{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotations(t):\n",
    "    # Return list of rotations of input string t\n",
    "    tt = t * 2\n",
    "    return [ tt[i:i+len(t)] for i in range(len(t)) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['cat', 'atc', 'tca']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rotations('cat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bwm(t):\n",
    "    # Return lexicographically sorted list of t’s rotations\n",
    "    return sorted(rotations(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['$abaaba', 'a$abaab', 'aaba$ab', 'aba$aba', 'abaaba$', 'ba$abaa', 'baaba$a']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bwm('abaaba$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$abaaba\n",
      "a$abaab\n",
      "aaba$ab\n",
      "aba$aba\n",
      "abaaba$\n",
      "ba$abaa\n",
      "baaba$a\n"
     ]
    }
   ],
   "source": [
    "print('\\n'.join(bwm('abaaba$')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bwtViaBwm(t):\n",
    "    # Given T, returns BWT(T) by way of the BWM\n",
    "    return ''.join(map(lambda x: x[-1], bwm(t)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'abba$aa'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bwtViaBwm('abaaba$') # we can see the result equals the last column of the matrix above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def suffixArray(s):\n",
    "    satups = sorted([(s[i:], i) for i in range(len(s))])\n",
    "    return map(lambda x: x[1], satups)\n",
    "\n",
    "def bwtViaSa(t):\n",
    "    # Given T, returns BWT(T) by way of the suffix array\n",
    "    bw = []\n",
    "    for si in suffixArray(t):\n",
    "        if si == 0:\n",
    "            bw.append('$')\n",
    "        else:\n",
    "            bw.append(t[si-1])\n",
    "    return ''.join(bw) # return string-ized version of list bw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('abba$aa', 'abba$aa')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bwtViaBwm('abaaba$'), bwtViaSa('abaaba$') # same result"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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