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   "cell_type": "code",
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   "source": [
    "# Non-greedy SCS, for comparison:\n",
    "\n",
    "import itertools\n",
    "\n",
    "def overlap(a, b, min_length=3):\n",
    "    \"\"\" Return length of longest suffix of 'a' matching\n",
    "        a prefix of 'b' that is at least 'min_length'\n",
    "        characters long.  If no such overlap exists,\n",
    "        return 0. \"\"\"\n",
    "    start = 0  # start all the way at the left\n",
    "    while True:\n",
    "        start = a.find(b[:min_length], start)  # look for b's suffx in a\n",
    "        if start == -1:  # no more occurrences to right\n",
    "            return 0\n",
    "        # found occurrence; check for full suffix/prefix match\n",
    "        if b.startswith(a[start:]):\n",
    "            return len(a)-start\n",
    "        start += 1  # move just past previous match\n",
    "\n",
    "def scs(ss):\n",
    "    \"\"\" Returns shortest common superstring of given\n",
    "        strings, which must be the same length \"\"\"\n",
    "    shortest_sup = None\n",
    "    for ssperm in itertools.permutations(ss):\n",
    "        sup = ssperm[0]  # superstring starts as first string\n",
    "        for i in range(len(ss)-1):\n",
    "            # overlap adjacent strings A and B in the permutation\n",
    "            olen = overlap(ssperm[i], ssperm[i+1], min_length=1)\n",
    "            # add non-overlapping portion of B to superstring\n",
    "            sup += ssperm[i+1][olen:]\n",
    "        if shortest_sup is None or len(sup) < len(shortest_sup):\n",
    "            shortest_sup = sup  # found shorter superstring\n",
    "    return shortest_sup  # return shortest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pick_maximal_overlap(reads, k):\n",
    "    \"\"\" Return a pair of reads from the list with a\n",
    "        maximal suffix/prefix overlap >= k.  Returns\n",
    "        overlap length 0 if there are no such overlaps.\"\"\"\n",
    "    reada, readb = None, None\n",
    "    best_olen = 0\n",
    "    for a, b in itertools.permutations(reads, 2):\n",
    "        olen = overlap(a, b, min_length=k)\n",
    "        if olen > best_olen:\n",
    "            reada, readb = a, b\n",
    "            best_olen = olen\n",
    "    return reada, readb, best_olen\n",
    "\n",
    "def greedy_scs(reads, k):\n",
    "    \"\"\" Greedy shortest-common-superstring merge.\n",
    "        Repeat until no edges (overlaps of length >= k)\n",
    "        remain. \"\"\"\n",
    "    read_a, read_b, olen = pick_maximal_overlap(reads, k)\n",
    "    while olen > 0:\n",
    "        reads.remove(read_a)\n",
    "        reads.remove(read_b)\n",
    "        reads.append(read_a + read_b[-(len(read_b) - olen):])\n",
    "        read_a, read_b, olen = pick_maximal_overlap(reads, k)\n",
    "    return ''.join(reads)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ABCDBCDA'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Small example where brute-force gives shorter superstring than greedy\n",
    "scs(['ABCD', 'CDBC', 'BCDA'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'CDBCABCDA'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "greedy_scs(['ABCD', 'CDBC', 'BCDA'], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Example from lecture notes\n",
    "greedy_sup = greedy_scs(['BAA', 'AAB', 'BBA', 'ABA', 'ABB', 'BBB', 'AAA', 'BAB'], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('AAABBBABAAB', 11)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "greedy_sup, len(greedy_sup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scs_sup = scs(['BAA', 'AAB', 'BBA', 'ABA', 'ABB', 'BBB', 'AAA', 'BAB'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('BAAABABBBA', 10)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Greedy SCS superstring might be longer than optimal\n",
    "scs_sup, len(scs_sup)"
   ]
  }
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