From e8c7b3d1e7c182c37bd14b93b5be5716c411fc33 Mon Sep 17 00:00:00 2001 From: Adrien Date: Wed, 28 Sep 2022 12:12:56 +0200 Subject: [PATCH] Add note about heap sort algorithm --- 20211230101331-software.org | 5 +- 20220928113147-heap_sort_algorithm.org | 71 ++++++++++++++++++ ...t2oqlq_mbPK3t1RE-WFQ_2022-09-28_11-43-09.png | Bin 0 -> 99093 bytes 3 files changed, 75 insertions(+), 1 deletion(-) create mode 100644 20220928113147-heap_sort_algorithm.org create mode 100644 Organisation des éléments dans le tableau/1*KSt2oqlq_mbPK3t1RE-WFQ_2022-09-28_11-43-09.png diff --git a/20211230101331-software.org b/20211230101331-software.org index d55799c..7b5472c 100644 --- a/20211230101331-software.org +++ b/20211230101331-software.org @@ -1,6 +1,6 @@ :PROPERTIES: :ID: ca50d517-3e8a-4d03-ba38-7ff411e87408 -:mtime: 20220910133708 +:mtime: 20220928120750 :ctime: 20211230101331 :END: #+title: Software @@ -18,6 +18,9 @@ Il est nécessaire que le language mis en oeuvre permette l'interception d'erreu * Design pattern TODO +* Classement/tri de données +** [[id:6af01039-a0a9-46fc-abe8-82f9662bc4b7][heap sort algorithm]] + * Langages ** Compilés *** [[id:ed8be72a-8a4d-4ef7-92e4-78d07095deaf][C++]] diff --git a/20220928113147-heap_sort_algorithm.org b/20220928113147-heap_sort_algorithm.org new file mode 100644 index 0000000..a07d49a --- /dev/null +++ b/20220928113147-heap_sort_algorithm.org @@ -0,0 +1,71 @@ +:PROPERTIES: +:ID: 6af01039-a0a9-46fc-abe8-82f9662bc4b7 +:mtime: 20220928120648 +:ctime: 20220928113147 +:END: +#+title: heap sort algorithm + +* Introduction + * Algorithme de classement /in-place/ d'un tableau en le divisant en deux sous-tableaux contenant les éléments classés et non +classés, + * Efficace : *O(nlog(n))* où n correspond au nombre d'éléments à classer, + * Le éléments non classés sont organisés dans une /heap data structure/, + * A chaque étape, l'élément max/min se trouvant à la racine du /heap/ est déplacé dans le sous-tableau des éléments + classés jusqu'à ce qu'il ne reste qu'un élément dans le sous-tableau des éléments non classés, + +* Organisation des éléments dans le tableau +#+DOWNLOADED: https://miro.medium.com/max/720/1*KSt2oqlq_mbPK3t1RE-WFQ.png @ 2022-09-28 11:43:09 +[[file:Organisation des éléments dans le tableau/1*KSt2oqlq_mbPK3t1RE-WFQ_2022-09-28_11-43-09.png]] + +* Implémentation +#+BEGIN_SRC python :results output +from typing import Any, List + +def heap_sort(array: List[Any]): + build_max_heap(array) + # start with the ending index all the way to 0 + for end_index in range(len(array)-1, 0, -1): + swap(array, 0, end_index) + # reduce heap size by 1 + # sift down the value we just swapped + heapify(0, end_index - 1, array) + # return array + +def build_max_heap(array: List[Any]): + last_non_leaf_node_index = (len(array) - 2) // 2 + for index in range(last_non_leaf_node_index, -1, -1): + heapify(index, len(array)-1, array) + +# sift down +def heapify(current_index: int, end_index: int, array: List[Any]): + left_child_index = 2 * current_index + 1 + while left_child_index <= end_index: + right_child_index = 2 * current_index + 2 if (2 * current_index + 2 <= end_index) else -1 + + largest_child_index = left_child_index + if right_child_index != -1 and array[left_child_index] < array[right_child_index]: + largest_child_index = right_child_index + + if array[current_index] < array[largest_child_index]: + swap(array, current_index, largest_child_index) + current_index = largest_child_index + left_child_index = 2 * current_index + 1 + else: + return + +def swap(array: List[Any], i: int, j: int): + array[i], array[j] = array[j], array[i] + +array = [1, -15, 22, 40, 9, 91] +print(f"Before sorting: {array}") +heap_sort(array) +print(f"After sorting: {array}") +#+END_SRC + +#+RESULTS: +: Before sorting: [1, -15, 22, 40, 9, 91] +: After sorting: [-15, 1, 9, 22, 40, 91] + +* Référence + * [[https://yuminlee2.medium.com/heap-sort-algorithm-6e200dc51845][Heap Sort Algorithm. 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