Expected Return Time Interview Questions
Expected return time interview prep for returning to states, hitting versus return time, Markov-chain intuition, and random-walk examples.
Advanced candidates working on random walks and Markov-chain-style interviews.
Return time versus hitting time
A hitting time asks when a process first reaches a target state. A return time asks when it comes back to a state after leaving or after at least one step.
Define the starting point
Return-time questions are sensitive to whether time zero counts. State whether the process starts at the state and must return after one or more moves.
Small-state examples
In a two-state chain that alternates every step, the return time to the starting state is exactly 2. More general chains need weighted equations.
First-step equations
Expected return times can be solved by conditioning on the next state and writing expected-time equations until the return state is reached.
Recurrence intuition
Some processes return quickly, some return eventually but slowly, and some may never return. Interview questions usually use finite or well-structured cases.
Common mistakes
Candidates often confuse returning to the current state with hitting a different target state. Name the target state and the first allowed return time.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.