{"id":363943,"date":"2024-08-01T14:14:01","date_gmt":"2024-08-01T13:14:01","guid":{"rendered":"https:\/\/ypsilon.dev\/ar\/blog\/%d9%85%d8%a7%d8%b0%d8%a7-%d9%8a%d8%b9%d9%86%d9%8a-recurrence-relation-%d9%81%d9%8a-%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d8%ae%d9%88%d8%a7%d8%b1%d8%b2%d9%85%d9%8a%d8%a7%d8%aa-%d9%88%d9%87%d9%8a%d8%a7\/"},"modified":"2024-08-01T14:14:01","modified_gmt":"2024-08-01T13:14:01","slug":"%d9%85%d8%a7%d8%b0%d8%a7-%d9%8a%d8%b9%d9%86%d9%8a-recurrence-relation-%d9%81%d9%8a-%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d8%ae%d9%88%d8%a7%d8%b1%d8%b2%d9%85%d9%8a%d8%a7%d8%aa-%d9%88%d9%87%d9%8a%d8%a7","status":"publish","type":"post","link":"https:\/\/ypsilon.dev\/ar\/%d9%85%d8%a7%d8%b0%d8%a7-%d9%8a%d8%b9%d9%86%d9%8a-recurrence-relation-%d9%81%d9%8a-%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d8%ae%d9%88%d8%a7%d8%b1%d8%b2%d9%85%d9%8a%d8%a7%d8%aa-%d9%88%d9%87%d9%8a%d8%a7\/","title":{"rendered":"\u0645\u0627\u0630\u0627 \u064a\u0639\u0646\u064a recurrence relation \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a"},"content":{"rendered":"<h2><strong>\u0645\u0627 \u0647\u0648 \u0645\u0641\u0647\u0648\u0645 &#8220;recurrence relation&#8221; \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u061f<\/strong><\/h2>\n<p>\u064a\u0639\u062a\u0628\u0631 \u0645\u0641\u0647\u0648\u0645 &#8220;recurrence relation&#8221; \u0645\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u062a\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0644\u0648\u0635\u0641 \u0627\u0644\u062a\u0633\u0644\u0633\u0644\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062a\u0643\u0631\u0631 \u0641\u064a\u0647\u0627 \u0627\u0644\u0642\u064a\u0645 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0642\u064a\u0645 \u0633\u0627\u0628\u0642\u0629. \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0645\u0647\u0645 \u0644\u0644\u063a\u0627\u064a\u0629 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0639\u0645\u0644 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u060c \u062e\u0627\u0635\u0629 \u062a\u0644\u0643 \u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u062a\u0642\u0633\u064a\u0645 \u0648\u0627\u0644\u062d\u0644\u060c \u0645\u062b\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 &#8220;divide and conquer&#8221;. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644\u060c \u0633\u0646\u062a\u0646\u0627\u0648\u0644 \u0634\u0631\u062d\u064b\u0627 \u062a\u0641\u0635\u064a\u0644\u064a\u064b\u0627 \u0644\u0645\u0641\u0647\u0648\u0645 &#8220;recurrence relation&#8221; \u0648\u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642\u0647 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<h3><strong>\u062a\u0639\u0631\u064a\u0641 &#8220;recurrence relation&#8221;<\/strong><\/h3>\n<p>\u064a\u064f\u0639\u0631\u0641 &#8220;recurrence relation&#8221; \u0639\u0644\u0649 \u0623\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0639\u0628\u0631 \u0639\u0646 \u0639\u0646\u0635\u0631 \u0641\u064a \u062a\u0633\u0644\u0633\u0644 \u0645\u0639\u064a\u0646 \u0643\u062f\u0627\u0644\u0629 \u0644\u0639\u0646\u0627\u0635\u0631 \u0633\u0627\u0628\u0642\u0629 \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u062a\u0633\u0644\u0633\u0644. \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u062a\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0644\u062a\u062d\u062f\u064a\u062f \u0642\u064a\u0645\u0629 \u0639\u0646\u0635\u0631 \u0645\u0639\u064a\u0646 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0642\u064a\u0645 \u0639\u0646\u0627\u0635\u0631 \u0633\u0627\u0628\u0642\u0629. \u062a\u0639\u062a\u0628\u0631 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0623\u062f\u0648\u0627\u062a \u0642\u0648\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0648\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0644\u0623\u0646\u0647\u0627 \u062a\u062a\u064a\u062d \u0644\u0646\u0627 \u062a\u062d\u0644\u064a\u0644 \u0648\u062a\u0648\u0642\u0639 \u0633\u0644\u0648\u0643 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<\/p>\n<h4><strong>\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 &#8220;recurrence relation&#8221;<\/strong><\/h4>\n<p>\u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0634\u0647\u064a\u0631\u0629 \u0639\u0644\u0649 &#8220;recurrence relation&#8221; \u0633\u0644\u0633\u0644\u0629 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a\u060c \u062d\u064a\u062b \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0641\u064a \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0639\u0646\u0635\u0631\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u064a\u0646 \u0644\u0647:<\/p>\n<p><strong>F(n) = F(n-1) + F(n-2)<\/strong><\/p>\n<p>\u062a\u0628\u062f\u0623 \u0647\u0630\u0647 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0628\u0642\u064a\u0645 \u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 F(0) = 0 \u0648F(1) = 1. \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0648\u0644\u064a\u062f \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0628\u0627\u0644\u0643\u0627\u0645\u0644:<\/p>\n<p><strong>0, 1, 1, 2, 3, 5, 8, 13, &#8230;<\/strong><\/p>\n<h3><strong>\u0623\u0646\u0648\u0627\u0639 &#8220;recurrence relation&#8221;<\/strong><\/h3>\n<p>\u062a\u0648\u062c\u062f \u0623\u0646\u0648\u0627\u0639 \u0645\u062a\u0639\u062f\u062f\u0629 \u0645\u0646 &#8220;recurrence relation&#8221;\u060c \u0648\u0643\u0644 \u0646\u0648\u0639 \u0644\u0647 \u062a\u0637\u0628\u064a\u0642\u0627\u062a\u0647 \u0648\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a\u0647 \u0627\u0644\u062e\u0627\u0635\u0629 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u064a\u0645\u0643\u0646 \u062a\u0635\u0646\u064a\u0641 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0625\u0644\u0649:<\/p>\n<h4><strong>1. \u0639\u0644\u0627\u0642\u0627\u062a \u062e\u0637\u064a\u0629<\/strong><\/h4>\n<p>\u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0647\u064a \u062a\u0644\u0643 \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0643\u0644 \u0645\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0633\u0627\u0628\u0642\u0629 \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u062b\u0627\u0628\u062a \u0645\u0639\u064a\u0646. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<p><strong>a(n) = c1 * a(n-1) + c2 * a(n-2) + &#8230; + ck * a(n-k)<\/strong><\/p>\n<h4><strong>2. \u0639\u0644\u0627\u0642\u0627\u062a \u063a\u064a\u0631 \u062e\u0637\u064a\u0629<\/strong><\/h4>\n<p>\u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u062e\u0637\u064a\u0629 \u062a\u0634\u0645\u0644 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636 \u0623\u0648 \u0645\u0631\u0641\u0648\u0639\u0629 \u0644\u0642\u0648\u0629 \u0645\u0639\u064a\u0646\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<p><strong>a(n) = a(n-1) * a(n-2)<\/strong><\/p>\n<h3><strong>\u062a\u0637\u0628\u064a\u0642\u0627\u062a &#8220;recurrence relation&#8221; \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a<\/strong><\/h3>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 &#8220;recurrence relation&#8221; \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u062a\u062d\u0644\u064a\u0644 \u062a\u0639\u0642\u064a\u062f\u0647\u0627 \u0648\u062a\u062d\u062f\u064a\u062f \u0623\u062f\u0627\u0626\u0647\u0627. \u0633\u0646\u0646\u0627\u0642\u0634 \u0628\u0639\u0636 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0634\u0627\u0626\u0639\u0629:<\/p>\n<h4><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u062a\u0642\u0633\u064a\u0645 \u0648\u063a\u0632\u0648 (Divide and Conquer)<\/strong><\/h4>\n<p>\u062a\u0639\u062a\u0645\u062f \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0644\u0649 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0625\u0644\u0649 \u0645\u0634\u0627\u0643\u0644 \u0623\u0635\u063a\u0631 \u0648\u062d\u0644\u0647\u0627 \u062b\u0645 \u062f\u0645\u062c \u0627\u0644\u062d\u0644\u0648\u0644. \u062a\u0633\u062a\u062e\u062f\u0645 &#8220;recurrence relation&#8221; \u0644\u0648\u0635\u0641 \u062a\u0639\u0642\u064a\u062f \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u062a\u0639\u0642\u064a\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062f\u0645\u062c (Merge Sort) \u064a\u0645\u0643\u0646 \u0648\u0635\u0641\u0647 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p><strong>T(n) = 2T(n\/2) + O(n)<\/strong><\/p>\n<h4><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u062b\u0646\u0627\u0626\u064a (Binary Search)<\/strong><\/h4>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 &#8220;recurrence relation&#8221; \u0623\u064a\u0636\u064b\u0627 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u062a\u0639\u0642\u064a\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u060c \u062d\u064a\u062b \u064a\u062a\u0645 \u062a\u0642\u0633\u064a\u0645 