Solving Sudoku requires more than just writing numbers in a column or row. Sitting down and playing a new Sudoku grid needs logic, puzzle-solving techniques, and a bit of guesswork. Knowing these can help you to solve even the most challenging puzzle.
This puzzle can be addictive, and that’s why some people still frequent bookstores to find exercises. Luckily, app developers also give such exercises through their apps. Besides that, some players are also using algorithms to find solutions for complicated puzzles. This article seeks to explain how algorithms will dominate Sudoku.
Reasons For Using Algorithms
Algorithms are steps that you require to solve a problem. It can be used to solve arithmetic problems like finding square roots or completing puzzles. Here are some reasons why puzzle players use algorithms:
- Quick At Solving Problems
Algorithms identify key decision points and variables that you need to solve problems. This identification divides the challenge into more manageable smaller steps. That means that problems that are difficult to solve because of their magnitude can be broken down into smaller units.
Because algorithms don’t reason like human beings, you can use them to make more efficient and consistent decisions. Algorithms function like reminder devices and help you identify smaller variables of challenging tasks that you can easily overlook. This way, you’ll get more accurate data and information that’ll make solving your Sudoku puzzles easier.
Using algorithms to solve puzzles can help you identify weaknesses and errors, preventing you from manually finding solutions. If you don’t understand how you arrived at a particular solution, you may not know the mistakes you made before arriving at that point. An algorithm can give you a detailed process that you can use to identify your errors.
Types Of Algorithms Used In Sudoku
Backtracking is a common algorithm that some players use to find solutions to puzzling problems. When it discovers that a number can’t solve the problem, it drops it (backtracks). That’s vital because it enables it to return to the previous stage and start analysis afresh.
Besides having the end goal and problem in mind, backtracking algorithms have constraints that programs should follow to be effective. The simplest implementation of backtracking uses little insight and logic to solve problems. However, instead of giving a practical solution, this program can lead to random guessing.
Backtracking defines the constraints of each project by verifying individual candidates. In Sudoku, a candidate is valid if the following constraints are true:
- 1-9 sub-grids have empty spaces or the numbers 1-9.
- Every row has distinct numbers from 1-9 or blank spaces.
- Every column has blank spaces or distinct numbers from 1-9.
Goal And Termination Conditions
The goal of Sudoku is similar to that of the algorithm. The goal is to fill the numbers from 1-9 in each column, row, and 3×3 region in this game. Most backtracking algorithms use a termination condition to avoid looping infinitely while looking for solutions to problems with no answers. They occur when:
- No empty spots are left for the algorithm to check, and the current candidate doesn’t reach the goal.
- The board is full, and there’s no white space.
Advantages Of Backtracking
- A guaranteed solution as long as the candidates are valid.
- It reduces the solving time regardless of the difficulty level.
- It’s simpler compared to other strong algorithms that are used in solving the most complicated puzzles.
- This algorithm may take longer to develop a solution than other developed algorithms using deductive methods. According to some programmers, backtracking algorithms may require as low as 15000 cycles or as many as 900000 cycles to find a solution to a Sudoku puzzle.
- Some Sudoku puzzles are developed to work against backtracking. That occurs when a player solves the puzzle from top to bottom. Puzzles with clues in the first rows that contain solutions can work against the algorithm. When this happens, the program may spend a lot of time counting before it gets to the grid that satisfies the puzzle. A programmer found that a backtracking program needed 6 hours to find a solution to Sudoku puzzles.
- Crook’s Algorithm
This algorithm was invented by a Winthrop University computer science professor known as James Crook. According to Crook, you can use this algorithm to solve a Sudoku puzzle physically. The algorithm implements the rules used in Sudoku though it takes a more mathematical approach. However, it doesn’t involve complex rules. Here are the steps you can use to solve Sudoku using Crook’s algorithm:
This step is relatively easy and requires you to list every possible number in each cell. If you’re playing Sudoku via an app, you can find a function that can allow you to write down some possible numbers. Just ensure you follow the rules of writing down the possible numbers.
- Find Singleton
The term singleton refers to locating if there’s a box, column, or row with one possible value throughout the box, column, or row. Since only one number is in each box, column, and row, the number should be in that cell if you find a cell with the respective number. Fill the cell with the number and update the markups in the affected box, column, or row.
- Find Preemptive Sets
This step is more complicated than the other two steps. Preemptive sets occur when a set of m numbers are within a markup of m cells in a box, column, or row. This combination of cells and numbers is called a preemptive set.
- Eliminate The Possible Numbers That Are Preemptive Sets
This is one of the most vital parts of this algorithm because it helps minimize the possible numbers of cells. The numbers in a preemptive set can’t be possible numbers for a cell outside the set. That’s because every number can only appear once in each box, row, or column. If this number is among the preemptive set, it must be placed in the set’s cells.
Because algorithms make solving Sudoku puzzles simpler, some players prefer using them. That’s because it can help them quickly find solutions to difficult problems requiring hours of working to come up with answers. Backtracking and Crook’s algorithm are some examples of programs that may dominate Sudoku in the future.