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write heap_sort_solution.ipynb

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Hyeongnam Jang 2018-11-29 09:03:42 +09:00
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sorting_searching/heap_sort/heap_sort_solution.ipynb
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"source": [ "source": [
"## Constraints\n", "## Constraints\n",
"\n", "\n",
"* Is a naive solution sufficient (ie not in-place)?\n", "* Is a naive solution sufficient?\n",
" * Yes\n", " * Yes\n",
"* Are duplicates allowed?\n", "* Are duplicates allowed?\n",
" * Yes\n", " * Yes\n",
@ -63,31 +63,23 @@
"## Algorithm\n", "## Algorithm\n",
"\n", "\n",
"Wikipedia's animation:\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", "\n",
"* Set pivot to the middle element in the data\n", "* Convert a given list to a max-heap\n",
"* For each element:\n", "* For i from n-1 to 0 (n is size of a given list) :\n",
" * If current element is the pivot, continue\n", " * Swap 0-th element with i-th element\n",
" * If the element is less than the pivot, add to left array\n", " * Heapfiy a sub-list(0 ~ i-1)\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",
"\n", "\n",
"Complexity:\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", "* Space: O(n)\n",
" * This implementation is in-place sort, so it needs no additional space.\n",
"\n", "\n",
"Misc:\n", "Misc:\n",
"\n", "\n",
"* More sophisticated implementations are in-place, although they still take up recursion depth space\n",
"* Most implementations are not stable\n", "* Most implementations are not stable\n",
"\n", "\n",
"See [Quicksort on wikipedia](https://en.wikipedia.org/wiki/Quicksort):\n", "See [Heapsort on wikipedia](https://en.wikipedia.org/wiki/Heapsort):\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)"
] ]
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