By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. So i have this program that should solve a futoshiki puzzle in C wich is loaded from a text file having this formatting :.

So I've managed to load the file, to check if it satisfies the math operators conditions, but I'm stuck on the recursive function. Did i choose the right way to store the matrix or I've should have divided the numbers from the logical operators?

How could I perform an recursive expansion on the matrix and how could I track the used number in a certain step in case I would have to backtrack? The way you store the matrix shouldn't matter too much.

This algorithm does a brute-force recursive search, trying every possible value for each spot, and backtracking if it enters an illegal state.

In the super-worst case, it runs in exponential time, but in practice, the isValid call at the beginning will short-circuit any obviously infeasible branches, so it should finish reasonably quickly for a 5x5 input. These checks should ignore spots whose value is 0, since they are just a placeholder meaning "not filled in yet". If you're concerned about speed, it should find a spot with the least number values that can be legally entered.

This will reduce the width of the search tree pretty considerably. After the -- start the rules, the meaning is clear to me at least : value at row 1, column 3 must be greater than value at row 2, column 3. When you have completed the preceding steps you have a partially maybe fully if you're lucky solved matrix, then you have to write a core function that tries every combination but considering the dynamic rules those in the file and the static rules those that make the game.

Learn more. Futoshiki C recursive solver Ask Question. Asked 8 years, 2 months ago. Active 7 years, 7 months ago. Viewed 4k times. So I've managed to load the file, to check if it satisfies the math operators conditions, but I'm stuck on the recursive function What I'd like to know: Did i choose the right way to store the matrix or I've should have divided the numbers from the logical operators?

Tim Lucian Enache Lucian Enache 2, 4 4 gold badges 27 27 silver badges 52 52 bronze badges. I'd keep numbers and operators separate. I'd also keep horizontal and vertical operators separate too. After all, you only ever want to update the numbers when solving, not the operators. Are you sure the example puzzle you posted has a solution? Working it out by hand, I keep getting two 1s in the second row from the bottom.

Could you provide the solution, then? Naturally, any good question about an algorithm ought to have a sample input and expected output Active Oldest Votes. Finally, setValue should set the given spot to the given value. Kevin Kevin Now I have to go out but I'll look into the code you posted tommorow and tell you if I find it useful,at the first look seems very well commented, thanks for the effort. I would remove the matrix size. About the solver, I would start as follows: search in the matrix if there's a rule involving a cell with a 2 that must be greater than another cell.

If yes, you can immediately insert a 1 in the other cell repeat point 1 for the entire matrix, so that you'll get a new, partially solved matrix as a starting point Same thing as above with 4s with the rule "less than".If you like Sudoku, then you'll love Futoshiki.

Futoshiki is another popular Japanese numeric puzzle game. Your aim is to put numbers from one to five in each row and column, so they do not repeat themselves. Numbers must also respect the relational signs placed between some cells. The game includes a generator offering the player three difficulty levels, from easy through medium to hard. For each generated puzzle only one unique solution is guaranteed. Your goal is to fill cells with numbers Each number can occur in row and column only once You also have to obey inequality signs between cells Tapping on selected cell toggles notes mode on and off Your goal is to fill cells with numbers Each number can occur in row and column only once You also have to obey inequality signs between cells Tapping on selected cell toggles notes mode on and off.

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### How to solve Futoshiki puzzles successfully

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On a bored August afternoon in I attempted a selection of logic games and became stuck on a particular Futoshiki puzzle. I decided that the task of a Futoshiki namely to order the numbers in each row and column fulfilling the logic present would be a reasonably simple puzzle for a computer program to solve, and that instead of figuring out the next step I should instead write a program to do the work for me. The first task was to setup a logic structure for the puzzles. I decided to split the logic and number sections into separate 2D arrays listsand wrote a function to print the two together.

The raw logic input is done in an easily readable way, however to use it practically one wishes to know what the logic is surrounding each square. A quick task, but a very important one, is to check that a solved Futoshiki is valid, that is that all squares fulfil the rules defined by the logic and only contain the numbers My validity checker valid puzzle, logic runs a logic tester on each square, but only checks the values right and below each square since it sweeps through all squares so those are the only tests necessary in this case the function could check all 4 neighbours but that would simply waste time.

Initially the solver assumes any of the numbers can go into each square, then gradually reduces the options by running through a set of algorithms.

