Added a Python 3 implementation of the problem from https://tianrunhe…

….wordpress.com/2012/11/04/merge-k-sorted-lists/

Merge-k-sorted-lists.ipynb

@@ -0,0 +1,140 @@
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+   "source": [
+    "# How to *Merge $k$ sorted lists* (in Python 3)\n",
+    "\n",
+    "The question comes from [this nice blog on programming](https://tianrunhe.wordpress.com/2012/11/04/merge-k-sorted-lists/).\n",
+    "I will solve it without giving much details, and test it quickly."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def merge_two(list1, list2):\n",
+    "    if len(list1) == 0:\n",
+    "        return list2[:]\n",
+    "    elif len(list2) == 0:\n",
+    "        return list1[:]\n",
+    "    else:\n",
+    "        if list1[0] < list2[0]:\n",
+    "            return [list1[0]] + merge_two(list1[1:], list2)\n",
+    "        else:\n",
+    "            return [list2[0]] + merge_two(list1, list2[1:])\n",
+    "    \n",
+    "\n",
+    "def merge(*lists):\n",
+    "    head = []\n",
+    "    for list_i in lists:\n",
+    "        head = merge_two(head, list_i)\n",
+    "    return head"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Tests"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import random\n",
+    "\n",
+    "def random_sorted_list(size):\n",
+    "    return sorted([random.randint(0, 100) for _ in range(size)])\n",
+    "\n",
+    "\n",
+    "def issorted(alist):\n",
+    "    return alist == sorted(alist) \n",
+    "\n",
+    "\n",
+    "for size in [10, 20, 30]:\n",
+    "    for k in range(2, 20):\n",
+    "        lists = [random_sorted_list(size) for _ in range(k)]\n",
+    "        merged_list = merge(*lists)\n",
+    "        assert issorted(merged_list)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Complexity\n",
+    "One can prove that the algorithm we proposed is:\n",
+    "\n",
+    "- correctly merging $k$ sorted list into a sorted list containing the values from all the list,\n",
+    "- and does so with an extra memory of at most $\\mathcal{O}(k n)$ if all the lists have size at most $n$,\n",
+    "- and does so with a time complexity of at most $\\mathcal{O}(k n)$ if all the lists have size at most $n$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Conclusion\n",
+    "*Et voilà.*"
+   ]
+  }
+ ],
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