The “Snake & Ladder Problem” is a common technical coding interview question asked by companies like Google, Facebook, Amazon, and Microsoft during their recruiting process. This problem tests a candidate’s skills in graph theory, breadthfirst search algorithms, objectoriented programming, and solving problems proactively.
In this comprehensive guide, we will examine the Snake & Ladder problem statement, analyze the problemsolving techniques, implement an objectoriented solution in Python, and discuss tips to ace this interview question.
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Overview of the Snake & Ladder Problem
The Snake & Ladder problem emulates the classic board game where players roll a sixsided die to navigate from the start of the board to the end, moving ahead or back based on landing on spaces containing ladders and snakes.
In the coding interview version, the candidate must write a program to find the minimum number of dice rolls required to reach the final position on the board, given the board configuration of snakes, ladders, and normal spaces.
This question tests a coder’s ability to:
 Model the problem effectively using objectoriented principles
 Implement graph search algorithms like breadthfirst search
 Optimize the code for efficiency
 Analyze space and time complexity tradeoffs
To solve this, we will use the following problemsolving techniques:
 Objectoriented programming to model boards, dice, players, etc.
 Graph algorithms like breadthfirst search to find the shortest path
 Queues for efficient BFS traversal of game board states
 Hash tables to store visited states and prevent infinite loops
StepbyStep Python Solution
Below we will walk through a stepbystep solution to the Snake & Ladder problem in Python.
1. Model the Problem Domain
We first need to model the key components of the problem using OOP principles:
Board
The board will contain N rows and N columns of squares where N is the size of the board. Each square will have:
 A position number used as the unique ID
 A boolean flag indicating if it is the final square
 Reference to the next square based on dice value
Dice
The dice will represent a sixsided die with possible values 1 to 6. It needs:
 A
roll()
method that returns a random integer between 1 to 6
Player
The player keeps track of:
 Current position on board
 Number of dice rolls
The player requires:
 A
take_turn()
method to roll the dice and move position
Snake
Each snake contains:
start
: Starting position of the snakeend
: Ending position of the snake
Ladder
Each ladder contains:
start
: Starting position of the ladderend
: Ending position of the ladder
2. Implement the Board Class
We will implement the Board
class to model the game board:
import random
class Board:
def __init__(self, snakes, ladders, size):
self.board = [[0 for _ in range(size)] for _ in range(size)]
self.snakes = snakes
self.ladders = ladders
self.final_pos = size * size
# Initialize board squares
for row in range(size):
for col in range(size):
self.board[row][col] = row * size + col + 1
# Set final square flag
self.board[size1][size1] = 1
def move(self, position, dice_value):
The __init__()
method initializes the 2D matrix to represent the board, sets the final square flag, and maps position numbers to the matrix indices.
We encapsulate the snake and ladder configurations as constructor parameters so the board can be customized.
The move()
method will apply the snakes, ladders and dice logic to calculate the next position. We will implement it next.
3. Add Snakes, Ladders and Dice Logic
Let’s update the Board
class to apply the effects of snakes, ladders and dice when moving:
# Inside Board class
def move(self, position, dice_value):
next_pos = position + dice_value
# Wrap around for cyclic board
if next_pos > self.final_pos:
next_pos = self.final_pos
# Apply snake/ladder logic
if next_pos in self.snakes:
next_pos = self.snakes[next_pos]
elif next_pos in self.ladders:
next_pos = self.ladders[next_pos]
return next_pos
We increment the current position by the dice value to get the next position. To simulate a cyclic board, we wrap around if the position exceeds the final square.
Using dict lookups, we map the next position to the end of a snake or ladder appropriately.
This encapsulates all the game logic required for a single dice roll turn.
4. Implement the Player Class
The Player
class will model a player with a current position and number of dice rolls:
class Player:
def __init__(self, board, position=0):
self.board = board
self.position = position
self.no_plays = 0
def take_turn(self, dice):
dice_value = dice.roll()
self.no_plays += 1
self.position = self.board.move(self.position, dice_value)
The take_turn()
method rolls the dice, increments dice rolls counter, and updates player’s position using the underlying Board
logic.
5. Implement BreadthFirst Search
Now we need a way to simulate the game by exploring all possible dice roll sequences using breadthfirst search until we find the shortest path.
from collections import deque
def simulate(player):
queue = deque()
queue.append((player, 0)) # Tuple of (player, no_of_turns)
visited = set() # Track states already visited
while queue:
current_player, turns = queue.popleft()
# Check if current state is final position
if current_player.position == current_player.board.final_pos:
return turns
curr_state = (current_player.position, turns)
if curr_state in visited:
continue
visited.add(curr_state)
# Generate all possible dice rolls
for i in range(1,7):
player_copy = copy(current_player)
player_copy.take_turn(Dice(i))
queue.append((player_copy, turns+1))
return 1 # Unreachable final position
We use a BFS queue to explore all possible game states in sequence. We check if the current player state has reached the final position, returning the number of turns if true.
To prevent infinite loops, we store the visited (position, turns)
states in a hash set.
For each state, we generate new player instances for all possible dice rolls and add them to the queue with incremented number of turns.
This allows us to simulate playing the game iteratively until we find the shortest path.
6. Initialize and Run the Simulation
Finally, we need to initialize the board, player, and dice instances and run the simulation:
# Set board size
board_size = 30
# Set snake and ladder configurations
snakes = {...}
ladders = {...}
# Create components
board = Board(snakes, ladders, board_size)
player = Player(board)
dice = Dice()
print(simulate(player))
This will output the minimum number of dice rolls needed to complete the game.
Analyzing Solution Complexity
The above BFS approach provides an optimal solution as we are exploring all possible dice roll sequences in increasing order of turns.
Time Complexity: O(N!)
In the worst case where no shortcuts are available, the time complexity is O(N!) where N is the board size since we need to enumerate all permutations of dice rolls.
Having shortcuts reduces the complexity as paths are cut short.
Space Complexity: O(N)
We need O(N) space for the BFS queue, visited set, and recursive stack depth.
Tips for Acing the Coding Interview
Here are some tips to ace the Snake & Ladder interview question:

Clarify assumptions upfront  board size, dice type, winning criteria etc.

Think out loud while solving the problem to convey your thought process.

Use examples to explain your approach and verify solutions.

Pseudocode the algorithm before diving into implementations.

Use data structures intelligently like using BFS queues and hash tables.

Modularize code into functions/classes to make it extensible.

Test thoroughly with different input configs and corner cases.

Discuss tradeoffs like complexity, scalability, and optimizations.

Explain how you would improve the design, error handling, and refactoring of the code.
Practical Applications
The Snake & Ladder problem demonstrates fundamental concepts like graphs, search algorithms, OOP, recursion, and dynamic programming that are applicable in many domains:
Path Finding  Finding shortest path in route planning, network routing.
AI  Game simulations, state space exploration in AI agents.
Operations Research  Logistics optimization.
Bioinformatics  DNA sequence alignment.
Machine Learning  Prediction of sequence/time series data.
Conclusion
In this guide, we covered a stepbystep objectoriented approach to solving the Snake & Ladder coding interview problem in Python using breadthfirst search.
Key concepts included graph modeling, OOP principles, BFS traversal, hash tables, recursion, and modular design. Mastering these foundations will help crack not just this problem but a variety of other algorithm and data structure problems.
With diligent practice of core CS fundamentals, strong analytical skills, and clear communication, you can successfully solve challenging technical interview questions like the Snake & Ladder problem.