Intelligent Sudoku Solver

INTELLIGENT SUDOKU SOLVER
Under the Guidance of
Dr. SUNIL PATEKAR
Group Members:
1. Amrish Jhaveri
2. Rohit Iyer
3. Krutika Parab
UNIVERSITY OF MUMBAI
2012-2013

CONTENTS
I. INTRODUCTION
II. AIMS & OBJECTIVES
III. PROBLEM STATEMENT
IV. SCOPE
V. PROPOSED SYSTEM
VI. METHODOLOGY – Expert System
VII. BACKTRACKING ALGORITHM
VIII. PATTERNS
IX. DESIGN – Flow Chart
2
X. FEATURES
XI. CODE SNIPPETS

I. INTRODUCTION
 Rule:
Fill a given grid(9x9) with the numbers 1 to 9, so that every column,
row, and 3x3 box the numbers 1 to 9, keeping in mind that the same
number doesn’t repeat in that particular row, column or the 3x3 box.
3

II. AIMS & OBJECTIVES
 To successfully implement a novel approach to solve
computationally intensive problems like Sudoku.
 To solve the classical Sudoku puzzle in a much more efficient way
than a conventional Brute Force and Backtracking approach.
4

III. PROBLEM STATEMENT
 Our job is to place a number into every empty box so that each
row across, each column down, and each small 9-box square
within the large square (there are 9 of these) will contain each
number from 1 through 9. Remember that no number may appear
more than once in any row across, any column down, or within
any small 9-box square. The numbers will be filled with the
help of pattern matching.
5

IV. SCOPE
 Our project aims at solving Sudoku using pattern matching.
 Assumptions:
• Fixed Grid Size: 9 x 9
• Fixed Symbols: 1-9
• Limitations on the number of patterns implemented.
6

V. PROPOSED SYSTEM
 Our project uses five main modules:
1. Reading the input from file.
2. Search for patterns.
3. Provide solution.
4. Solve by Backtracking.
5. Compare the run-time.
7

VI. EXPERT SYSTEM
 In Artificial Intelligence, an Expert System is a computer
system that emulates the decision-making ability of a human
expert.
 It consists of a rule-base (permanent data), an inference engine
(process), and a workspace or working memory (temporary
data). Not part of the basic reasoning process, but essential to
applications, is the user interface.
8

VI. EXPERT SYSTEM
9

VI. EXPERT SYSTEM
 In our approach the components of expert system are as follows:
• Client interface is a command line interface or GUI.
• Knowledge base are set of data structures stored which contain prior
information needed to proceed.
• Rule translator is a function which translates the rule from human
understandable form to machine understandable form. For e.g. A function called
HiddenSingles() may translate the rule in such a way that the Rule Engine (in
our case – our main program)understands.
• Knowledge base editor would be a simple text editor which can change/add
the built-in rules in the code.
• Rule Engine is another function which checks every pattern if it matches a
rule or not. 10

VII. BACKTRACKING ALGORITHM
 We basically check that the same number is not present in
current row, current column and current 3X3 sub grid. After
checking for safety, we assign the number, and recursively check
whether this assignment leads to a solution or not. If the
assignment doesn’t lead to a solution, then we try next number
for current empty cell. And if none of number (1 to 9) lead to
solution, we return false.
11

VIII. PATTERNS
 NAKED SINGLE
 Any cells which have only one candidate can safely be
assigned that value.
 It is very important whenever a value is assigned to a cell,
that this value is also excluded as a candidate from all other
blank cells sharing the same row, column and box
12

 NAKED SINGLE
13
VIII. PATTERNS

 NAKED PAIR
 A Naked Pair (also known as a Conjugate Pair) is a set of two
candidate numbers sited in two cells that belong to at least
one unit in common. That is they reside in the same row, box
or column.
14
VIII. PATTERNS

IX. PATTERNS
 NAKED PAIR
15

 HIDDEN SINGLE
 Very frequently, there is only one candidate for a given
row, column or box, but it is hidden among other candidates.
 In the example on the right, the
candidate 6 is only found in the
middle right cell of the 3x3 box.
Since every box must have a
6, this cell must be that 6.
16
VIII. PATTERNS

 Locked Candidates -I
 Sometimes a candidate within a box is
restricted to one row or column. Since one of
these cells must contain that specific
candidate, the candidate can safely be
excluded from the remaining cells in that row
or column outside of the box.
VIII. PATTERNS

 Locked Candidates – I Example
In the example above, the right box only has candidate 2's in its bottom row.
Since, one of those cells must be a 2, no cells in that row outside that box
can be a 2. Therefore 2 can be excluded as a candidate from the highlighted
cells.
VIII. PATTERNS

 Locked Candidates – II
 Sometimes a candidate within a row or
column is restricted to one box. Since one of
these cells must contain that specific
candidate, the candidate can safely be
excluded from the remaining cells in the box.
VIII. PATTERNS

 Locked Candidates – II Example
In the example on the right, the left column
has candidate 9's only in the middle box.
Therefore, since one of these cells must be a
9 (otherwise the column would be without a
9), 9's can safely be excluded from all cells in
this middle box except those in the left
column.
VIII. PATTERNS

IX. DESIGN (FLOW CHART)
21
Yes
No
Yes
No
Reading Sudoku
from a file
Search patterns
Take necessary
action
Solved?
Print Solution
Stop
Start
Make a smart
guess Found

X. FEATURES
 A Java based Sudoku Solver
 Benchmarked at solving 49151 random puzzles within 16159
milliseconds.
 Used optimized pattern detection strategies like Naked Singles,
Hidden
 Singles and Locked Candidates to aid solving.
 Reviewed the performance of our solver with existing Sudoku
Solvers in the world.
 Comprehensive statistical and graphical results to record the solver's
performance using JFreeChart API.

We conducted a test on
some of the world’s popular
and fastest Sudoku solvers.
The test consisted of
solving 1000 very hard
puzzles.
We fed the same set of
1000 puzzles to all solvers
and result is here….

OUR OPPONENT….
… a puzzle took 15.5 billion nanoseconds!!!

OUR INTELLIGENT SOLVER….
… a puzzle took 25 million nanoseconds!!!

NO COMPARISON!!!
… can’t compare millions with billions!!!

XI. CODE SNIPPETS
28

XI. CODE SNIPPETS
30

XI. CODE SNIPPETS
32

Our paper titled -
has been reviewed
and accepted by International
Journal of Scientific Research
and Publications and will be
published in Volume 3, Issue
5, May 2013.

THANK YOU
 We would like to thank our project guide Dr. Sunil Patekar &
Prof Mahesh Bhave for helping us identify the flaws and correcting
them. We would also like to thank Assistant Professors Rugved
Deolekar and Aman Mahadeshwar for their inputs.
35

Intelligent Sudoku Solver

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