write heap_sort_solution.ipynb

sorting_searching/heap_sort/heap_sort_solution.ipynb

@@ -34,7 +34,7 @@
    "source": [
     "## Constraints\n",
     "\n",
-    "* Is a naive solution sufficient (ie not in-place)?\n",
+    "* Is a naive solution sufficient?\n",
     "    * Yes\n",
     "* Are duplicates allowed?\n",
     "    * Yes\n",
@@ -63,31 +63,23 @@
     "## Algorithm\n",
     "\n",
     "Wikipedia's animation:\n",
-    "![alt text](http://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif)\n",
+    "![alt text](https://upload.wikimedia.org/wikipedia/commons/1/1b/Sorting_heapsort_anim.gif)\n",
     "\n",
-    "* Set pivot to the middle element in the data\n",
-    "* For each element:\n",
-    "    * If current element is the pivot, continue\n",
-    "    * If the element is less than the pivot, add to left array\n",
-    "    * Else, add to right array\n",
-    "* Recursively apply quicksort to the left array\n",
-    "* Recursively apply quicksort to the right array\n",
-    "* Merge the left array + pivot + right array\n",
+    "* Convert a given list to a max-heap\n",
+    "* For i from n-1 to 0 (n is size of a given list) :\n",
+    "    * Swap 0-th element with i-th element\n",
+    "    * Heapfiy a sub-list(0 ~ i-1)\n",
     "\n",
     "Complexity:\n",
-    "* Time: O(n log(n)) average, best, O(n^2) worst\n",
+    "* Time: O(n log(n)) average, best, worst\n",
     "* Space: O(n)\n",
+    "    * This implementation is in-place sort, so it needs no additional space.\n",
     "\n",
     "Misc:\n",
     "\n",
-    "* More sophisticated implementations are in-place, although they still take up recursion depth space\n",
     "* Most implementations are not stable\n",
     "\n",
-    "See [Quicksort on wikipedia](https://en.wikipedia.org/wiki/Quicksort):\n",
-    "\n",
-    "Typically, quicksort is significantly faster in practice than other Θ(nlogn) algorithms, because its inner loop can be efficiently implemented on most architectures [presumably because it has good cache locality], and in most real-world data, it is possible to make design choices which minimize the probability of requiring quadratic time.\n",
-    "\n",
-    "See: [Quicksort vs merge sort](http://stackoverflow.com/questions/70402/why-is-quicksort-better-than-mergesort)"
+    "See [Heapsort on wikipedia](https://en.wikipedia.org/wiki/Heapsort):\n"
    ]
   },
   {
@@ -99,7 +91,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -148,7 +140,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -196,7 +188,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {