{"id":4643,"date":"2025-11-09T10:51:14","date_gmt":"2025-11-09T07:51:14","guid":{"rendered":"https:\/\/usaker.com\/?p=4643"},"modified":"2025-11-09T10:51:32","modified_gmt":"2025-11-09T07:51:32","slug":"%d8%a7%d9%84%d8%ae%d9%88%d8%a7%d8%b1%d8%b2%d9%85%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%a3%d9%88%d9%84%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b1%d8%aa%d9%8a%d8%a8-%d9%88%d8%a7%d9%84%d8%a8%d8%ad%d8%ab","status":"publish","type":"post","link":"https:\/\/usaker.com\/en\/\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a-\u0627\u0644\u0623\u0648\u0644\u064a\u0629-\u0627\u0644\u062a\u0631\u062a\u064a\u0628-\u0648\u0627\u0644\u0628\u062d\u062b\/","title":{"rendered":"\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629: \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0648\u0627\u0644\u0628\u062d\u062b \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f"},"content":{"rendered":"<p>&nbsp;<\/p>\n<h1 style=\"text-align: center;\"><strong>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629: \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0648\u0627\u0644\u0628\u062d\u062b \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f (Sorting, Searching &amp; Complexity Analysis)<\/strong><\/h1>\n<p><strong>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a (Algorithms) \u0647\u064a \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0644\u0643\u0644 \u0628\u0631\u0646\u0627\u0645\u062c \u0646\u0627\u062c\u062d \u2014 \u0641\u0647\u064a \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u064a\u0641\u064a\u0629 \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u062a\u0646\u0638\u064a\u0645\u0647\u0627\u060c \u0648\u0627\u062a\u062e\u0627\u0630 \u0627\u0644\u0642\u0631\u0627\u0631\u0627\u062a.<\/strong><br \/>\n<strong>\u0628\u062f\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u0639\u0627\u0644\u0629\u060c \u062a\u0635\u0628\u062d \u0627\u0644\u0628\u0631\u0627\u0645\u062c \u0628\u0637\u064a\u0626\u0629 \u0648\u063a\u064a\u0631 \u0639\u0645\u0644\u064a\u0629 \u0645\u0647\u0645\u0627 \u0643\u0627\u0646\u062a \u0628\u0646\u064a\u062a\u0647\u0627 \u0642\u0648\u064a\u0629.<\/strong><\/p>\n<p><strong>\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644\u060c \u0633\u0646\u062a\u0639\u0645\u0642 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644 \u062d\u062c\u0631 \u0627\u0644\u0623\u0633\u0627\u0633 \u0641\u064a <a href=\"https:\/\/usaker.com\/en\/\u0645\u0642\u062f\u0645\u0629-\u0625\u0644\u0649-\u0627\u0644\u0628\u0631\u0645\u062c\u0629-\u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645-\u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\/\">\u0627\u0644\u0628\u0631\u0645\u062c\u0629<\/a>:<\/strong><\/p>\n<ul>\n<li><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0631\u062a\u064a\u0628 (Sorting Algorithms)<\/strong><\/li>\n<li><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0628\u062d\u062b (Searching Algorithms)<\/strong><\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0632\u0645\u0646\u064a \u0648\u0627\u0644\u0645\u0643\u0627\u0646\u064a (Time &amp; Space Complexity)<\/strong><\/li>\n<\/ul>\n<p><strong>\u0648\u0633\u0646\u0642\u062f\u0645 \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629\u060c \u062c\u062f\u0627\u0648\u0644 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u060c \u0648\u0631\u0648\u0627\u0628\u0637 \u0645\u0648\u062b\u0648\u0642\u0629 \u062a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0633\u0639 \u0641\u064a \u0627\u0644\u0641\u0647\u0645 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642.<\/strong><\/p>\n<hr \/>\n<h2><strong>\ud83e\udde9 \u0623\u0648\u0644\u064b\u0627: \u0645\u0627 \u0647\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u061f<\/strong><\/h2>\n<p><strong>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0647\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642\u064a\u0629 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0627\u0644\u062a\u064a \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0645\u0639\u064a\u0646\u0629 \u0623\u0648 \u062a\u0646\u0641\u064a\u0630 \u0645\u0647\u0645\u0629 \u0645\u0627.<\/strong><\/p>\n<blockquote><p><strong>\ud83d\udc68\u200d\ud83d\udcbb \u0645\u062b\u0627\u0644 \u0628\u0633\u064a\u0637:<\/strong><br \/>\n<strong>\u0644\u0625\u064a\u062c\u0627\u062f \u0623\u0643\u0628\u0631 \u0631\u0642\u0645 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0623\u0639\u062f\u0627\u062f\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0645\u0631\u0648\u0631 \u0639\u0644\u0649 \u0643\u0644 \u0631\u0642\u0645 \u0648\u0645\u0642\u0627\u0631\u0646\u062a\u0647 \u0628\u0627\u0644\u0623\u0643\u0628\u0631 \u062d\u062a\u0649 \u0627\u0644\u0622\u0646 \u2014 \u0647\u0630\u0647 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629.<\/strong><\/p><\/blockquote>\n<p><strong>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u0627 \u062a\u0631\u062a\u0628\u0637 \u0628\u0644\u063a\u0629 \u0628\u0631\u0645\u062c\u0629 \u0645\u0639\u064a\u0646\u0629\u060c \u0628\u0644 \u062a\u064f\u062a\u0631\u062c\u0645 \u0625\u0644\u0649 \u0643\u0648\u062f \u0641\u064a \u0623\u064a \u0644\u063a\u0629 \u0645\u062b\u0644 <a href=\"https:\/\/usaker.com\/en\/\u062a\u0639\u0644\u0645-\u0627\u0644\u0628\u0631\u0645\u062c\u0629-\u0645\u0646-\u0627\u0644\u0635\u0641\u0631-\u062d\u062a\u0649-\u0627\u0644\u0627\u062d\u062a\u0631\u0627\u0641\/\">Python<\/a> \u0623\u0648 <a href=\"https:\/\/usaker.com\/en\/\u0623\u0641\u0636\u0644-\u0644\u063a\u0627\u062a-\u0627\u0644\u0628\u0631\u0645\u062c\u0629-\u0644\u062a\u0637\u0648\u064a\u0631-\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a-\u0641\u064a-20\/\">Java<\/a> \u0623\u0648 C++.<\/strong><\/p>\n<hr \/>\n<h2><strong>\u2699\ufe0f \u062b\u0627\u0646\u064a\u064b\u0627: \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0631\u062a\u064a\u0628 (Sorting Algorithms)<\/strong><\/h2>\n<p><strong>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0644\u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 (\u0645\u062b\u0644 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0623\u0648 \u0627\u0644\u0623\u0633\u0645\u0627\u0621) \u062a\u0635\u0627\u0639\u062f\u064a\u064b\u0627 \u0623\u0648 \u062a\u0646\u0627\u0632\u0644\u064a\u064b\u0627.<\/strong><br \/>\n<strong>\u0648\u0647\u064a \u0645\u0646 \u0623\u0643\u062b\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u064b\u0627 \u0641\u064a \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c <a href=\"https:\/\/usaker.com\/en\/\u0623\u0641\u0636\u0644-\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0627\u062a-\u062a\u062d\u0633\u064a\u0646-\u0633\u0631\u0639\u0629-\u0627\u0644\u0645\u0648\u0627\u0642\u0639\/\">\u0627\u0644\u0645\u062a\u0627\u062c\u0631 \u0627\u0644\u0625\u0644\u0643\u062a\u0631\u0648\u0646\u064a\u0629<\/a>\u060c \u0648\u0645\u062d\u0631\u0643\u0627\u062a \u0627\u0644\u0628\u062d\u062b.