X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=09-resolving-the-bill%2Fresolving-the-bill-solution.ipynb;h=dc846ae48a37dd38c6d0f608bde46ee34550e1d0;hb=7feed95175973490721236795cc7895e252965e2;hp=3d9d63f1059b62509f1f2f78c3fc30745edc1964;hpb=c78bf218fb6d75d478fef09b8067a23332d4de45;p=ou-summer-of-code-2017.git

diff --git a/09-resolving-the-bill/resolving-the-bill-solution.ipynb b/09-resolving-the-bill/resolving-the-bill-solution.ipynb
index 3d9d63f..dc846ae 100644
--- a/09-resolving-the-bill/resolving-the-bill-solution.ipynb
+++ b/09-resolving-the-bill/resolving-the-bill-solution.ipynb
@@ -78,7 +78,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "sys.setrecursionlimit(10**6)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -87,7 +99,7 @@
        "148"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -100,7 +112,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {
     "collapsed": true
    },
@@ -114,7 +126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
@@ -134,7 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
    "metadata": {
     "collapsed": true
    },
@@ -158,7 +170,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 7,
    "metadata": {
     "collapsed": true
    },
@@ -178,7 +190,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def is_subseq_greedy(s1, s2):\n",
+    "    i = j = 0\n",
+    "    while i < len(s1) and j < len(s2):\n",
+    "        if s1[i] == s2[j]:\n",
+    "            i += 1\n",
+    "        j += 1\n",
+    "    return i == len(s1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "metadata": {
     "collapsed": true
    },
@@ -233,7 +262,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 10,
    "metadata": {
     "collapsed": true
    },
@@ -284,7 +313,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -293,7 +322,7 @@
        "22"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -306,7 +335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -315,7 +344,7 @@
        "22"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -328,14 +357,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "22"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(1 for s in bills\n",
+    "   if s != 0\n",
+    "   if is_subseq_greedy(bills[0], bills[s]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 8.02 s per loop\n"
+      "100 loops, best of 3: 13.1 ms per loop\n"
      ]
     }
    ],
@@ -343,19 +394,19 @@
     "%%timeit\n",
     "sum(1 for s in bills\n",
     "   if s != 0\n",
-    "   if is_subseq(bills[0], bills[s]))"
+    "   if is_subseq_greedy(bills[0], bills[s]))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 3.04 s per loop\n"
+      "1 loop, best of 3: 7.88 s per loop\n"
      ]
     }
    ],
@@ -363,12 +414,12 @@
     "%%timeit\n",
     "sum(1 for s in bills\n",
     "   if s != 0\n",
-    "   if is_subseq_rows(bills[0], bills[s]))"
+    "   if is_subseq(bills[0], bills[s]))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 15,
    "metadata": {
     "scrolled": true
    },
@@ -400,7 +451,7 @@
        " 146]"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -413,15 +464,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 168 ms, sys: 0 ns, total: 168 ms\n",
-      "Wall time: 166 ms\n"
+      "CPU times: user 148 ms, sys: 4 ms, total: 152 ms\n",
+      "Wall time: 150 ms\n"
      ]
     },
     {
@@ -430,7 +481,7 @@
        "(True, False)"
       ]
      },
-     "execution_count": 65,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -441,7 +492,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -452,7 +503,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -679,7 +730,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 31,
    "metadata": {
     "collapsed": true
    },
@@ -690,20 +741,24 @@
     "        return s2 == s3\n",
     "    elif not s2:\n",
     "        return s1 == s3\n",
+    "    elif len(s1) + len(s2) != len(s3):\n",
+    "        return False\n",
     "    else:\n",
-    "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
