Danyel Koca Danyel Koca

How to Algorithmically Solve Sudoku Using Javascript

Published: May 27, 2024

How to Algorithmically Solve Sudoku Using Javascript

Background

In a previous blogpost, I had written about how to create a complete sudoku grid like below. (Note that this sudoku grid is created in real time, so whenever you are visiting this page, the grid will change)

5
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6

This is a follow-up post, where we will create a sudoku game out of this grid by removing some of the numbers and develop an algorithm to solve it.

Sudoku Data Generation

The most difficult part of creating and solving a Sudoku game is creating the complete grid, which we already solved. There are 81 numbers in the grid, and we store those numbers in an array of size 81. This is how the generated data looks like:

let grid = [{ "row": 0, "col": 0, "block": "0-0", "value": 5 },

{ "row": 0, "col": 1, "block": "0-0", "value": 3 },

{ "row": 0, "col": 2, "block": "0-0", "value": 2 },

{ "row": 0, "col": 3, "block": "0-1", "value": 9 },

{ "row": 0, "col": 4, "block": "0-1", "value": 8 },

{ "row": 0, "col": 5, "block": "0-1", "value": 6 },

{ "row": 0, "col": 6, "block": "0-2", "value": 1 },

{ "row": 0, "col": 7, "block": "0-2", "value": 4 },

{ "row": 0, "col": 8, "block": "0-2", "value": 7 },

{ "row": 1, "col": 0, "block": "0-0", "value": 1 },

{ "row": 1, "col": 1, "block": "0-0", "value": 9 },

{ "row": 1, "col": 2, "block": "0-0", "value": 8 },

{ "row": 1, "col": 3, "block": "0-1", "value": 4 },

{ "row": 1, "col": 4, "block": "0-1", "value": 5 },

{ "row": 1, "col": 5, "block": "0-1", "value": 7 },

{ "row": 1, "col": 6, "block": "0-2", "value": 3 },

{ "row": 1, "col": 7, "block": "0-2", "value": 6 },

{ "row": 1, "col": 8, "block": "0-2", "value": 2 },

{ "row": 2, "col": 0, "block": "0-0", "value": 7 },

{ "row": 2, "col": 1, "block": "0-0", "value": 6 },

{ "row": 2, "col": 2, "block": "0-0", "value": 4 },

{ "row": 2, "col": 3, "block": "0-1", "value": 3 },

{ "row": 2, "col": 4, "block": "0-1", "value": 2 },

{ "row": 2, "col": 5, "block": "0-1", "value": 1 },

{ "row": 2, "col": 6, "block": "0-2", "value": 9 },

{ "row": 2, "col": 7, "block": "0-2", "value": 5 },

{ "row": 2, "col": 8, "block": "0-2", "value": 8 },

{ "row": 3, "col": 0, "block": "1-0", "value": 4 },

{ "row": 3, "col": 1, "block": "1-0", "value": 7 },

{ "row": 3, "col": 2, "block": "1-0", "value": 5 },

{ "row": 3, "col": 3, "block": "1-1", "value": 1 },

{ "row": 3, "col": 4, "block": "1-1", "value": 3 },

{ "row": 3, "col": 5, "block": "1-1", "value": 2 },

{ "row": 3, "col": 6, "block": "1-2", "value": 6 },

{ "row": 3, "col": 7, "block": "1-2", "value": 8 },

{ "row": 3, "col": 8, "block": "1-2", "value": 9 },

{ "row": 4, "col": 0, "block": "1-0", "value": 2 },

{ "row": 4, "col": 1, "block": "1-0", "value": 8 },

{ "row": 4, "col": 2, "block": "1-0", "value": 6 },

{ "row": 4, "col": 3, "block": "1-1", "value": 5 },

{ "row": 4, "col": 4, "block": "1-1", "value": 7 },

{ "row": 4, "col": 5, "block": "1-1", "value": 9 },

{ "row": 4, "col": 6, "block": "1-2", "value": 4 },

{ "row": 4, "col": 7, "block": "1-2", "value": 3 },

{ "row": 4, "col": 8, "block": "1-2", "value": 1 },

{ "row": 5, "col": 0, "block": "1-0", "value": 3 },

{ "row": 5, "col": 1, "block": "1-0", "value": 1 },

{ "row": 5, "col": 2, "block": "1-0", "value": 9 },

{ "row": 5, "col": 3, "block": "1-1", "value": 6 },

{ "row": 5, "col": 4, "block": "1-1", "value": 4 },

{ "row": 5, "col": 5, "block": "1-1", "value": 8 },

{ "row": 5, "col": 6, "block": "1-2", "value": 2 },

{ "row": 5, "col": 7, "block": "1-2", "value": 7 },

{ "row": 5, "col": 8, "block": "1-2", "value": 5 },

{ "row": 6, "col": 0, "block": "2-0", "value": 6 },

{ "row": 6, "col": 1, "block": "2-0", "value": 5 },

{ "row": 6, "col": 2, "block": "2-0", "value": 7 },

{ "row": 6, "col": 3, "block": "2-1", "value": 2 },

{ "row": 6, "col": 4, "block": "2-1", "value": 9 },

{ "row": 6, "col": 5, "block": "2-1", "value": 3 },

{ "row": 6, "col": 6, "block": "2-2", "value": 8 },

{ "row": 6, "col": 7, "block": "2-2", "value": 1 },

{ "row": 6, "col": 8, "block": "2-2", "value": 4 },

{ "row": 7, "col": 0, "block": "2-0", "value": 8 },

{ "row": 7, "col": 1, "block": "2-0", "value": 2 },

{ "row": 7, "col": 2, "block": "2-0", "value": 1 },

{ "row": 7, "col": 3, "block": "2-1", "value": 7 },

{ "row": 7, "col": 4, "block": "2-1", "value": 6 },

{ "row": 7, "col": 5, "block": "2-1", "value": 4 },

{ "row": 7, "col": 6, "block": "2-2", "value": 5 },

{ "row": 7, "col": 7, "block": "2-2", "value": 9 },

{ "row": 7, "col": 8, "block": "2-2", "value": 3 },

{ "row": 8, "col": 0, "block": "2-0", "value": 9 },

{ "row": 8, "col": 1, "block": "2-0", "value": 4 },

{ "row": 8, "col": 2, "block": "2-0", "value": 3 },

{ "row": 8, "col": 3, "block": "2-1", "value": 8 },