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0625\u0644\u0649 \u0646\u0635\u0641\u064a\u0646 \u0641\u064a \u0643\u0644 \u062e\u0637\u0648\u0629. \u062a\u0639\u0642\u064a\u062f \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u064a\u0645\u0643\u0646 \u0648\u0635\u0641\u0647 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p><strong>T(n) = T(n\/2) + O(1)<\/strong><\/p>\n<h3><strong>\u062d\u0644 &#8220;recurrence relation&#8221;<\/strong><\/h3>\n<p>\u0644\u062d\u0644 &#8220;recurrence relation&#8221;\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0635\u064a\u063a\u0629 \u0645\u063a\u0644\u0642\u0629 \u062a\u0639\u0628\u0631 \u0639\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0628\u062f\u0644\u0627\u0644\u0629 n \u0641\u0642\u0637. \u0647\u0646\u0627\u0643 \u0639\u062f\u0629 \u0637\u0631\u0642 \u0644\u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a\u060c \u0645\u0646 \u0628\u064a\u0646\u0647\u0627:<\/p>\n<h4><strong>\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u0643\u0631\u0627\u0631 (Iteration Method)<\/strong><\/h4>\n<p>\u062a\u062a\u0636\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u062d\u0633\u0627\u0628 \u0639\u062f\u0629 \u062d\u062f\u0648\u062f \u0645\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0648\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0646\u0645\u0637 \u064a\u0645\u0643\u0646 \u062a\u0639\u0645\u064a\u0645\u0647. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0644\u062d\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 T(n) = 2T(n\/2) + n\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p>1. T(n) = 2T(n\/2) + n<\/p>\n<p>2. T(n\/2) = 2T(n\/4) + n\/2<\/p>\n<p>3. T(n\/4) = 2T(n\/8) + n\/4<\/p>\n<p>\u0628\u062a\u062c\u0645\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0645\u0644\u0627\u062d\u0638\u0629 \u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p>T(n) = 2^k * T(n\/2^k) + kn<\/p>\n<p>\u0639\u0646\u062f\u0645\u0627 n\/2^k = 1\u060c \u0646\u062c\u062f \u0623\u0646 k = log(n)\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p>T(n) = n * T(1) + nlog(n)<\/p>\n<p>\u0648\u0628\u0645\u0627 \u0623\u0646 T(1) \u062b\u0627\u0628\u062a\u060c \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0635\u064a\u063a\u0629 \u0625\u0644\u0649:<\/p>\n<p><strong>T(n) = O(nlog(n))<\/strong><\/p>\n<h4><strong>\u0637\u0631\u064a\u0642\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 (Characteristic Equation Method)<\/strong><\/h4>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0644\u062d\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0644\u062d\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 a(n) = 3a(n-1) &#8211; 2a(n-2)\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0641\u062a\u0631\u0627\u0636 \u062d\u0644 \u0639\u0644\u0649 \u0634\u0643\u0644 a(n) = r^n\u060c \u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p>r^n = 3r^(n-1) &#8211; 2r^(n-2)<\/p>\n<p>\u0628\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0635\u0627\u0626\u0635:<\/p>\n<p>r^2 &#8211; 3r + 2 = 0<\/p>\n<p>\u0628\u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u0646\u062c\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0645\u064a\u0632\u0629 \u0644\u0640 r\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u062d\u0644 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u0639\u0644\u0627\u0642\u0629.<\/p>\n<h3><strong>\u0623\u0647\u0645\u064a\u0629 &#8220;recurrence relation&#8221; \u0641\u064a \u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/h3>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 &#8220;recurrence relation&#8221; \u0623\u064a\u0636\u064b\u0627 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0644\u062a\u062d\u0644\u064a\u0644 \u0623\u062f\u0627\u0621 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0625\u062f\u0631\u0627\u062c \u0648\u0627\u0644\u062d\u0630\u0641 \u0641\u064a \u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u0623\u0634\u062c\u0627\u0631 \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u0623\u0643\u0648\u0627\u0645 (Heaps).<\/p>\n<h4><strong>\u0627\u0644\u0623\u0634\u062c\u0627\u0631 \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 (Binary Trees)<\/strong><\/h4>\n<p>\u064a\u0645\u0643\u0646 \u0648\u0635\u0641 \u0627\u0631\u062a\u0641\u0627\u0639 \u0627\u0644\u0634\u062c\u0631\u0629 \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 &#8220;recurrence relation&#8221;. