Takuzu Solver (Easy mode)

Statement

Goal

Takuzu (aka 'Binary Sudoku' or 'Binairo') is a variant of Sudoku that only allows the numbers 0 and 1. The following three rules must be met for a valid solution:
1. Each row and column must contain an equal number of 0s and 1s (e.g. 5 of each for a 10x10 grid).
2. No row or column may contain a sequence of three or more repeating digits (e.g. 1 1 0 is valid but 1 1 1 is invalid) (Hint: you can solve this 'Easy mode' puzzle with just this rule)
3. No rows (or columns) can be duplicates of other rows (or columns).

Given an integer n and an incomplete nxn binary grid of 0s and 1s, with . symbols for unknown values, complete the grid by replacing all the unknown values with 0s and 1s, obeying the required rules.

There will only be one valid solution.

Hard version: https://www.codingame.com/training/hard/takuzu-solver (Hint: you will need to include a backtracking algorithm and use all three rules)

Input

Line 1 : An integer n, the size of the grid (always even)
Next n lines : A row of n characters: 0, 1 or . (for unknown values)

Output

n lines : The completed board, with all . replaced with valid 0s and 1s, following the rules.

Constraints

4 < n < 16
n is even
All boards have a single valid solution
All boards can be solved using rule 2 alone (easy mode).

Example

Input

6
.0...1
0.11..
..1..0
.1...0
....1.
11.0.0

Output

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+13

Make the contribution public (lvl 20+)

Comments

32 Comments

SackPhantom Unnamed CodinGamer

about 5 months ago

✅ Approved the contribution. Comment: Nice work! It’s a good starting point for solving Takuzu puzzle! Thanks for your submission! 🚀

FredericLocquet Unnamed CodinGamer

about 5 months ago

✅ Approved the contribution. Comment: Very nice puzzle, I didn't know this takuzu! This exercise can be solved with only rule number 2, so it's rather easy to code. Well done !

SackPhantom Unnamed CodinGamer

about 5 months ago

Hello, What makes this version an easy one ? How are grid made so they are "easy" ? Is there a way to explain it more clearly in the statement ? Right now, apart from the "hint", there is no way to differentiate it from an harder Takuzu: am I right ?

StepBack13 Unnamed CodinGamer

about 5 months ago

Hi, thanks, I've put two hints in the statement and mentioned it again in the constraint to make it extra clear. It's easy because you only need to use rule 2 to find the correct solution. For other boards (hard version), you'd need to check the other 2 rules to further investigate boards that appear to be solutions, but would actually fail those other rules. For this puzzle, there will only ever be a single board that passes rule 2, so no further investigation is needed. Which means you don't need a backtracking algorithm.

DeanTheMachine Unnamed CodinGamer

about 6 months ago

✅ Approved the contribution. Comment: Knowing that only Rule 2 is needed kept my solution simple.

CodinBot Unnamed CodinGamer

about 6 months ago

Hey CodinGamer! Your contribution has unfortunately not been moderated on time and will temporarily be removed from the system... But no worries! You can republish it anytime to give it another chance! :)

Pepperonies Unnamed CodinGamer

about 6 months ago

✅ Approved the contribution. Comment: Really funny, haha !

StepBack13 Unnamed CodinGamer

about 6 months ago

Was this a scripted, generic comment? It's strange, your comment doesn't seem to relate to this puzzle (nothing funny about the puzzle). Also, your approval has not been recognised by the system (it still says 1/3 approved, with np_C0dM91 as the only approver).

np_C0dM91 Unnamed CodinGamer

about 6 months ago

✅ Approved the contribution. Comment: This puzzle was easier to test out in different test cases. Also, I love the problem because I used backtracking while applying Rule 2 (no three consecutive digits) as the primary constraint for solving "easy mode" puzzles. I hope that more people will appreciate the puzzle.

StepBack13 Unnamed CodinGamer

about 6 months ago

This didn't get enough approvals in the end, but if you were able to approve again this time, it might. :)

CodinBot Unnamed CodinGamer

about 7 months ago

TimesCantCode Unnamed CodinGamer

about 7 months ago

Great work implementing the Takuzu solver using just Rule 2 — impressive that you solved all test cases without backtracking! Your logic cleanly avoids triplets and respects the constraints. For future improvements, consider layering in Rule 1 (equal 0s and 1s) as a secondary heuristic — it could speed up convergence in edge cases. Also, really appreciate how readable your code is for an NxN board. Keep it up!

np_C0dM91 Unnamed CodinGamer

about 7 months ago

This puzzle was great. I loved that the values in the code allowed me to generate a binary grid. I look forward to other inspiring puzzles.