<\/strong><\/p>\n<h3><strong>\ud83d\udd39 1. \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0641\u0642\u0627\u0639\u0627\u062a (Bubble Sort)<\/strong><\/h3>\n<p><strong>\u0645\u0646 \u0623\u0628\u0633\u0637 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u060c \u062a\u0639\u0645\u0644 \u0639\u0628\u0631 \u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0648\u0627\u0644\u0630\u064a \u064a\u0644\u064a\u0647 \u0648\u062a\u0628\u062f\u064a\u0644\u0647\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u0627 \u0641\u064a \u062a\u0631\u062a\u064a\u0628 \u062e\u0627\u0637\u0626.<\/strong><\/p>\n<p><strong>\u0645\u062b\u0627\u0644 \u0628\u0644\u063a\u0629 Python:<\/strong><\/p>\n<pre><strong><code class=\"language-python\">arr = [5, 2, 9, 1, 5, 6]\r\n\r\nfor i in range(len(arr)):\r\n    for j in range(0, len(arr)-i-1):\r\n        if arr[j] &gt; arr[j+1]:\r\n            arr[j], arr[j+1] = arr[j+1], arr[j]\r\n\r\nprint(arr)\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd38 \u0627\u0644\u0639\u064a\u0628: \u0628\u0637\u064a\u0626\u0629 \u062c\u062f\u064b\u0627 \u0645\u0639 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629.<\/strong><br \/>\n<strong>\ud83d\udd38 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n\u00b2)<\/strong><\/p>\n<hr \/>\n<h3><strong>\ud83d\udd39 2. \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062a\u062d\u062f\u064a\u062f (Selection Sort)<\/strong><\/h3>\n<p><strong>\u062a\u0639\u0645\u0644 \u0639\u0628\u0631 \u0627\u0644\u0628\u062d\u062b \u0639\u0646 \u0623\u0635\u063a\u0631 \u0639\u0646\u0635\u0631 \u0641\u064a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0648\u0648\u0636\u0639\u0647 \u0641\u064a \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0635\u062d\u064a\u062d \u0641\u064a \u0643\u0644 \u062f\u0648\u0631\u0629.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">arr = [29, 10, 14, 37, 14]\r\n\r\nfor i in range(len(arr)):\r\n    min_index = i\r\n    for j in range(i+1, len(arr)):\r\n        if arr[j] &lt; arr[min_index]:\r\n            min_index = j\r\n    arr[i], arr[min_index] = arr[min_index], arr[i]\r\n\r\nprint(arr)\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd38 \u0627\u0644\u0628\u0633\u0627\u0637\u0629: \u0633\u0647\u0644\u0629 \u0627\u0644\u0641\u0647\u0645 \u0644\u0643\u0646\u0647\u0627 \u063a\u064a\u0631 \u0641\u0639\u0627\u0644\u0629 \u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629.<\/strong><br \/>\n<strong>\ud83d\udd38 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n\u00b2)<\/strong><\/p>\n<hr \/>\n<h3><strong>\ud83d\udd39 3. \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0625\u062f\u0631\u0627\u062c (Insertion Sort)<\/strong><\/h3>\n<p><strong>\u062a\u064f\u062f\u062e\u0644 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0641\u064a \u0645\u0643\u0627\u0646\u0647 \u0627\u0644\u0635\u062d\u064a\u062d \u0643\u0645\u0627 \u064a\u0641\u0639\u0644 \u0627\u0644\u0625\u0646\u0633\u0627\u0646 \u0628\u062a\u0631\u062a\u064a\u0628 \u0623\u0648\u0631\u0627\u0642 \u0627\u0644\u0644\u0639\u0628.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">arr = [12, 11, 13, 5, 6]\r\n\r\nfor i in range(1, len(arr)):\r\n    key = arr[i]\r\n    j = i - 1\r\n    while j &gt;= 0 and key &lt; arr[j]:\r\n        arr[j + 1] = arr[j]\r\n        j -= 1\r\n    arr[j + 1] = key\r\n\r\nprint(arr)\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd38 \u0641\u0639\u0627\u0644\u0629 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0623\u0648 \u0634\u0628\u0647 \u0627\u0644\u0645\u0631\u062a\u0628\u0629.<\/strong><br \/>\n<strong>\ud83d\udd38 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n\u00b2)<\/strong><\/p>\n<hr \/>\n<h3><strong>\ud83d\udd39 4. \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062f\u0645\u062c (Merge Sort)<\/strong><\/h3>\n<p><strong>\u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u0628\u062f\u0623 \u0627\u0644\u062a\u0642\u0633\u064a\u0645 \u062b\u0645 \u0627\u0644\u062f\u0645\u062c.