When a consistent set is found, the values are returned so a human can see what the computer "thinks" should go where. This also showed where the computer was unsure ie there was more than one option left for a squarewhich highlighted when a new algorithm was needed.

A simple way of doing this is to ensure that "5" isn't an option in any location that is "less than" another, and that "1" isn't an option in any location "more than" another. My functions go a step further and examine the possible values in neighbouring squares, only allowing those that make logical sense. I'm particularly proud of the recursive nature of the function, which will check if there is logic restricting neighbouring squares and re-run itself so that changes are rippled through logic-linked cells.

A simple thing to see when looking at the list of possible values for a line or column is that a single number is only able to go in one location. This is a slightlier trickier strategy to code and explain. If two positions in a line have the same two possible values, then this pair of options cannot feasibly be possible values for any other place in the line. The same can be said for three positions with three matching possible values and so on, but also if the same three possible values are shared across a 2, 3, 3 number of possible values configuration across three positions.

This logic could be extended to 3, 3, 4, 4 setups but would involve more complex checks and likely not help with narrowing down options. As a task in proper Python structuring, I decided to re-write my code to be object-oriented, and thus usable as a library more easily. This restructuring led to some algorithm re-factoring, most notably that I rethought my logic recursion to run from a top-down or bottom-up approach, leading to fewer iterations required through the puzzle for a completed solution to be found.

If the program can solve a puzzle using its algorithms it returns the puzzle for a user to try. If the program cannot, it generates a new set of logic and tries again. If we create more complex solution algorithms then the generated puzzles will in turn become more complex.

Since the current algorithms are ones that I think are easily understandable, the generated puzzles are not too complex. One issue at the moment is that starting to brute force puzzles from the minimum possibility cells leads to 'solvable' puzzles where some of the logic has already been used and those numbers filled in. A very useful improvement to the current program would be in the brute forcing algorithm. Currently the algorithm 'guesses' as few numbers as possible and uses its algorithms to try and solve after that.

This means that possible values are always selected from a valid list, however occasionally it also results in situations where there are no possible values for a certain cell raising a KeyError.

An improved algorithm would handle these exceptions to infer whether the last attempted value for a cell can therefore be ignored as incorrect, however currently the next value is simply attempted. Running the solution algorithms on 9x9 grids or any complex puzzles each time a new value is guessed results in slow operation which must be able to be sped up. At one point I considered whether multithreading the application might be the solution for example brute forcing different cells in different threads but I think changing the algorithm itself will lead to the best solution.

Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.Account Options Sign in. Top charts. New releases. Futoshiki Aliaksandr Uvarau Puzzle.

Add to Wishlist. What is Futoshiki? Futoshiki is a funny logic puzzle game from Japan. In this game you need to fill all cells with numbers. Some cells can be filled initially, the rest is filled by the player.

The game is very similar to the game "Sudoku", but it has a difference. On the playing field, in addition to numbers, there may also be signs more, less. The sign between two cells means that one number is greater than the other.

A correctly filled square must satisfy the following three conditions: 1. The numbers in each line should not be repeated. The numbers in each column should not be repeated. If there are signs arrows on the field, then the condition must be met. One number is smaller than the other.

In the program you can choose 6 difficulty levels 4x4, 5x5, 6x6, 7x7, 8x8 and 9x9. The larger the square, the more difficult it is to go through. If you play Futoshiki for the first time, we recommend that you start with a 4x4 square. At each level of complexity you will be offered unique game levels. The higher the number the more difficult. Level is the most complex.Account Options Sign in.

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Futoshiki Kerem Baydogan Puzzle. Add to Wishlist. If you were seduced by Sudoku, prepare for Futoshiki fever - The Guardian Futoshiki may look straightforward, but the experienced puzzler knows not to be fooled by appearances.

You will love Futoshiki A simple and challenging puzzle game that will enhance your mental flexibility! With beautiful graphics and killer features, Futoshiki Free is the best brain-teaser puzzle for Mobile. No more tedious switching between entry mode and note mode to complete your puzzle.

Top class puzzles with selectable level of difficulty. With 6, total puzzles, you won't run out of puzzles any time soon. No blurry graphics. Everything is crystal clear. Download now to see it with your own eyes. Download Futoshiki for Free! Reviews Review Policy. Minor Bug Fixes. View details. Flag as inappropriate. Privacy Policy. See more. Aliaksandr Uvarau. Entertaining logic game, levels. Lunar Interactive Arts.

