{"id":477440,"date":"2023-08-09T09:15:09","date_gmt":"2023-08-09T09:15:09","guid":{"rendered":""},"modified":"2023-09-05T11:14:42","modified_gmt":"2023-09-05T11:14:42","slug":"heapsort","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/ir\/wiki\/heapsort\/","title":{"rendered":"Heapsort"},"content":{"rendered":"<p>Heapsort \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc \u0628\u0647 \u0646\u0627\u0645 heap \u0628\u0631\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u062f\u0631 \u0645\u062d\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. Heapsort \u06a9\u0647 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f \u062e\u0648\u062f \u0634\u0646\u0627\u062e\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f\u060c \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0639\u0644\u0648\u0645 \u0631\u0627\u06cc\u0627\u0646\u0647 \u0627\u0632 \u062c\u0645\u0644\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u060c \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 \u0648 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0632\u06cc\u0631\u0633\u0627\u062e\u062a \u0634\u0628\u06a9\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h2>\u062e\u0627\u0633\u062a\u06af\u0627\u0647 Heapsort<\/h2>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u0627\u0648\u0644\u06cc\u0646 \u0628\u0627\u0631 \u062f\u0631 \u0633\u0627\u0644 1964 \u062a\u0648\u0633\u0637 JWJ Williams \u0645\u0639\u0631\u0641\u06cc \u0634\u062f. \u0627\u06cc\u062f\u0647 \u067e\u0634\u062a Heapsort \u0627\u0632 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u06a9\u0627\u0631\u0622\u0645\u062f \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 \u0632\u06cc\u0627\u062f\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u062f\u0648\u0646 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0641\u0636\u0627\u06cc \u062d\u0627\u0641\u0638\u0647 \u0627\u0636\u0627\u0641\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0646\u062f\u060c \u067e\u062f\u06cc\u062f\u0627\u0631 \u0634\u062f. \u0648\u06cc\u0644\u06cc\u0627\u0645\u0632 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0647\u06cc\u067e \u0631\u0627 \u0628\u0631\u0627\u06cc \u0686\u0646\u06cc\u0646 \u06a9\u0627\u0631\u06cc \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u06a9\u0631\u062f \u06a9\u0647 \u0645\u0646\u062c\u0631 \u0628\u0647 \u062a\u0648\u0633\u0639\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u0634\u062f.<\/p>\n<p>\u062f\u0631 \u0633\u0627\u0644 1978\u060c \u0631\u0627\u0628\u0631\u062a \u0633\u062c\u0648\u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u0631\u0627 \u0627\u0635\u0644\u0627\u062d \u06a9\u0631\u062f \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0622\u0646 \u0631\u0627 \u0628\u0647\u0628\u0648\u062f \u0628\u062e\u0634\u06cc\u062f\u060c \u06a9\u0647 \u0628\u0647 \u067e\u0630\u06cc\u0631\u0634 \u06af\u0633\u062a\u0631\u062f\u0647 \u0622\u0646 \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0639\u0644\u0648\u0645 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u06a9\u0645\u06a9 \u06a9\u0631\u062f.<\/p>\n<h2>\u062d\u0644 \u06a9\u0631\u062f\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort<\/h2>\n<p>Heapsort \u0627\u0628\u062a\u062f\u0627 \u0628\u0627 \u062a\u0628\u062f\u06cc\u0644 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0648\u0631\u0648\u062f\u06cc \u0628\u0647 \u06cc\u06a9 max heap \u0639\u0645\u0644 \u0645\u06cc \u06a9\u0646\u062f - \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0627\u06cc\u0646\u0631\u06cc \u06a9\u0627\u0645\u0644 \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u0642\u062f\u0627\u0631 \u0647\u0631 \u06af\u0631\u0647 \u0648\u0627\u0644\u062f \u0628\u0632\u0631\u06af\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0641\u0631\u0632\u0646\u062f \u0627\u0633\u062a. \u0633\u067e\u0633 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u06cc\u0634\u0647 \u067e\u0634\u062a\u0647 (\u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u0642\u062f\u0627\u0631) \u0631\u0627 \u0628\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0627\u0632 \u067e\u0634\u062a\u0647 \u062a\u0639\u0648\u06cc\u0636 \u0645\u06cc \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u0647\u06cc\u067e \u0631\u0627 \u06a9\u0648\u0686\u06a9 \u0645\u06cc \u06a9\u0646\u062f \u0648 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u0642\u062f\u0627\u0631 \u0631\u0627 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0635\u062d\u06cc\u062d \u062e\u0648\u062f \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u0645\u0628\u0627\u062f\u0644\u0647 \u0648 \u06a9\u0627\u0647\u0634 \u067e\u0634\u062a\u0647 \u0628\u0647 \u0637\u0648\u0631 \u0645\u06a9\u0631\u0631 \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc \u06cc\u0627\u0628\u062f \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u06a9\u0644 \u0622\u0631\u0627\u06cc\u0647 \u0648\u0631\u0648\u062f\u06cc \u0628\u0647 \u06cc\u06a9 \u062f\u0646\u0628\u0627\u0644\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646\u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u062f\u0631 \u062c\u0627\u06cc \u062e\u0648\u062f \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062d\u0627\u0641\u0638\u0647 \u0627\u0636\u0627\u0641\u06cc \u0646\u062f\u0627\u0631\u062f\u060c \u06a9\u0647 \u0628\u0627\u0639\u062b \u0645\u06cc\u200c\u0634\u0648\u062f \u0641\u0636\u0627 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0627\u0634\u062f.<\/p>\n<h2>Heapsort \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f: \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062e\u0644\u06cc<\/h2>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u0627\u0632 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647 \u0627\u0635\u0644\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<ol>\n<li>\n<p><strong>Heapify<\/strong>: \u0627\u06cc\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u062a\u0628\u062f\u06cc\u0644 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u0628\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0627\u0633\u062a. \u0628\u0627 \u062a\u06a9\u0631\u0627\u0631 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0632 \u0648\u0633\u0637 \u0628\u0647 \u0627\u0628\u062a\u062f\u0627 \u0648 \u0641\u0634\u0627\u0631 \u062f\u0627\u062f\u0646 \u0647\u0631 \u0622\u06cc\u062a\u0645\u06cc \u06a9\u0647 \u062e\u0627\u0635\u06cc\u062a heap \u0631\u0627 \u0646\u0642\u0636 \u0645\u06cc \u06a9\u0646\u062f \u0628\u0647 \u0633\u0645\u062a \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0645\u0648\u0642\u0639\u06cc\u062a \u0635\u062d\u06cc\u062d \u062e\u0648\u062f \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062d\u0630\u0641<\/strong>: \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a\u060c \u0645\u0627\u06a9\u0632\u06cc\u0645\u0645 \u0622\u06cc\u062a\u0645 (\u0631\u06cc\u0634\u0647 \u067e\u0634\u062a\u0647) \u0628\u0647 \u0637\u0648\u0631 \u0645\u06a9\u0631\u0631 \u0628\u0627 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f \u0627\u0632 \u067e\u0634\u062a\u0647 (\u0627\u0646\u062a\u0647\u0627\u06cc \u0622\u0631\u0627\u06cc\u0647) \u062a\u0639\u0648\u06cc\u0636 \u0645\u06cc \u0634\u0648\u062f \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u067e\u0634\u062a\u0647 \u06cc\u06a9 \u0639\u062f\u062f \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f. \u067e\u0633 \u0627\u0632 \u0647\u0631 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc\u060c \u0631\u06cc\u0634\u0647 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc\u0627\u0628\u06cc \u0648\u06cc\u0698\u06af\u06cc heap &quot;\u0627\u0644\u06a9&quot; \u0645\u06cc \u0634\u0648\u062f\u060c \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0622\u06cc\u062a\u0645 \u0631\u0627 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0635\u062d\u06cc\u062d \u062e\u0648\u062f \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<\/li>\n<\/ol>\n<p>\u0627\u06cc\u0646 \u0645\u0631\u0627\u062d\u0644 \u062a\u0627 \u0645\u0631\u062a\u0628 \u0634\u062f\u0646 \u06a9\u0644 \u0622\u0631\u0627\u06cc\u0647 \u062a\u06a9\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h2>\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u06a9\u0644\u06cc\u062f\u06cc Heapsort<\/h2>\n<p>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Heapsort \u0628\u0627 \u0686\u0646\u062f\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u0645\u0647\u0645 \u0645\u0634\u062e\u0635 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<ul>\n<li>\n<p><strong>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631 \u0645\u062d\u0644<\/strong>: Heapsort \u0628\u0647 \u0641\u0636\u0627\u06cc \u0627\u0636\u0627\u0641\u06cc \u0646\u06cc\u0627\u0632 \u0646\u062f\u0627\u0631\u062f \u0648 \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0628\u0647\u0631\u0647 \u0648\u0631\u06cc \u0632\u0645\u0627\u0646<\/strong>: Heapsort \u062f\u0631 \u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a \u0648 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc O(n log n) \u062f\u0627\u0631\u062f \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0632\u0645\u0627\u0646\u06cc \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u0639\u062f\u0645 \u062b\u0628\u0627\u062a<\/strong>: Heapsort \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u067e\u0627\u06cc\u062f\u0627\u0631 \u0646\u06cc\u0633\u062a. \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u0627\u0633\u062a \u06a9\u0647 \u0639\u0646\u0627\u0635\u0631 \u0628\u0627 \u0627\u0631\u0632\u0634 \u0645\u0633\u0627\u0648\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0646\u0638\u0645 \u0646\u0633\u0628\u06cc \u062e\u0648\u062f \u0631\u0627 \u062f\u0631 \u062e\u0631\u0648\u062c\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062d\u0641\u0638 \u0646\u06a9\u0646\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062c\u0647\u0627\u0646\u06cc \u0628\u0648\u062f\u0646<\/strong>: Heapsort \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0647\u0631 \u0646\u0648\u0639 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc \u0631\u0627 \u06a9\u0647 \u0642\u0627\u0628\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0639\u0645 \u0627\u0632 \u0639\u062f\u062f\u06cc \u06cc\u0627 \u0637\u0628\u0642\u0647\u200c\u0627\u06cc\u060c \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u06a9\u0646\u062f.<\/p>\n<\/li>\n<\/ul>\n<h2>\u0627\u0646\u0648\u0627\u0639 Heapsort<\/h2>\n<p>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0627\u0635\u0644 \u0627\u0633\u0627\u0633\u06cc Heapsort \u06cc\u06a9\u0633\u0627\u0646 \u0627\u0633\u062a\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641 heaps \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0631\u062f. \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0627\u0646\u0648\u0627\u0639 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0646\u0648\u0639 \u0647\u06cc\u067e<\/th>\n<th>\u0634\u0631\u062d<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0647\u06cc\u067e \u0628\u0627\u06cc\u0646\u0631\u06cc<\/td>\n<td>\u0627\u06cc\u0646 \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0647\u06cc\u067e \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631 \u0627\u062c\u0631\u0627\u06cc Heapsort \u0627\u0633\u062a. \u0647\u0631 \u06af\u0631\u0647 \u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0628\u0627\u06cc\u0646\u0631\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u062f\u0648 \u0641\u0631\u0632\u0646\u062f \u062f\u0627\u0631\u062f.<\/td>\n<\/tr>\n<tr>\n<td>\u0633\u0647 \u062a\u0627\u06cc\u06cc \u0647\u06cc\u067e<\/td>\n<td>\u062f\u0631 \u06cc\u06a9 \u067e\u0634\u062a\u0647 \u0633\u0647 \u062a\u0627\u06cc\u06cc\u060c \u0647\u0631 \u06af\u0631\u0647 \u062a\u0627 \u0633\u0647 \u0641\u0631\u0632\u0646\u062f \u062f\u0627\u0631\u062f. \u06cc\u06a9 \u0647\u06cc\u067e \u0633\u0647 \u062a\u0627\u06cc\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u062f\u0631 \u0628\u0631\u062e\u06cc \u0645\u0648\u0627\u0631\u062f \u0639\u0645\u0644\u06a9\u0631\u062f \u06a9\u0645\u06cc \u0628\u0647\u062a\u0631 \u0627\u0632 \u0647\u06cc\u067e \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u062f.<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc \u0647\u06cc\u067e<\/td>\n<td>\u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0628\u0631\u0627\u06cc Heapsort \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0646\u0645\u06cc \u0634\u0648\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u067e\u0634\u062a\u0647 \u0641\u06cc\u0628\u0648\u0646\u0627\u0686\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647\u0628\u0648\u062f \u06cc\u0627\u0641\u062a\u0647 \u0627\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u0648\u0627\u0639 \u062e\u0627\u0635\u06cc \u0627\u0632 \u062a\u0648\u0632\u06cc\u0639 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Heapsort: \u0641\u0631\u0635\u062a \u0647\u0627 \u0648 \u0686\u0627\u0644\u0634 \u0647\u0627<\/h2>\n<p>Heapsort \u0628\u0647 \u0637\u0648\u0631 \u06af\u0633\u062a\u0631\u062f\u0647 \u062f\u0631 \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0632 \u062c\u0645\u0644\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u060c \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646\u06cc \u0648 \u06af\u0631\u0627\u0641\u06cc\u06a9 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f. \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0622\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639 \u0648 \u062f\u0631 \u0645\u062d\u0644 \u062f\u0627\u0631\u0646\u062f \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>Heapsort \u0628\u0627 \u0648\u062c\u0648\u062f \u0645\u0632\u0627\u06cc\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0627\u0631\u062f\u060c \u0628\u0627 \u0686\u0627\u0644\u0634\u200c\u0647\u0627\u06cc\u06cc \u0631\u0648\u0628\u0631\u0648\u0633\u062a. \u067e\u0627\u06cc\u062f\u0627\u0631 \u0646\u06cc\u0633\u062a\u060c \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u0646\u062f \u0645\u0634\u06a9\u0644 \u0633\u0627\u0632 \u0628\u0627\u0634\u062f. \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646\u060c \u06a9\u0627\u0631\u0627\u06cc\u06cc Heapsort \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0627 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u0632 \u0642\u0628\u0644 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647\u200c\u0627\u0646\u062f\u060c \u06a9\u0627\u0647\u0634 \u06cc\u0627\u0628\u062f.