-    "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "        if s1[-1] == s3[-1] and s2[-1] == s3[-1]:\n",
+    "            return (is_interleave_recursive(s1[:-1], s2, s3[:-1]) \n",
+    "                    or \n",
+    "                    is_interleave_recursive(s1, s2[:-1], s3[:-1]) )\n",
     "        elif s1[-1] == s3[-1]:\n",
     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
     "        elif s2[-1] == s3[-1]:\n",
-    "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "            return is_interleave_recursive(s1, s2[:-1], s3[:-1])\n",
     "        else:\n",
     "            return False"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 20,
    "metadata": {
     "collapsed": true
    },
@@ -779,7 +834,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 21,
    "metadata": {
     "collapsed": true
    },
@@ -852,7 +907,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 22,
    "metadata": {
     "collapsed": true
    },
@@ -932,7 +987,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 23,
    "metadata": {
     "collapsed": true
    },
@@ -956,7 +1011,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
@@ -965,7 +1020,7 @@
        "[30]"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -977,7 +1032,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
@@ -986,7 +1041,7 @@
        "[30]"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -998,7 +1053,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
@@ -1007,7 +1062,7 @@
        "[30]"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1019,7 +1074,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[30]"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[s for s in bills\n",
+    "   if is_subseq(bills[0], bills[s])\n",
+    "   if is_subseq(bills[1], bills[s])]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
@@ -1236,7 +1313,7 @@
        "True"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1250,7 +1327,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -1259,7 +1336,7 @@
        "[30]"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1271,14 +1348,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 2.68 s per loop\n"
+      "1 loop, best of 3: 3.12 s per loop\n"
      ]
     }
    ],
@@ -1290,14 +1367,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 1.06 s per loop\n"
+      "1 loop, best of 3: 971 ms per loop\n"
      ]
     }
    ],
@@ -1309,7 +1386,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
@@ -1328,14 +1405,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 660 ms per loop\n"
+      "1000 loops, best of 3: 510 µs per loop\n"
      ]
     }
    ],
@@ -1362,7 +1439,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
@@ -1371,7 +1448,7 @@
        "(4.223305555555555, 4, 13, 23.899999999999636)"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1387,7 +1464,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
@@ -1396,7 +1473,7 @@
        "(11.13438888888889, 11, 8, 3.8000000000029104)"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1412,7 +1489,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
@@ -1421,7 +1498,7 @@
        "(15.36486111111111, 15, 21, 53.5)"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1435,6 +1512,194 @@
     ")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "# Explanations"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "starget = 'acba'\n",
+    "swrong = 'cdabcaca'\n",
+    "sinterleave = 'abcacbba'\n",
+    "ssubseq = 'aaccabab'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_subseq_md_table(short, long, table):\n",
+    "    header = '|   |' + '|'.join('{}<br />{}'.format('<br />'.join(str(long[:i])), i) for i in range(len(long) + 1)) + '|'\n",
+    "    separator = '|:---:' * (len(long) + 2) + '|'\n",
+    "    rows = []\n",
+    "    columns = sorted(set(k[1] for k in table))\n",
+    "    for r in range(len(short) + 1):\n",
+    "        row = '|{}<br />{}|'.format(r, short[:r])\n",
+    "        row += '|'.join('T' if table[r, c] else '.' for c in columns)\n",
+    "        row += '|'\n",
