# Project Euler Problem 96 Solution

## Question

Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept. Its origin is unclear, but credit must be attributed to Leonhard Euler who invented a similar, and much more difficult, puzzle idea called Latin Squares. The objective of Su Doku puzzles, however, is to replace the blanks (or zeros) in a 9 by 9 grid in such that each row, column, and 3 by 3 box contains each of the digits 1 to 9. Below is an example of a typical starting puzzle grid and its solution grid.

 0 0 39 0 00 0 1 0 2 03 0 58 0 6 6 0 00 0 14 0 0 0 0 87 0 00 0 6 1 0 20 0 07 0 8 9 0 00 0 82 0 0 0 0 28 0 00 0 5 6 0 92 0 30 1 0 5 0 00 0 93 0 0

 4 8 39 6 72 5 1 9 2 13 4 58 7 6 6 5 78 2 14 9 3 5 4 87 2 91 3 6 1 3 25 6 47 9 8 9 7 61 3 82 4 5 3 7 28 1 46 9 5 6 8 92 5 34 1 7 5 1 47 6 93 8 2

A well constructed Su Doku puzzle has a unique solution and can be solved by logic, although it may be necessary to employ “guess and test” methods in order to eliminate options (there is much contested opinion over this). The complexity of the search determines the difficulty of the puzzle; the example above is considered easy because it can be solved by straight forward direct deduction.

The 6K text file, sudoku.txt (right click and ‘Save Link/Target As…’), contains fifty different Su Doku puzzles ranging in difficulty, but all with unique solutions (the first puzzle in the file is the example above).

By solving all fifty puzzles find the sum of the 3-digit numbers found in the top left corner of each solution grid; for example, 483 is the 3-digit number found in the top left corner of the solution grid above.

## JavaScript

const fs = require("fs")
const digits = "123456789"

function parseGames(gameFile) {
return gameFile.toString().split(/Grid \d+\n/).slice(1).map((gameString) => {
return gameString.split("\n").join("")
})
}

function parseGame(gameString) {
const game = []
for (let x = 0; x < 9; x++) {
game[x] = []
for (let y = 0; y < 9; y++) {
game[x][y] = digits
}
}
gameString.split("").forEach((c, i) => {
const x = i % 9
const y = Math.floor(i / 9)
if (c !== "0") {
move(game, x, y, c)
}
})
return game
}

function units(x, y) {
const result = [[], [], []]
for (let i = 0; i < 9; i++) {
const col = [x, i]
result[0].push(col)
const row = [i, y]
result[1].push(row)
}
for (let sx = Math.floor(x / 3) * 3, i = sx; i < sx + 3; i++) {
for (let sy = Math.floor(y / 3) * 3, j = sy; j < sy + 3; j++) {
const box = [i, j]
result[2].push(box)
}
}
return result.map((unit) => {
return unit.filter(([ux, uy]) => !(ux === x && uy === y))
})
}

const peerCache = {}
function peers(x, y) {
if (peerCache[[x, y]]) {
return peerCache[[x, y]]
}
const result = []
const seen = {}
units(x, y).forEach((unit) => {
unit.forEach((pos) => {
if (!seen[pos]) {
seen[pos] = 1
result.push(pos)
}
})
})
peerCache[[x, y]] = result
return result
}

function move(game, x, y, c) {
const otherValues = game[x][y].replace(c, "").split("")
return otherValues.every((oc) => propagate(game, x, y, oc)) && game
}

function propagate(game, x, y, c) {
if (game[x][y].indexOf(c) < 0) {
return game
}
game[x][y] = game[x][y].replace(c, "")
if (game[x][y].length === 0) {
return false
} else if (game[x][y].length === 1) {
const ps = peers(x, y)
for (let i = 0, l = ps.length; i < l; i++) {
const [px, py] = ps[i]
if (!propagate(game, px, py, game[x][y])) {
return false
}
}
}
const us = units(x, y)
for (let i = 0, l = us.length; i < l; i++) {
const unit = us[i]
const places = unit.filter(([ux, uy]) => game[ux][uy].indexOf(c) >= 0)
if (places.length === 0) {
return false
} else if (places.length === 1) {
const [px, py] = places[0]
if (!move(game, px, py, c)) {
return false
}
}
}
return game
}

function isSolved(game) {
for (let x = 0; x < 9; x++) {
for (let y = 0; y < 9; y++) {
if (game[x][y].length !== 1) {
return false
}
}
}
return true
}

function copyGame(game) {
const copy = []
for (let x = 0; x < 9; x++) {
copy[x] = []
for (let y = 0; y < 9; y++) {
copy[x][y] = game[x][y]
}
}
return copy
}

function solve(game) {
if (!game) {
return false
} else if (isSolved(game)) {
return game
}
let nx, ny
let min = Infinity
for (let x = 0; x < 9; x++) {
for (let y = 0; y < 9; y++) {
if (game[x][y].length > 1 && game[x][y].length < min) {
min = game[x][y].length
nx = x
ny = y
}
}
}
const choices = game[nx][ny].split("")
for (let i = 0, l = choices.length; i < l; i++) {
const copy = copyGame(game)
const solution = solve(move(copy, nx, ny, choices[i]))
if (solution) {
return solution
}
}
return false
}

const games = parseGames(fs.readFileSync(__dirname + "/sudoku.txt"))
console.log(games.reduce((acc, gameString) => {
const game = parseGame(gameString)
const solution = solve(game)
const topLeft = parseInt(solution[0][0] + solution[1][0] + solution[2][0])
return acc + topLeft
}, 0))
\$ time node --use-strict sudoku.js
real   0m1.349s
user   0m1.348s
sys    0m0.004s