullet is 2, 3 or 4 chambers further on. The probability is 3/6 = 0.5.

Example 3

chambers = 6bulletLayout = "adjacent"return = 0.25

There are 6 pairs of neighboring chambers. 2 of them use the fired chamber, leaving 4. Only one of those has a bullet in the next chamber: the pair made of the next chamber and the one after it. The probability is 1/4 = 0.25.

Constraints

4 <= chambers <= 1000
bulletLayout is "unknown", "nonadjacent" or "adjacent".