TikTok·Machine Learning Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026Remote

Summary

TikTok ML engineer round, basically one meaty algorithm problem that took up the whole session. The follow-up discussion on pruning and worst-case inputs was where things got interesting.

Questions Asked (1)

Given a sorted array of distinct integers representing stone positions in a river (starting at 0), determine whether a frog can reach the last stone. The frog starts at position 0, its first jump must be exactly 1 unit, and each subsequent jump can be k-1, k, or k+1 units where k was the previous jump length (and must be greater than 0). Design an efficient algorithm, justify its correctness, and analyze time and space complexity. Also discuss pruning strategies and what inputs would hit worst-case behavior.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight to DP with a hash map keyed on stone index storing the set of jump sizes that can land there.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then propose a dynamic programming solution using a hash map to track reachable positions and jump lengths. Discuss optimizations like pruning and analyze complexity, and finally address worst-case inputs and potential improvements.

Pro tip: Mention that the problem is equivalent to the 'Frog Jump' LeetCode problem and that using a hash map of sets is more efficient than a 2D DP array when positions are sparse. Also, highlight that the algorithm can be adapted for streaming or large inputs by processing stones in order.

1. Understand the problem and constraints

Restate the problem to ensure clarity: the frog starts at 0, first jump must be 1, and subsequent jumps can be k-1, k, or k+1 where k is the previous jump length. Note that the array is sorted and contains distinct integers, and the goal is to determine if the last stone is reachable.

2. Design a DP approach

Use a hash map where keys are stone positions and values are sets of possible jump lengths that can reach that stone. Initialize with position 0 and jump length 0. For each stone, iterate through its possible jump lengths and update reachable stones by adding k-1, k, and k+1 (if positive).

3. Optimize with pruning and early termination

Prune jumps that go beyond the last stone or to positions not in the stone set. Also, if the last stone is reached, return true immediately. Consider using a set for stone positions for O(1) lookups.

4. Analyze correctness and complexity

Justify correctness by induction: the DP state correctly represents all possible jump lengths to reach each stone. Time complexity is O(n * m) where n is number of stones and m is average number of jump lengths per stone (bounded by O(sqrt(max jump))). Space complexity is O(n * m) for the DP map.

5. Discuss worst-case inputs and further optimizations

Worst-case inputs are those where many jump lengths are possible for each stone, such as stones placed at all positions up to a large number. Mention that the algorithm is efficient for sparse stones but can degrade if stones are dense. Potential optimizations include using bitsets or limiting jump lengths based on remaining distance.

Key Points to Mention

Dynamic programming with memoization using a hash map of sets.
State definition: dp[position] = set of jump lengths that can reach this position.
Transition: for each jump length k in dp[pos], add pos + k-1, pos + k, pos + k+1 if they are valid stones.
Pruning: ignore jumps that exceed the last stone or land on non-stone positions.
Time complexity: O(n * sqrt(max_distance)) in practice, but worst-case O(n^2) if many jump lengths per stone.
Space complexity: O(n * sqrt(max_distance)) for storing jump lengths.
Worst-case inputs: dense stone placements where many jump lengths are possible, e.g., stones at every integer from 0 to N.
Alternative approaches: BFS with memoization, or using a 2D boolean array if positions are dense.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.