NQueens in Julia

NQueens.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "module NQueens\n",
    "\n",
    "export solve\n",
    "\n",
    "\n",
    "type Board\n",
    "    cols      :: Int\n",
    "    nodes     :: Int\n",
    "    diag45    :: Int\n",
    "    diag135   :: Int\n",
    "    solutions :: Int\n",
    "\n",
    "    Board() = new(0, 0, 0, 0, 0)\n",
    "end\n",
    "\n",
    "\"Marks occupancy.\"\n",
    "function mark!(b::Board, k::Int, j::Int)\n",
    "    b.cols    $= (1 << j)\n",
    "    b.diag135 $= (1 << (j + k))\n",
    "    b.diag45  $= (1 << (32 + j - k))\n",
    "end\n",
    "\n",
    "\"Tests if a square is menaced.\"\n",
    "function test(b::Board, k::Int, j::Int)\n",
    "    b.cols    & (1 << j)            +\n",
    "    b.diag135 & (1 << (j + k))      +\n",
    "    b.diag45  & (1 << (32 + j - k)) == 0\n",
    "end\n",
    "\n",
    "\"Backtracking solver.\"\n",
    "function solve!(b::Board, niv::Int, dx::Int)\n",
    "    if niv > 0\n",
    "        for i in 0:dx - 1\n",
    "            if test(b, niv, i) == true\n",
    "                mark!(b, niv, i)\n",
    "                solve!(b, niv - 1, dx)\n",
    "                mark!(b, niv, i)\n",
    "            end\n",
    "        end\n",
    "    else\n",
    "        for i in 0:dx - 1\n",
    "            if test(b, 0, i) == true\n",
    "                b.solutions += 1\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    b.nodes += 1\n",
    "    b.solutions\n",
    "end\n",
    "\n",
    "solve(n::Int) = solve!(Board(), n -1, n)\n",
    "\n",
    "\n",
    "end\n",
    "\n",
    "\n",
    "using  NQueens\n",
    "\n",
    "\n",
    "solve(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 1\n",
      "elapsed time: 3.574e-6 seconds\n",
      "solutions = 1\n",
      "\n",
      "n = 2\n",
      "elapsed time: 2.383e-6 seconds\n",
      "solutions = 0\n",
      "\n",
      "n = 3\n",
      "elapsed time: 3.024e-6 seconds\n",
      "solutions = 0\n",
      "\n",
      "n = 4\n",
      "elapsed time: 3.691e-6 seconds\n",
      "solutions = 2\n",
      "\n",
      "n = 5\n",
      "elapsed time: 4.51e-6 seconds\n",
      "solutions = 10\n",
      "\n",
      "n = 6\n",
      "elapsed time: 9.331e-6 seconds\n",
      "solutions = 4\n",
      "\n",
      "n = 7\n",
      "elapsed time: 2.9897e-5 seconds\n",
      "solutions = 40\n",
      "\n",
      "n = 8\n",
      "elapsed time: 0.000112309 seconds\n",
      "solutions = 92\n",
      "\n",
      "n = 9\n",
      "elapsed time: 0.000462868 seconds\n",
      "solutions = 352\n",
      "\n",
      "n = 10\n",
      "elapsed time: 0.002111329 seconds\n",
      "solutions = 724\n",
      "\n",
      "n = 11\n",
      "elapsed time: 0.01052219 seconds\n",
      "solutions = 2680\n",
      "\n",
      "n = 12\n",
      "elapsed time: 0.057378663 seconds\n",
      "solutions = 14200\n",
      "\n",
      "n = 13\n",
      "elapsed time: 0.330716909 seconds\n",
      "solutions = 73712\n",
      "\n",
      "n = 14\n",
      "elapsed time: 2.041111961 seconds\n",
      "solutions = 365596\n",
      "\n",
      "n = 15\n",
      "elapsed time: 13.423782691 seconds\n",
      "solutions = 2279184\n",
      "\n",
      "n = 16\n",
      "elapsed time: 97.125055795 seconds\n",
      "solutions = 14772512\n",
      "\n",
      "n = 17\n",
      "elapsed time: 712.622606898 seconds\n",
      "solutions = 95815104\n",
      "\n"
     ]
    }
   ],
   "source": [
    "function nqueens_test()\n",
    "    for n = 1:17\n",
    "        gc()\n",
    "        @show n\n",
    "        tic()\n",
    "        solutions = solve(n)\n",
    "        toc()\n",
    "        @show solutions\n",
    "        println()\n",
    "    end\n",
    "end\n",
    "\n",
    "nqueens_test()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0-dev",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}