Wed, 03 Mar 2021

Solving puzzles need more than arranging blocks or writing numbers in rows and columns. Instead, it requires luck, puzzle-solving strategies, and logic. Recently, players found that you can solve Sudoku free puzzles by using algorithms. These algorithms are mostly used to find answers to advanced games. Some gamers even predict that algorithms may dominate puzzle-solving techniques in the future. This article discusses some algorithms that can help you to solve your morning Sudoku smartly.

1. Backtracking

This algorithm is one of the methods that expert players use to find solutions to tricky Sudoku puzzles. It's vital, especially when you're stuck and can't move to the next level. When it realizes that the number can't complete a level, it'll backtrack or drop and return the player to the previous level so that they can start a new analysis.

Using backtracking to solve Sudoku is excellent because it has the problem and ends target in mind. However, for various programs using backtracking to be effective, they need to comply with its constraints. Though backtracking uses logic and insights to create solutions, sometimes it may result in random guessing.

It functions by defining the problems of the game and verifying every individual candidate. In most Sudoku puzzles, candidates will be valid if they meet some constraints. These algorithms' goal is formulated to resemble that of the game-the aim is to fill the numbers in each row, column, and 3 x 3 region.

Most backtracking algorithms employ elimination conditions to prevent infinite looping while trying to find answers to problems. A termination condition will happen when there are no empty spaces left for the algorithm to verify, and the current candidate can't reach the goal. It may also occur if the grid is full and has no white space left.

Some pros of using backtracking include a guaranteed solution provided that the candidates are verified and valid, minimized solving time for even the most difficult levels, and simplicity of use.

However, backtracking needs patience because it may take quite some time before creating a solution. It's slower than other algorithms that use deductive methods and require between 15000 and 900000 to create a solution for a complicated puzzle. Also, some Sudoku puzzles are done with programs that repel backtracking. This may prevent the player from making a solution, significantly if they're solving the puzzles from top to bottom.

Some players found that backtracking may take up to 6 hours to find a Sudoku puzzle solution. Therefore, as much as it's advisable to use this algorithm to come up with solutions quickly, you also need to complement it with other Sudoku-solving techniques to quickly find the right answers.

2. Crook's Algorithm

Crook's algorithm was created by a computer science professor, James Crook. He aimed to develop an algorithm that can help gamers to find Sudoku solutions physically. This algorithm uses Sudoku rules but assumes a more mathematical approach. Fortunately, its rules aren't complicated, and you can follow a few simple steps to find solutions to a challenging puzzle.

Here are the steps to follow:

  • Markup

In this step, you'll be required to write the possible numbers in every square. Most Sudoku apps have functions that enable players to write down possible numbers. However, you need to abide by the rules of writing the numbers to avoid getting stuck.

  • Finding Singleton

In this step, a player needs to find a row or column that can accommodate one possible value throughout the entire column or row. Because every row, column, and box only require one number, it'll give you a hint of the numbers you need in other cells. Once you locate the square with this number, upgrade the markups in the affected columns, boxes, or rows.

  • Finding Preemptive Sets

A preemptive set may occur when a particular set of numbers are within specific markup cells in the rows, columns, and boxes. Finding these numbers may be a little complicated and requires logical thinking. But when you find them, solving the puzzles become easier.

  • Eliminate Preemptive Sets

Eliminating the numbers in the combined cells is vital because it will reduce the possible cell numbers. That's because these numbers can't be possible numbers for cells outside the set. The rules require that only one number appear in every box, column, or row. This may only happen if the number isn't among the preemptive set.

  • Random-Based Algorithms

Random-based algorithms are also known as optimization or stochastic search methods. This method minimizes the number of mistakes when numbers are randomly assigned to blank squares and the number of errors calculated. When the mistakes go down to zero, you'll find a solution to the puzzle.

There are several ways for shuffling the numbers, including tabu search, simulated annealing, and genetic algorithm. Using these algorithms will get you your solutions fast, though you may have to use other deductive techniques as well. Also, because they don't need the challenges to be logic-solvable to get answers, you can use them to solve many difficult Sudoku problems.

Random-based algorithms view Sudoku puzzles as integer linear problems. That's why they generate their solution quickly and end up indicating whether the answer is valid or not valid. If the Sudoku has more than one answer, the algorithm will answer fractional amounts in more than one square.

Algorithms present vital steps that every player yearns for to solve puzzles. They'll help you identify critical variables and decision points that you need to know to develop the right solution. This identification also helps split the problem into more manageable units and is useful for solving challenging problems.

Because algorithms aren't rational, the decisions they make are more effective and consistent. They're more like reminder devices that help you locate smaller variables of challenging tasks that you may easily overlook. That way, they give you more accurate information that simplifies solving the puzzle.

Wrapping Up

As days go by, more Sudoku-solving algorithms will be invented to solve the most complicated puzzles easier. No doubt, using algorithms will help you find solutions that will otherwise take hours to locate quickly. However, they need you to understand their rules to be successful.

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