{ "row": 8, "col": 4, "block": "2-1", "value": 1 },

{ "row": 8, "col": 5, "block": "2-1", "value": 5 },

{ "row": 8, "col": 6, "block": "2-2", "value": 7 },

{ "row": 8, "col": 7, "block": "2-2", "value": 2 },

{ "row": 8, "col": 8, "block": "2-2", "value": 6 }]

Creating Sudoku Game by Removing Numbers

Now let's randomly remove some numbers and create a newGrid. This will be our sudoku board.

You can choose the number of cells to be dropped below. You can drop between 10-50 cells.

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The code for dropping cells can be found below:

let dropCount = 20;

function drop(dC) {
	let indicesToBeDropped = Array.from({ length: grid.length }, (_, index) => index)
		.map((value) => ({ value, sort: Math.random() }))
		.sort((a, b) => a.sort - b.sort)
		.map(({ value }) => value)
		.slice(0, dC);

	let nG = grid.map((number, index) => {
		let newNumber = { ...number };
		if (indicesToBeDropped.includes(index)) {
			newNumber.value = '';
			newNumber.empty = true;
		}
		return newNumber;
	});

	return nG;
}

let newGrid = drop(dropCount);

Solving the Sudoku Game

Here comes the interesting part as we'll solve the board and bring it back to its complete state, if we can.

But we don't know for sure whether the game is actually solvable so let's go ahead and solve it. Our data structure makes it super easy to solve this game as each number has an associated row, column and block number. We just need to filter the data that share the same row/ column/ block and see what number would fit in an empty cell.

Below is the code that solve the grid. The logic is explained in the code, but let me know in the comments if you have any question.

// Copy the earlier grid so that we don't modify it
// $ sign makes the new grid reactive based on earlier grid in svelte 
$: gameGrid = newGrid.map((n) => {
	return { ...n };
});

// For sleeping when each number is filled
// so that the user can see the algorithm working step by step
let timeout;
function sleep(time) {
	return new Promise((resolve) => {
		timeout = setTimeout(resolve, time);
		return timeout;
	});
}

// We keep a count so that if we exceed 1000 trials, we stop trying
let count = 0;

// Keep track of solving situation so that we can show a message
let solved = false;

// Solver function
async function solve() {
	solved = false;

	// Continue iterating until there is no cell where value === "" (ie empty cell)
	while (gameGrid.filter((n) => n.value === '').length !== 0 && count < 1000) {
		count++;
		// Loop through all cells
		for (let cellIndex = 0; cellIndex < gameGrid.length; cellIndex++) {
			let cell = gameGrid[cellIndex];
			// For an empty cell
			if (cell.value === '') {
				// Find numbers on the same row, column, and block as this cell
				let rowNumbers = gameGrid.filter((i) => i.row === cell.row).map((i) => i.value);
				let colNumbers = gameGrid.filter((i) => i.col === cell.col).map((i) => i.value);
				let blockNumbers = gameGrid.filter((i) => i.block === cell.block).map((i) => i.value);

				// Find numbers that can be put in this cell that are not present in row, column, and block
				let rowPossibleNumbers = numbers.filter((i) => !rowNumbers.includes(i));
				let colPossibleNumbers = numbers.filter((i) => !colNumbers.includes(i));
				let blockPossibleNumbers = numbers.filter((i) => !blockNumbers.includes(i));

				// Find the intersection of all possible numbers for this cell
				let possibleNumbers = [rowPossibleNumbers, colPossibleNumbers, blockPossibleNumbers];
				possibleNumbers = possibleNumbers.reduce((a, b) => a.filter((c) => b.includes(c)));

				// If there is only 1 possible number, we found the correct number!
				// Fill it in and sleep
				if (possibleNumbers.length === 1) {
					cell.value = possibleNumbers[0];

					// update gameGrid so that it is visible in HTML DOM
					gameGrid = [...gameGrid];
					await sleep(100);
					break;
				}
			}
		}
	}
	clearTimeout(timeout);
	solved = true;
}

Now, click below button to see if the algorithm is working as expected:

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Tried 0 times

Try playing with the input field that was introduced above where you could control # number cells to be dropped. You'll see that as you approach dropping 50 cells, it becomes super difficult to solve the board within 1,000 tries.

Conclusion

In this blogpost we have devised a way to create a sudoku game out of complere board. The complete board creation topic was covered in an earlier blog.

After removing certain number of cells based on user input, we then use a brute-force approach to fill in the cells by looking at conditions such as whether the number is feasible w.r.t row, column, and block conditions.

If you have any questions, feel free to let me know by dropping a comment below.

Until further notice, happy hacking :)

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