CodinBot Unnamed CodinGamer

about 8 months ago

I hope you received enough feedback from the community to improve your contribution. Once you have made the necessary updates, publish your contribution!

Timinator Unnamed CodinGamer

about 8 months ago

I'm still undecided on your puzzle. I have two more concerns: 1) Because your puzzle is meant to be solved strictly with logic, there is no way to create a test case that makes sure the user's code addresses your 3rd rule of Takuzu. The only way to test the 3rd rule is to have a test case that cannot be solved without guessing. 2) As designed, your test cases do not require any attention to your 1st rule of Takuzu. How do I know that? Your solution does not ever test for equal numbers of 0s and 1s in a line. Could a test case be designed that really did require the algorithm to use rule #1 to get to a solution? I don't know. If you determine it could be done, then an appropriate test case should be added. What you have right now is not really a Takuzu test suite. It is a test suite that requires an algorithm that ensures no row or column has a sequence of three or more repeating digits. The algorithm does not need to concern itself with any other rules of Takuzu. Maybe your puzzle shouldn't really be related to Takuzu? Maybe it should just be a logic puzzle, that happens to be a little bit like Takuzu? Could you vary the number of consecutive digits that cause a rules violation in addition to the number of rows/columns?

StepBack13 Unnamed CodinGamer

about 8 months ago

Thanks for sharing and sorry I missed this comment til now. I intentionally wanted this puzzle to only rely on one of the rules, which is what would make it an easy stepping stone towards the hard version. Before I realised someone else already had a hard version, I was thinking I'd make a medium version that needs all three rules, but doesn't require any backtracking, then a hard version that requires everything. I mention in the statement and constraints that you only need rule 2 to solve this, but all answers do conform to all three rules. If you go to https://www.binarypuzzle.com/... and stick to small, easy puzzles. Just using rule 2 is enough to solve pretty much all of them. So this challenge represents the basic skills needed to start solving Takuzu puzzles, while the hard version represents the skills needed to solve Takuzu of *any* difficulty (up to large, very hard ones). I would rather keep it related to Takuzu than change it so that it's a different problem. To me, this is Takuzu on "easy mode" where the trickier rules aren't needed, because all of the test cases I've given are taken from "Easy" examples on that site.

Timinator Unnamed CodinGamer

about 9 months ago

Having already solved Takuzu Solver, your puzzle took me about 3 minutes - 2 minutes to find and then cut and paste my Takuzu Solver code and then <1 minute to change my input. I think you have an uphill battle getting this puzzle approved due to it not being unique. My suggestion is that you try repositioning this puzzle as a stepping stone for Takuzu Solver: 1 - Reformat all your input/output to match Takuzu Solver. 2 - Reword your goal statement to match Takuzu Solver as much as possible 3 - An explanation of how the logic techniques used in this puzzle, combined with a backtracking algorithm, such as Algorithm X, is what is needed to solve the hard version. Obviously, there is nothing in your puzzle that doesn't already exist in Takuzu Solver. If you are going to get this approved, I think you need to sell the community on why an easier "skill building" puzzle is good for Takuzu Solver that has only been solved 101 times in 2+ years. If it were me, I would reach out to the Takuzu Solver author to get another opinion - probably after doing 1, 2, and 3 above. Without that author's support, I think your chances of approval drop quite a bit.

5DN1L Unnamed CodinGamer

about 9 months ago

I agree with @Timinator. A very compelling reason must exist to justify another Takuzu puzzle.

StepBack13 Unnamed CodinGamer

about 9 months ago

Notes to self: https://www.binarypuzzle.com/... (can get puzzles from here, then use below JS to scrape the puzzle) a=[...document.querySelectorAll( 'p[id^=celpar]')].map(i=>i.innerText=="" ?"_" :+i.innerText); l=parseInt(a.length**0.5); b=[l]; for(i=0;i<l;i++){b.push(a.slice(i*l, i*l+l.join(" "))};b ATO.pxeger.com link for multi-solving: https://ato.pxeger.com/...

StepBack13 Unnamed CodinGamer

about 9 months ago

Similar contributions: Binary Sudoku Error Checker: https://www.codingame.com/... Binario Grid Validator: https://www.codingame.com/...

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