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0631\u062a\u0641\u0627\u0639 \u0634\u062c\u0631\u0629 \u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u062a\u0648\u0627\u0632\u0646\u0629 \u064a\u0645\u0643\u0646 \u0648\u0635\u0641\u0647 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p><strong>H(n) = H(n\/2) + 1<\/strong><\/p>\n<p>\u0628\u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629\u060c \u0646\u062c\u062f \u0623\u0646 \u0627\u0631\u062a\u0641\u0627\u0639 \u0627\u0644\u0634\u062c\u0631\u0629 \u0647\u0648 O(log(n)).<\/p>\n<h4><strong>\u0627\u0644\u0623\u0643\u0648\u0627\u0645 (Heaps)<\/strong><\/h4>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 &#8220;recurrence relation&#8221; \u0623\u064a\u0636\u064b\u0627 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0623\u062f\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u0623\u0643\u0648\u0627\u0645. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u062a\u0639\u0642\u064a\u062f \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0628\u0646\u0627\u0621 \u0641\u064a \u0627\u0644\u0623\u0643\u0648\u0627\u0645 \u064a\u0645\u0643\u0646 \u0648\u0635\u0641\u0647 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p><strong>T(n) = T(n\/2) + O(log(n))<\/strong><\/p>\n<h3><strong>\u0627\u0644\u062e\u0627\u062a\u0645\u0629<\/strong><\/h3>\n<p>\u062a\u0639\u062f &#8220;recurrence relation&#8221; \u0645\u0646 \u0627\u0644\u0623\u062f\u0648\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0648\u0641\u0647\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0642\u062f\u064a\u0631 \u062a\u0639\u0642\u064a\u062f \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u062a\u062d\u0633\u064a\u0646 \u0623\u062f\u0627\u0626\u0647\u0627. \u0633\u0648\u0627\u0621 \u0643\u0646\u062a \u062a\u0639\u0645\u0644 \u0639\u0644\u0649 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u062a\u0642\u0633\u064a\u0645 \u0648\u063a\u0632\u0648 \u0623\u0648 \u062a\u062d\u0644\u064a\u0644 \u0623\u062f\u0627\u0621 \u0647\u064a\u0643\u0644 \u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0639\u064a\u0646\u060c \u0641\u0625\u0646 \u0641\u0647\u0645 &#8220;recurrence relation&#8221; \u0633\u064a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u062a\u062d\u0642\u064a\u0642 \u0646\u062a\u0627\u0626\u062c \u0623\u0641\u0636\u0644 \u0648\u0623\u062f\u0627\u0621 \u0623\u0643\u062b\u0631 \u0641\u0639\u0627\u0644\u064a\u0629.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0627 \u0647\u0648 \u0645\u0641\u0647\u0648\u0645 &#8220;recurrence relation&#8221; \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u061f \u064a\u0639\u062a\u0628\u0631 \u0645\u0641\u0647\u0648\u0645 &#8220;recurrence relation&#8221; \u0645\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u062a\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0644\u0648\u0635\u0641 \u0627\u0644\u062a\u0633\u0644\u0633\u0644\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062a\u0643\u0631\u0631 \u0641\u064a\u0647\u0627 \u0627\u0644\u0642\u064a\u0645 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0642\u064a\u0645 \u0633\u0627\u0628\u0642\u0629. \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0645\u0647\u0645 \u0644\u0644\u063a\u0627\u064a\u0629 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0639\u0645\u0644 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u060c \u062e\u0627\u0635\u0629 \u062a\u0644\u0643 \u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u062a\u0642\u0633\u064a\u0645 \u0648\u0627\u0644\u062d\u0644\u060c \u0645\u062b\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[304],"tags":[],"class_list":["post-363943","post","type-post","status-publish","format-standard","hentry","category-fast-facts"],"acf":[],"_links":{"self":[{"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/posts\/363943","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/comments?post=363943"}],"version-history":[{"count":0,"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/posts\/363943\/revisions"}],"wp:attachment":[{"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/media?parent=363943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/categories?post=363943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ypsilon.dev\/ar\/wp-json\/wp\/v2\/tags?post=363943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}