<\/strong><br \/>\n<strong>\u062a\u0642\u0633\u0645 \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0625\u0644\u0649 \u0646\u0635\u0641\u064a\u0646\u060c \u062a\u0631\u062a\u0628 \u0643\u0644 \u0646\u0635\u0641 \u0639\u0644\u0649 \u062d\u062f\u0629\u060c \u062b\u0645 \u062a\u062f\u0645\u062c\u0647\u0645\u0627.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">def merge_sort(arr):\r\n    if len(arr) &gt; 1:\r\n        mid = len(arr)\/\/2\r\n        L = arr[:mid]\r\n        R = arr[mid:]\r\n        merge_sort(L)\r\n        merge_sort(R)\r\n        i = j = k = 0\r\n        while i &lt; len(L) and j &lt; len(R):\r\n            if L[i] &lt; R[j]:\r\n                arr[k] = L[i]\r\n                i += 1\r\n            else:\r\n                arr[k] = R[j]\r\n                j += 1\r\n            k += 1\r\n        while i &lt; len(L):\r\n            arr[k] = L[i]\r\n            i += 1\r\n            k += 1\r\n        while j &lt; len(R):\r\n            arr[k] = R[j]\r\n            j += 1\r\n            k += 1\r\n\r\narr = [38, 27, 43, 3, 9, 82, 10]\r\nmerge_sort(arr)\r\nprint(arr)\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd38 \u0641\u0639\u0627\u0644\u0629 \u062c\u062f\u064b\u0627 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629.<\/strong><br \/>\n<strong>\ud83d\udd38 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n log n)<\/strong><\/p>\n<hr \/>\n<h3><strong>\ud83d\udd39 5. \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0633\u0631\u064a\u0639 (Quick Sort)<\/strong><\/h3>\n<p><strong>\u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u0628\u062f\u0623 \u0627\u062e\u062a\u064a\u0627\u0631 \u0639\u0646\u0635\u0631 \u0645\u062d\u0648\u0631\u064a (Pivot) \u0648\u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u062d\u0648\u0644\u0647.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">def quick_sort(arr):\r\n    if len(arr) &lt;= 1:\r\n        return arr\r\n    else:\r\n        pivot = arr[0]\r\n        less = [x for x in arr[1:] if x &lt;= pivot]\r\n        greater = [x for x in arr[1:] if x &gt; pivot]\r\n        return quick_sort(less) + [pivot] + quick_sort(greater)\r\n\r\narr = [10, 7, 8, 9, 1, 5]\r\nprint(quick_sort(arr))\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd38 \u062a\u064f\u0639\u062f \u0645\u0646 \u0623\u0633\u0631\u0639 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u0645\u0644\u064a\u064b\u0627.<\/strong><br \/>\n<strong>\ud83d\udd38 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n log n)<\/strong><\/p>\n<hr \/>\n<h2><strong>\ud83d\udd0d \u062b\u0627\u0644\u062b\u064b\u0627: \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0628\u062d\u062b (Searching Algorithms)<\/strong><\/h2>\n<p><strong>\u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0639\u0646\u0635\u0631 \u0645\u0639\u064a\u0646 \u062f\u0627\u062e\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/strong><\/p>\n<h3><strong>\ud83d\udd38 1. \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u062e\u0637\u064a (Linear Search)<\/strong><\/h3>\n<p><strong>\u064a\u0645\u0631 \u0639\u0644\u0649 \u0643\u0644 \u0639\u0646\u0635\u0631 \u062d\u062a\u0649 \u064a\u062c\u062f \u0627\u0644\u0645\u0637\u0644\u0648\u0628.