{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fun with Trees\n",
    "\n",
    "In this homework, let us experiment with creating and parsing expression trees in Julia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tree (generic function with 6 methods)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree(v::Tuple) = tree(v...)\n",
    "tree(a,b) = throw(\"Need an odd number of arguments\") # throw an error\n",
    "tree(a) = throw(\"Need at least three arguments\")\n",
    "tree(a,b,c) = Expr(:call,a,b,c)\n",
    "tree(v...) = Expr(:call,v[1],tree(v[2:end-1]),v[end])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tree(:*, :+, :^, :x, 3, :y, 4) = :((x ^ 3 + y) * 4)\n",
      "tree(:*, :^, :+, :x, :y, 3, 4) = :((x + y) ^ 3 * 4)\n",
      "tree(:*, :^, :+, :x, 3, :y, 4) = :((x + 3) ^ y * 4)\n"
     ]
    }
   ],
   "source": [
    "@show tree(:*,:+,:^,:x,3,:y,4)\n",
    "# Interchange args 2&3, and 5&6\n",
    "@show tree(:*,:^,:+,:x,:y,3,4);\n",
    "@show tree(:*,:^,:+,:x,3,:y,4);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using Pkg\n",
    "#Pkg.add(\"Latexify\")\n",
    "using Latexify"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the [latexify and how Julia's metaprogramming makes it so useful](https://www.youtube.com/watch?v=wpV0Nz-93Hk) video from juliacon!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left( x^{3} + y \\right) \\cdot 4$"
      ],
      "text/plain": [
       "L\"$\\left( x^{3} + y \\right) \\cdot 4$\""
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latexify(tree(:*,:+,:^,:x,3,:y,4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\left( x + y \\right)^{3} \\cdot 4$"
      ],
      "text/plain": [
       "L\"$\\left( x + y \\right)^{3} \\cdot 4$\""
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latexify(tree(:*,:^,:+,:x,:y,3,4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\frac{\\left( x^{3} + y \\right) \\cdot 4}{\\left( x + y \\right)^{3} \\cdot 4}$"
      ],
      "text/plain": [
       "L\"$\\frac{\\left( x^{3} + y \\right) \\cdot 4}{\\left( x + y \\right)^{3} \\cdot 4}$\""
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latexify(Expr(:call,:/,tree(:*,:+,:^,:x,3,:y,4),tree(:*,:^,:+,:x,:y,3,4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: \n",
    "\n",
    "Build a [reverse polish](https://en.wikipedia.org/wiki/Reverse_Polish_notation_) calculator in julia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My high school math teacher [(Gil Kessler)](https://www.wnyc.org/story/302441-where-math-teachers-go-to-get-energized)\n",
    "proudly showed me his reverse Polish HP calculator at a time when I had only heard of Texas Instruments.  I believe it was a model like this [HP 25](https://en.wikipedia.org/wiki/HP-25)\n",
    "I thought reverse Polish was very strange, but he insisted it was way faster (fewer keystrokes)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```julia\n",
    "\n",
    "#Answer:\n",
    "\n",
    "#reverse_polish(v::Tuple) = \n",
    "#reverse_polish(a,b,c) =\n",
    "#reverse_polish(v...) = \n",
    "\n",
    "# @test reverse_polish(3,4,5,:*,:-) == :(3 - 4 * 5)\n",
    "# @test eval(reverse_polish(4,5,:*)) == 20\n",
    "```"
   ]
  }
 ],
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