<\/p>\n<h2>\u0645\u0642\u0627\u06cc\u0633\u0647 Heapsort \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0634\u0627\u0628\u0647<\/h2>\n<p>Heapsort \u0627\u063a\u0644\u0628 \u0628\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0645\u0634\u0627\u0628\u0647 \u0645\u0627\u0646\u0646\u062f Quicksort \u0648 Mergesort \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645<\/th>\n<th>\u0628\u0647\u062a\u0631\u06cc\u0646 \u0645\u0648\u0631\u062f<\/th>\n<th>\u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0645\u0648\u0631\u062f<\/th>\n<th>\u0628\u062f\u062a\u0631\u06cc\u0646 \u062d\u0627\u0644\u062a<\/th>\n<th>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0641\u0636\u0627<\/th>\n<th>\u062b\u0628\u0627\u062a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Heapsort<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>O (1)<\/td>\n<td>\u062e\u06cc\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0633\u0631\u06cc\u0639<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>O (n\u00b2)<\/td>\n<td>O (log n)<\/td>\n<td>\u062e\u06cc\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u062f\u063a\u0627\u0645<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<td>\u0628\u0631)<\/td>\n<td>\u0622\u0631\u0647<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0686\u0634\u0645 \u0627\u0646\u062f\u0627\u0632\u0647\u0627 \u0648 \u0641\u0646\u0627\u0648\u0631\u06cc \u0647\u0627\u06cc \u0622\u06cc\u0646\u062f\u0647<\/h2>\n<p>\u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0642\u062f\u0631\u062a \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0648 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0646\u062f\u0627\u0632\u0647 \u0648 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u060c \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u0627\u0646\u0646\u062f Heapsort \u0647\u0645\u0686\u0646\u0627\u0646 \u0627\u062f\u0627\u0645\u0647 \u062f\u0627\u0631\u062f. \u062a\u062d\u0642\u06cc\u0642\u0627\u062a \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0648\u0627\u0632\u06cc \u0648 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0631\u0627\u0647\u200c\u0647\u0627\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f\u062a\u0631\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc Heapsort \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0634\u0627\u0628\u0647 \u0628\u0627\u0632 \u06a9\u0646\u062f.<\/p>\n<h2>Heapsort \u0648 \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0648\u06a9\u0633\u06cc<\/h2>\n<p>\u062f\u0631 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0633\u0631\u0648\u0631 \u067e\u0631\u0648\u06a9\u0633\u06cc\u060c Heapsort \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0631 \u0645\u062f\u06cc\u0631\u06cc\u062a \u0644\u0627\u06af \u0647\u0627\u060c \u0622\u062f\u0631\u0633 \u0647\u0627\u06cc IP \u0648 \u0628\u0633\u062a\u0647 \u0647\u0627\u06cc \u0634\u0628\u06a9\u0647 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f. \u0645\u0627\u0647\u06cc\u062a \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u062f\u0631 \u0645\u062d\u0644 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u062f\u06cc\u0631\u06cc\u062a \u062d\u062c\u0645 \u0632\u06cc\u0627\u062f\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0639\u0645\u0648\u0644\u06cc \u062f\u0631 \u062a\u0631\u0627\u0641\u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0645\u06cc \u06a9\u0646\u062f. \u0628\u0627 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0622\u062f\u0631\u0633\u200c\u0647\u0627\u06cc IP \u06cc\u0627 \u0628\u0633\u062a\u0647\u200c\u0647\u0627\u060c \u0645\u062f\u06cc\u0631\u0627\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u062a\u0631\u0627\u0641\u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0631\u0627 \u0628\u0647\u062a\u0631 \u062a\u062d\u0644\u06cc\u0644 \u06a9\u0646\u0646\u062f \u0648 \u062a\u0635\u0645\u06cc\u0645\u0627\u062a \u0622\u06af\u0627\u0647\u0627\u0646\u0647\u200c\u062a\u0631\u06cc \u0628\u06af\u06cc\u0631\u0646\u062f.