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Sudoku Solver Comparison. A comparative analysis of algorithms for solving Sudoku. What is a Sudoku Puzzle?. A pencil-and-paper puzzle, much like a numeric crossword puzzle A special type of latin square Seen in many newspapers, including our own K-State Collegian A highly-connected CSP

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sudoku solver comparison

Sudoku Solver Comparison

A comparative analysis of algorithms for solving Sudoku

what is a sudoku puzzle
What is a Sudoku Puzzle?
  • A pencil-and-paper puzzle, much like a numeric crossword puzzle
    • A special type of latin square
    • Seen in many newspapers, including our own K-State Collegian
  • A highly-connected CSP
    • Typical 9 x 9 configuration
      • 81 variables, each constrained by 24 other variables
      • Total of 972 constraints
      • A valid solution is a 9-coloring of the constraint graph
sudoku rules
Sudoku Rules
  • Common Sudoku puzzles are a 9 x 9 grid of 81 cells
    • There are 9 rows and 9 columns
    • Also divided into 9 3 x3 boxes
    • Each cell can hold one number, an integer between 1 and 9, inclusive
    • Some subset of the cells are given
    • Each number can only appear once in each row, column, and box
    • Valid Sudoku have enough cells given that there is a unique solution
sudoku images
Sudoku images

Solved

Given

algorithms
Algorithms
  • General constraint satisfaction algorithms
    • Backtracking search
      • A “brute force” approach
      • Serves as the baseline
    • Backtracking with MRV
      • Look for values that are the “most constrained” in the current state
  • Sudoku specific algorithms
    • Human-like approach
      • Avoid guessing (and backtracking!)
    • Some additional constraints can be deduced from values of non-adjacent cells