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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Not a great way to build a suffix array, but we'll use it\n",
    "# for the small examples here\n",
    "def naiveBuildSA(t):\n",
    "    satups = sorted([(t[i:], i) for i in range(len(t))])\n",
    "    return list(map(lambda x: x[1], satups))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 5, 2, 3, 0, 4, 1]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naiveBuildSA('abaaba$') # works on a simple example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binarySearchSA(t, sa, p):\n",
    "    assert t[-1] == '$' # t already has terminator\n",
    "    assert len(t) == len(sa) # sa is the suffix array for t\n",
    "    if len(t) == 1: return 1\n",
    "    l, r = 0, len(sa) # invariant: sa[l] < p < sa[r]\n",
    "    while True:\n",
    "        c = (l + r) // 2\n",
    "        # determine whether p < T[sa[c]:] by doing comparisons\n",
    "        # starting from left-hand sides of p and T[sa[c]:]\n",
    "        plt = True # assume p < T[sa[c]:] until proven otherwise\n",
    "        i = 0\n",
    "        while i < len(p) and sa[c]+i < len(t):\n",
    "            if p[i] < t[sa[c]+i]:\n",
    "                break # p < T[sa[c]:]\n",
    "            elif p[i] > t[sa[c]+i]:\n",
    "                plt = False\n",
    "                break # p > T[sa[c]:]\n",
    "            i += 1 # tied so far\n",
    "        if plt:\n",
    "            if c == l + 1: return c\n",
    "            r = c\n",
    "        else:\n",
    "            if c == r - 1: return r\n",
    "            l = c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 'abaaba$'\n",
    "sa = naiveBuildSA(t)\n",
    "binarySearchSA(t, sa, 'aba')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarySearchSA(t, sa, 'bb') # p is greater than all suffixes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarySearchSA(t, sa, 'aa')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def suffixLcp(t, toff, p):\n",
    "    i = 0\n",
    "    while i < len(p) and i + toff < len(t):\n",
    "        if p[i] != t[i + toff]:\n",
    "            return i\n",
    "        i += 1\n",
    "    return i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suffixLcp('abaaba$', 0, 'aba')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suffixLcp('abaaba$', 0, 'abab')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suffixLcp('abaaba$', 0, 'abaabaaba')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binarySearchSA_lcp1(t, sa, p):\n",
    "    assert t[-1] == '$' # t already has terminator\n",
    "    assert len(t) == len(sa) # sa is the suffix array for t\n",
    "    if len(t) == 1: return 1\n",
    "    l, r = 0, len(sa) # invariant: sa[l] < p < sa[r]\n",
    "    lcp_lp, lcp_rp = 0, 0\n",
    "    while True:\n",
    "        c = (l + r) // 2\n",
    "        # determine whether p < T[sa[c]:] by doing comparisons\n",
    "        # starting from left-hand sides of p and T[sa[c]:]\n",
    "        plt = True # assume p < T[sa[c]:] until proven otherwise\n",
    "        i = min(lcp_lp, lcp_rp)\n",
    "        while i < len(p) and sa[c]+i < len(t):\n",
    "            if p[i] < t[sa[c]+i]:\n",
    "                break # p < T[sa[c]:]\n",
    "            elif p[i] > t[sa[c]+i]:\n",
    "                plt = False\n",
    "                break # p > T[sa[c]:]\n",
    "            i += 1 # tied so far\n",
    "        if plt:\n",
    "            if c == l + 1: return c\n",
    "            r = c\n",
    "            lcp_rp = i\n",
    "        else:\n",
    "            if c == r - 1: return r\n",
    "            l = c\n",
    "            lcp_lp = i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarySearchSA_lcp1(t, sa, 'aba')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarySearchSA_lcp1(t, sa, 'bb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarySearchSA_lcp1(t, sa, 'aa')"
   ]
  }
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