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In a Snake and Ladder game design, what is the time complexity of checking and updating a player's position after a dice roll if snakes and ladders are stored in a hash map keyed by start position?

medium🪤 Complexity Trap Q5 of Q15

OOP & Design Patterns - Design Snake and Ladder Game - LLD End-to-End

In a Snake and Ladder game design, what is the time complexity of checking and updating a player's position after a dice roll if snakes and ladders are stored in a hash map keyed by start position?

AO(log n) if snakes and ladders are stored in a balanced tree

BO(1) average time due to direct hash map lookup

CO(n) where n is the number of snakes and ladders, due to iteration

DO(n^2) because each move triggers multiple lookups

Step-by-Step Solution

Solution:

Step 1: Identify data structure
Snakes and ladders stored in hash map keyed by start position.
Step 2: Lookup operation
Checking if current position has snake/ladder is a direct hash map lookup -> O(1) average.
Step 3: Update position
Updating player position is O(1).
Final Answer:
Option B -> Option B
Quick Check:
Hash map lookup is constant time on average [OK]

Quick Trick: Hash map lookup -> O(1) average [OK]

Common Mistakes:

MISTAKES

Assuming iteration over all snakes/ladders
Confusing balanced tree lookup with hash map
Overestimating complexity due to multiple moves

Trap Explanation:

PITFALL

Candidates often think checking all snakes/ladders requires iteration, missing direct hash map access advantage.

Interviewer Note:

CONTEXT

Tests understanding of data structure impact on operation complexity

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