+    "        rows += [row]\n",
+    "    return '\\n'.join([header] + [separator] + rows)\n",
+    "#     return '\\n'.join(\n",
+    "#         ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
+    "#         for i in sorted(set([k[0] for k in table])))        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      ". . . . . . . . .\n",
+      ". a a c c a b a b\n",
+      ". . . c c a b a b\n",
+      ". . . . . . b a b\n",
+      ". . . . . . . a b\n",
+      "AcCaBAb\n"
+     ]
+    }
+   ],
+   "source": [
+    "v, bp, t = is_subseq(starget, ssubseq, return_backpointers=True, return_table=True)\n",
+    "print(show_annotated_table(t, bp))\n",
+    "print(show_backtrace_s(bp))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "T T T T T T T T T\n",
+      ". T T T T T T T T\n",
+      ". . . T T T T T T\n",
+      ". . . . . . T T T\n",
+      ". . . . . . . T T\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(show_table(t))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "|   |<br />0|a<br />1|a<br />a<br />2|a<br />a<br />c<br />3|a<br />a<br />c<br />c<br />4|a<br />a<br />c<br />c<br />a<br />5|a<br />a<br />c<br />c<br />a<br />b<br />6|a<br />a<br />c<br />c<br />a<br />b<br />a<br />7|a<br />a<br />c<br />c<br />a<br />b<br />a<br />b<br />8|\n",
+      "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
+      "|0<br />|T|T|T|T|T|T|T|T|T|\n",
+      "|1<br />a|.|T|T|T|T|T|T|T|T|\n",
+      "|2<br />ac|.|.|.|T|T|T|T|T|T|\n",
+      "|3<br />acb|.|.|.|.|.|.|T|T|T|\n",
+      "|4<br />acba|.|.|.|.|.|.|.|T|T|\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(show_subseq_md_table(starget, ssubseq, t))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "|   |<br />0|a<br />1|a<br />a<br />2|a<br />a<br />c<br />3|a<br />a<br />c<br />c<br />4|a<br />a<br />c<br />c<br />a<br />5|a<br />a<br />c<br />c<br />a<br />b<br />6|a<br />a<br />c<br />c<br />a<br />b<br />a<br />7|a<br />a<br />c<br />c<br />a<br />b<br />a<br />b<br />8|\n",
+    "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
+    "|0<br />|T|T|T|T|T|T|T|T|T|\n",
+    "|1<br />a|.|T|T|T|T|T|T|T|T|\n",
+    "|2<br />ac|.|.|.|T|T|T|T|T|T|\n",
+    "|3<br />acb|.|.|.|.|.|.|T|T|T|\n",
+    "|4<br />acba|.|.|.|.|.|.|.|T|T|"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      ". . . . . . . . .\n",
+      ". . . a b c a c a\n",
+      ". . . . . c a c a\n",
+      ". . . . . . . . .\n",
+      ". . . . . . . . .\n",
+      "ACa\n"
+     ]
+    }
+   ],
+   "source": [
+    "v, bp, t = is_subseq(starget, swrong, return_backpointers=True, return_table=True)\n",
+    "print(show_annotated_table(t, bp))\n",
+    "print(show_backtrace_s(bp))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "|   |<br />0|c<br />1|c<br />d<br />2|c<br />d<br />a<br />3|c<br />d<br />a<br />b<br />4|c<br />d<br />a<br />b<br />c<br />5|c<br />d<br />a<br />b<br />c<br />a<br />6|c<br />d<br />a<br />b<br />c<br />a<br />c<br />7|c<br />d<br />a<br />b<br />c<br />a<br />c<br />a<br />8|\n",
+      "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
+      "|0<br />|T|T|T|T|T|T|T|T|T|\n",
+      "|1<br />a|.|.|.|T|T|T|T|T|T|\n",
+      "|2<br />ac|.|.|.|.|.|T|T|T|T|\n",
+      "|3<br />acb|.|.|.|.|.|.|.|.|.|\n",
+      "|4<br />acba|.|.|.|.|.|.|.|.|.|\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(show_subseq_md_table(starget, swrong, t))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "|   |<br />0|c<br />1|c<br />d<br />2|c<br />d<br />a<br />3|c<br />d<br />a<br />b<br />4|c<br />d<br />a<br />b<br />c<br />5|c<br />d<br />a<br />b<br />c<br />a<br />6|c<br />d<br />a<br />b<br />c<br />a<br />c<br />7|c<br />d<br />a<br />b<br />c<br />a<br />c<br />a<br />8|\n",
+    "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
+    "|0<br />|T|T|T|T|T|T|T|T|T|\n",
+    "|1<br />a|.|.|.|T|T|T|T|T|T|\n",
+    "|2<br />ac|.|.|.|.|.|T|T|T|T|\n",
+    "|3<br />acb|.|.|.|.|.|.|.|.|.|\n",
+    "|4<br />acba|.|.|.|.|.|.|.|.|.|"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,