Snapchat·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026Remote

Summary

Snapchat SWE interview with a tree-based game theory problem that looks like a standard DP question until you realize the two-player simultaneous movement makes it way messier than expected.

Questions Asked (1)

You're given a rooted tree where each node holds some coins. Player 1 starts at the root and moves toward leaves one edge at a time, collecting coins. Player 2 picks any starting node and moves toward the root one edge at a time, also collecting. They move simultaneously. If they land on the same node at the same time, coins split (floor for Player 1). Game ends when Player 1 hits a leaf or Player 2 hits the root. Player 1 maximizes coins, Player 2 minimizes Player 1's total. Both play optimally. Return Player 1's coin count.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at this for a solid minute before I even understood the meeting condition.

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AI HintsAI Generated

Suggested Approach

First, clarify the rules and edge cases (e.g., simultaneous moves, coin splitting, game termination). Then, model the game as a two-player zero-sum game on a tree, where Player 1 chooses a downward path and Player 2 chooses an upward path. Use dynamic programming or minimax with memoization to compute the optimal coin count for Player 1, considering all possible starting nodes for Player 2 and simultaneous moves.

Pro tip: Demonstrate strong problem-solving by discussing the time and space complexity of your solution and possible optimizations, such as pruning or iterative DP. Also, mention how you would handle large trees and whether the solution scales.

1. Clarify rules and constraints

Ask questions to confirm details: Are moves truly simultaneous? How are coins split exactly (floor for Player 1)? What if both reach the same node at different times? Can Player 2 start at any node, including the root? What if Player 1 starts at a leaf?

2. Model the game

Represent the tree with parent-child relationships. Define the state as (Player 1's current node, Player 2's current node, time step). Since moves are simultaneous, time step increments each turn. The game ends when Player 1 reaches a leaf or Player 2 reaches the root.

3. Define optimal strategies

Player 1 maximizes total coins, Player 2 minimizes Player 1's total. At each state, Player 1 chooses a child to move to (if not at leaf), Player 2 chooses a parent to move to (if not at root). If they land on the same node, coins are split: Player 1 gets floor(coins/2), Player 2 gets the rest.

4. Design DP/minimax solution

Use memoization to compute the value of each state. Since Player 2 can start at any node, iterate over all possible starting nodes for Player 2 and compute the minimum Player 1 total (since Player 2 minimizes). Player 1's optimal total is the maximum over Player 1's choices at each step.

5. Analyze complexity and optimize

The state space is O(N^2 * H) where N is number of nodes and H is height. Discuss possible optimizations, such as noting that Player 2's optimal start might be determined by tree structure, or using bottom-up DP. Consider if the game can be solved in O(N) or O(N log N) time.

Key Points to Mention

Simultaneous moves and coin splitting rule: floor for Player 1.
Game termination conditions: Player 1 hits a leaf or Player 2 hits the root.
Zero-sum game with perfect information; use minimax with memoization.
Player 2 chooses starting node to minimize Player 1's total; iterate over all nodes.
State representation: (node1, node2, turn) and transitions based on moves.
Time and space complexity: O(N^2 * H) naive, discuss optimizations.

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