Mastering Sudoku Solver: A Comprehensive Interview Guide
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Chapter 1: Introduction to Sudoku Solver
In the realm of technical interviews, mastering algorithmic questions is crucial. One common challenge is developing a program to solve a Sudoku puzzle by filling in the empty spaces. The solution must adhere to the following rules:
- Each digit from 1 to 9 must appear exactly once in each row.
- Each digit from 1 to 9 must appear exactly once in each column.
- Each digit from 1 to 9 must appear exactly once in each of the nine 3x3 sub-grids.
In this context, the '.' symbol represents empty cells.
For example:
Input: board = [["5","3",".",".","7",".",".",".","."],
["6",".",".","1","9","5",".",".","."],
[".","9","8",".",".",".",".","6","."],
["8",".",".",".","6",".",".",".","3"],
["4",".",".","8",".","3",".",".","1"],
["7",".",".",".","2",".",".",".","6"],
[".","6",".",".",".",".","2","8","."],
[".",".",".","4","1","9",".",".","5"],
[".",".",".",".","8",".",".","7","9"]]
The output would be:
Output: [["5","3","4","6","7","8","9","1","2"],
["6","7","2","1","9","5","3","4","8"],
["1","9","8","3","4","2","5","6","7"],
["8","5","9","7","6","1","4","2","3"],
["4","2","6","8","5","3","7","9","1"],
["7","1","3","9","2","4","8","5","6"],
["9","6","1","5","3","7","2","8","4"],
["2","8","7","4","1","9","6","3","5"],
["3","4","5","2","8","6","1","7","9"]]
Section 1.1: Constraints and Approaches
The input board consists of 9 rows and 9 columns, containing either a digit or the '.' character. It is guaranteed that there is only one valid solution for any given input.
#### Subsection 1.1.1: Brute Force Method
Initially, one might consider a brute-force approach, generating all potential combinations of the digits 1 through 9 to fill in the cells. This method, however, is impractical due to the astronomical number of operations, specifically (9^{81}).
#### Subsection 1.1.2: Backtracking Technique
A more efficient strategy involves backtracking, which utilizes two primary concepts:
- Constrained Programming: This technique imposes restrictions after placing each number, thereby excluding that number from further use within the corresponding row, column, and sub-grid. This reduces the number of combinations to evaluate.
- Backtracking: If a number placement does not yield a valid solution, backtracking allows for the adjustment of previously placed numbers and the continuation of the search for a valid configuration.
Section 1.2: Implementing the Solution
To systematically approach the problem, we can use the following Python code:
from collections import defaultdict
class Solution:
def solveSudoku(self, board):
...
This code structure facilitates the backtracking process by checking valid placements and recursively filling the board until a solution is found.
Chapter 2: Video Resources
Here are two valuable video resources to help you further understand the Sudoku solving process:
The first video, "Pass Your Next Tech Interview With Valid Sudoku," provides insights into the interview process related to Sudoku solving techniques.
The second video, "GOOGLE INTERVIEW QUESTION - SUDOKU SOLVER (BACKTRACKING EXPLAINED)," dives deeper into the backtracking method and its applications in coding interviews.
Stay tuned for more engaging interview questions and insights from my experiences as a senior software engineer at MANNG.