<\/p>\n<h2>\u0644\u06cc\u0646\u06a9 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647<\/h2>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0645\u0648\u0631\u062f Heapsort\u060c \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0646\u0627\u0628\u0639 \u062f\u06cc\u062f\u0646 \u06a9\u0646\u06cc\u062f:<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Heapsort\" target=\"_new\" rel=\"noopener nofollow\">Heapsort - \u0648\u06cc\u06a9\u06cc \u067e\u062f\u06cc\u0627<\/a><\/li>\n<li><a href=\"https:\/\/www.geeksforgeeks.org\/heap-sort\/\" target=\"_new\" rel=\"noopener nofollow\">Heapsort \u2013 Geeks for Geeks<\/a><\/li>\n<li><a href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/algorithms\/heapsort\/a\/intro-to-heap-sort\" target=\"_new\" rel=\"noopener nofollow\">\u0645\u0642\u062f\u0645\u0647 \u0627\u06cc \u0628\u0631 Heapsort \u2013 Khan Academy<\/a><\/li>\n<li><a href=\"https:\/\/www.tutorialspoint.com\/data_structures_algorithms\/heap_sort_algorithm.htm\" target=\"_new\" rel=\"noopener nofollow\">\u0622\u0645\u0648\u0632\u0634 Heapsort \u2013 Tutorialspoint<\/a><\/li>\n<\/ul>","protected":false},"featured_media":468531,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477440","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Heapsort: A Powerful Sorting Algorithm<\/mark>","faq_items":[{"question":"What is Heapsort?","answer":"<p>Heapsort is an efficient comparison-based sorting algorithm that uses a data structure called a 'heap' to sort data in place. This method is particularly beneficial when handling large volumes of data, as it doesn't require additional memory.<\/p>"},{"question":"Who invented the Heapsort algorithm?","answer":"<p>The Heapsort algorithm was first introduced by J. W. J. Williams in 1964. Later, Robert Sedgewick refined the algorithm in 1978, enhancing its efficiency and promoting its wide adoption in the field of computer science.<\/p>"},{"question":"How does the Heapsort algorithm work?","answer":"<p>Heapsort operates by transforming an input array into a max heap, then repeatedly swapping the root of the heap with the last item, thereby shrinking the heap and placing the maximum value in its correct sorted position. This process continues until the entire array is sorted.<\/p>"},{"question":"What are the key features of Heapsort?","answer":"<p>Heapsort is characterized by its in-place sorting, time efficiency, non-stability, and universality. It does not require additional space, sorts elements within the given array, and has a worst-case and average time complexity of O(n log n). However, it is not a stable sorting algorithm, which means equal-value elements may not maintain their relative order in the sorted output. It can sort any type of data that can be compared, whether numerical or categorical.<\/p>"},{"question":"Are there different types of Heapsort?","answer":"<p>Yes, Heapsort can be implemented using different types of heaps, including Binary Heaps, Ternary Heaps, and Fibonacci Heaps. The type of heap used can have an impact on the efficiency of the sorting process.<\/p>"},{"question":"What are some uses and challenges of Heapsort?","answer":"<p>Heapsort is widely used in a range of applications, including data analysis, machine learning, and computer graphics. Despite its benefits, Heapsort is not stable, and its efficiency can decrease with nearly sorted data.<\/p>"},{"question":"How does Heapsort compare with other sorting algorithms like Quicksort and Mergesort?","answer":"<p>Heapsort, Quicksort, and Mergesort all have best-case and average-case time complexities of O(n log n). However, Heapsort and Mergesort have better worst-case time complexities of O(n log n), compared to Quicksort's O(n\u00b2). Heapsort is an in-place sort and does not require extra memory, unlike Mergesort. None of these algorithms, except Mergesort, are stable.<\/p>"},{"question":"How is Heapsort relevant to proxy server management?","answer":"<p>In proxy server management, Heapsort can be utilized to handle logs, IP addresses, and network packets efficiently. Its in-place nature and efficiency make it suitable for managing the large volumes of data typically associated with network traffic.<\/p>"},{"question":"What are the future perspectives and technologies related to Heapsort?","answer":"<p>As we advance in computational power and as data increases in size and complexity, the need for efficient sorting algorithms like Heapsort continues. Current research into parallel computing and quantum computing may unlock more efficient ways to implement Heapsort and similar algorithms.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki\/477440","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki\/477440\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media\/468531"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media?parent=477440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}