Find minimal time for four people crossing
Problem: The Bridge and Flashlight Puzzle
Four individuals need to cross a narrow bridge at night, and they possess only a single flashlight.
Constraints and Rules:
- Each person
ihas a distinct, known timet_irequired to cross the bridge alone. - A maximum of two people can be on the bridge simultaneously.
- The flashlight is mandatory for any crossing and must be carried by the person(s) crossing.
- When two people cross together, their crossing time is determined by the slower of the two, i.e.,
max(t_a, t_b). - The flashlight cannot be transferred across the bridge by any means other than being physically carried by a person walking back.
- You are provided with the four positive integer crossing times:
t1, t2, t3, t4. For simplicity, assume these times are already sorted in non-decreasing order:t1 <= t2 <= t3 <= t4.
Tasks:
- Devise a strategy, detailing the sequence of crossings and returns, that achieves the absolute minimum total time for all four people to successfully reach the other side of the bridge, with the flashlight also ending up on the destination side.
- Clearly express this minimal total time using the given variables
t1, t2, t3, t4. Provide a step-by-step description of the optimal crossing sequence, specifying who crosses in each direction and who carries the flashlight.
Deliverable:
Do not write any code. Your solution should consist solely of the final minimal total time and a clear, step-by-step explanation of the optimal crossing strategy.
AI interview prep
Core dilemma
Optimally sequencing forward crossings and flashlight returns to minimize total elapsed time, where return trips are pure overhead and the slowest person dictates crossing time for a pair.
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Find minimal time for four people crossing
Problem: The Bridge and Flashlight Puzzle
Four individuals need to cross a narrow bridge at night, and they possess only a single flashlight.
Constraints and Rules:
- Each person
ihas a distinct, known timet_irequired to cross the bridge alone. - A maximum of two people can be on the bridge simultaneously.
- The flashlight is mandatory for any crossing and must be carried by the person(s) crossing.
- When two people cross together, their crossing time is determined by the slower of the two, i.e.,
max(t_a, t_b). - The flashlight cannot be transferred across the bridge by any means other than being physically carried by a person walking back.
- You are provided with the four positive integer crossing times:
t1, t2, t3, t4. For simplicity, assume these times are already sorted in non-decreasing order:t1 <= t2 <= t3 <= t4.
Tasks:
- Devise a strategy, detailing the sequence of crossings and returns, that achieves the absolute minimum total time for all four people to successfully reach the other side of the bridge, with the flashlight also ending up on the destination side.
- Clearly express this minimal total time using the given variables
t1, t2, t3, t4. Provide a step-by-step description of the optimal crossing sequence, specifying who crosses in each direction and who carries the flashlight.
Deliverable:
Do not write any code. Your solution should consist solely of the final minimal total time and a clear, step-by-step explanation of the optimal crossing strategy.