NINES is a new and exciting hexa block puzzle game. Slitherlink X. Ejelta LLC. Find a hidden closed loop by following numeric clues.Futoshiki Solving Tips Futoshiki is a simple and fun logic puzzle, that is great when you have a few minutes to spare for 5x5 puzzles or considerably longer for large puzzles which are usually 7x7 in size, but sometimes even 8x8 or possibly 9x9.

Chains where all the cells are in a region are also useful. For instance, if a c is the pattern facing you, and the three cells are in the same region, then you know that 'b' must be at least 3, whilst 'a' and 'c', as stands to reason, cannot be 5.

Note that a c where, say, a is in the same row as b and c in the same column, we cannot say that 'b' must be at least three, as 1,2,1 would be a valid solution. The common rules of sudoku are also useful in futoshiki, particularly when you have placed quite a few numbers then the once-per-row and once-per-column rule are useful.

With the hard futoshiki puzzles in the Guardian, you will also need to look at the sets of possible candidates. For instance, if you know that the candidates for a region are 34, 35,and in a 5x5 puzzle then you can see that cells three and four must contain the 1 and the 2, so this can be whittled fown to 34, 35, 12, 12, Play Futoshiki Puzzles Online.

In the following tutorial, basic and advanced techniques for solving Futoshiki puzzles are presented step by step, with accompanying illustrations to show-case the methods on specific board configurations.

The starting point for reaching a solution is the definition of the game itself: Futoshiki requires the user to find out a board where every digit appears once on every row and column, by respecting the board's inequalities. By using this criterion, progress towards a solution can be made by completing, step by step, empty board squares with specific digits because they are the only way to respect the board's restrictions. If a square's column and row already contain all possible digits, except one, then that square must contain the missing digit.

In the example above, the green square must be 4 since it would not be allowed to have any other value as the other possible digits are already found in its row or its column. The length of the chain guarantees that this sequence is the only possible solution that satisfies the monotone condition imposed by the inequality chain.

Squares that are less than 2 must implicitly have the value 1 as it is the only admissible value on the board which respects that condition. Similarly, squares that are greater than the board size minus 1 must be equal to the board size.

In the example above, the only possible value for the green square less than 2 is 1. Squares that are greater than other squares cannot be 1the lowest value allowed on the board, as there is no value smaller than 1.

Similarly, squares that are lower than other squares cannot contain the max allowed value, as there would be nothing greater to be filled on the other side of the inequality. In the example above, 1 cannot be filled in the red squares as they are all greater than other board squares, so the only possible placement for 1 on the first row of the board is the green square. Sometimes multiple rules must be used in order to reach a conclusion.

This is the case in the example above, where we try to place the value 1 on the second row of the board. The first red square is eliminated due to a column exclusion we already have a 1 on that columnwhile the second and third red squares are eliminated due to an exclusion of min values as those places have 'greater than' inequalities associated with them. Therefore the green square remains the only possible place for placing 1 in that row. Sometimes, especially on difficult boards, there are no other ways to figure out the correct digit for a square except for diving into the implications of each possibility until a contradiction is reached.

In the example above, all red and orange squares are initially blank. We want to figure out if the square A contains 1 or 2. We assume that it contains 2 and we check to see if we reach a contradiction based on this assumption.

## Futoshiki Solver

If square A has a 2then square B would have a 1 the only remaining value on the bottom row. Square C can be 1 or 2 as it has a chain of inequalities that requires to have available 2 greater numbers, but now it cannot be 1 due to the column exclusion of square B, so square C is a 2and square D is a 3 the only value between 2 and 4.

Due to column exclusions, square E is 1 and square F is 3. Now, if we look at the orange squares, we notice the contradiction: if square G were to be 2square H would have to be either 3 or 4which are not allowed due to a row exclusion. If square G were to be 3square H would have to be 4 which is not allowed due to the same reason.

### More or Less (Futoshiki)

As we've ran out of possibilities for square G, it means that we've reached a dead-lock and our initial assumption was wrong: 2 is not a valid move for square A, so we can go ahead and place 1 in it, the only other possible value. We've shown above how to solve a Futoshiki puzzle successfully by covering a range of techniques that can help you deduce the next move even in difficult situations.

The other key ingredient for becoming proficient and fast at solving Futoshiki puzzles is experience: the more you practice, the better and faster you'll become.

If you're up for a challenge, you can play right now a random Futoshiki puzzle by clicking the button below. Good luck! Play Futoshiki.

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