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">def linear_search(arr, x):\r\n    for i in range(len(arr)):\r\n        if arr[i] == x:\r\n            return i\r\n    return -1\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd39 \u0627\u0644\u0628\u0633\u0627\u0637\u0629: \u0633\u0647\u0644 \u0627\u0644\u062a\u0646\u0641\u064a\u0630<\/strong><br \/>\n<strong>\ud83d\udd39 \u0627\u0644\u0639\u064a\u0628: \u0628\u0637\u064a\u0621 \u0641\u064a <a href=\"https:\/\/usaker.com\/en\/\u0647\u064a\u0627\u0643\u0644-\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a-\u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629-\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a\/\">\u0627\u0644\u0642\u0648\u0627\u0626\u0645<\/a> \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/strong><br \/>\n<strong>\ud83d\udd39 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(n)<\/strong><\/p>\n<hr \/>\n<h3><strong>\ud83d\udd38 2. \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u062b\u0646\u0627\u0626\u064a (Binary Search)<\/strong><\/h3>\n<p><strong>\u064a\u062a\u0637\u0644\u0628 \u0642\u0627\u0626\u0645\u0629 \u0645\u0631\u062a\u0628\u0629 \u0645\u0633\u0628\u0642\u064b\u0627 \u0648\u064a\u0642\u0633\u0645\u0647\u0627 \u0641\u064a \u0643\u0644 \u062e\u0637\u0648\u0629 \u0625\u0644\u0649 \u0646\u0635\u0641\u064a\u0646.<\/strong><\/p>\n<pre><strong><code class=\"language-python\">def binary_search(arr, x):\r\n    low = 0\r\n    high = len(arr) - 1\r\n    while low &lt;= high:\r\n        mid = (low + high)\/\/2\r\n        if arr[mid] == x:\r\n            return mid\r\n        elif arr[mid] &lt; x:\r\n            low = mid + 1\r\n        else:\r\n            high = mid - 1\r\n    return -1\r\n<\/code><\/strong><\/pre>\n<p><strong>\ud83d\udd39 \u0641\u0639\u0627\u0644\u0629 \u062c\u062f\u064b\u0627 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0631\u062a\u0628\u0629.<\/strong><br \/>\n<strong>\ud83d\udd39 \u0627\u0644\u062a\u0639\u0642\u064a\u062f: O(log n)<\/strong><\/p>\n<hr \/>\n<h2><strong>\ud83d\udcca \u062c\u062f\u0648\u0644 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u0623\u0647\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a<\/strong><\/h2>\n<table>\n<thead>\n<tr>\n<th><strong>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629<\/strong><\/th>\n<th><strong>\u0627\u0644\u0646\u0648\u0639<\/strong><\/th>\n<th><strong>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0632\u0645\u0646\u064a<\/strong><\/th>\n<th><strong>\u0627\u0644\u0645\u0645\u064a\u0632\u0627\u062a<\/strong><\/th>\n<th><strong>\u0627\u0644\u0639\u064a\u0648\u0628<\/strong><\/th>\n<th><strong>\u0627\u0644\u0623\u0641\u0636\u0644 \u0644\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Bubble Sort<\/strong><\/td>\n<td><strong>\u062a\u0631\u062a\u064a\u0628<\/strong><\/td>\n<td><strong>O(n\u00b2)<\/strong><\/td>\n<td><strong>\u0633\u0647\u0644\u0629<\/strong><\/td>\n<td><strong>\u0628\u0637\u064a\u0626\u0629<\/strong><\/td>\n<td><strong>\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Merge Sort<\/strong><\/td>\n<td><strong>\u062a\u0631\u062a\u064a\u0628<\/strong><\/td>\n<td><strong>O(n log n)<\/strong><\/td>\n<td><strong>\u0633\u0631\u064a\u0639\u0629<\/strong><\/td>\n<td><strong>\u062a\u062d\u062a\u0627\u062c \u0630\u0627\u0643\u0631\u0629 \u0625\u0636\u0627\u0641\u064a\u0629<\/strong><\/td>\n<td><strong>\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Quick Sort<\/strong><\/td>\n<td><strong>\u062a\u0631\u062a\u064a\u0628<\/strong><\/td>\n<td><strong>O(n log n)<\/strong><\/td>\n<td><strong>\u0641\u0639\u0627\u0644\u0629 \u062c\u062f\u064b\u0627<\/strong><\/td>\n<td><strong>\u0623\u062f\u0627\u0621 \u0636\u0639\u064a\u0641 \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u062d\u0627\u0644\u0627\u062a<\/strong><\/td>\n<td><strong>\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Linear Search<\/strong><\/td>\n<td><strong>\u0628\u062d\u062b<\/strong><\/td>\n<td><strong>O(n)<\/strong><\/td>\n<td><strong>\u0628\u0633\u064a\u0637<\/strong><\/td>\n<td><strong>\u0628\u0637\u064a\u0621<\/strong><\/td>\n<td><strong>\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0635\u063a\u064a\u0631\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Binary Search<\/strong><\/td>\n<td><strong>\u0628\u062d\u062b<\/strong><\/td>\n<td><strong>O(log n)<\/strong><\/td>\n<td><strong>\u0633\u0631\u064a\u0639<\/strong><\/td>\n<td><strong>\u064a\u062a\u0637\u0644\u0628 \u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0631\u062a\u0628\u0629<\/strong><\/td>\n<td><strong>\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2><strong>\ud83e\uddee \u0631\u0627\u0628\u0639\u064b\u0627: \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f (Complexity Analysis)<\/strong><\/h2>\n<p><strong>\u0643\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u062a\u064f\u0642\u0627\u0633 \u0628\u0643\u0641\u0627\u0621\u062a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644:<\/strong><\/p>\n<ul>\n<li><strong>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0632\u0645\u0646\u064a (Time Complexity): \u0643\u0645 \u0645\u0646 \u0627\u0644\u0648\u0642\u062a \u062a\u062d\u062a\u0627\u062c\u061f<\/strong><\/li>\n<li><strong>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0645\u0643\u0627\u0646\u064a (Space Complexity): \u0643\u0645 \u0645\u0646 \u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u062a\u0633\u062a\u0647\u0644\u0643\u061f<\/strong><\/li>\n<\/ul>\n<p><strong>\u0627\u0644\u0631\u0645\u0648\u0632 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629:<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th><strong>\u0627\u0644\u0631\u0645\u0632<\/strong><\/th>\n<th><strong>\u0627\u0644\u0645\u0639\u0646\u0649<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>O(1)<\/strong><\/td>\n<td><strong>\u062b\u0627\u0628\u062a \u2014 \u0627\u0644\u0623\u0633\u0631\u0639<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>O(log n)<\/strong><\/td>\n<td><strong>\u0634\u0628\u0647 \u062e\u0637\u064a \u2014 \u0633\u0631\u064a\u0639 \u062c\u062f\u064b\u0627<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>O(n)<\/strong><\/td>\n<td><strong>\u062e\u0637\u064a \u2014 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062d\u062c\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>O(n\u00b2)<\/strong><\/td>\n<td><strong>\u062a\u0631\u0628\u064a\u0639\u064a \u2014 \u0628\u0637\u064a\u0621<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>O(2\u207f)<\/strong><\/td>\n<td><strong>\u0623\u064f\u0633\u064a \u2014 \u0627\u0644\u0623\u0633\u0648\u0623 \u0641\u064a \u0627\u0644\u0623\u062f\u0627\u0621<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2><strong>\ud83e\udde0 \u062e\u0627\u0645\u0633\u064b\u0627: \u0623\u0641\u0636\u0644 \u0645\u0645\u0627\u0631\u0633\u0627\u062a \u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a<\/strong><\/h2>\n<ol>\n<li><strong>\u0627\u0628\u062f\u0623 \u0628\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0623\u0628\u0633\u0637 \u062b\u0645 \u0637\u0648\u0651\u0631\u0647\u0627.<\/strong><\/li>\n<li><strong>\u0627\u062e\u062a\u0628\u0631 \u0627\u0644\u0623\u062f\u0627\u0621 \u0639\u0644\u0649 \u0628\u064a\u0627\u0646\u0627\u062a \u062d\u0642\u064a\u0642\u064a\u0629.<\/strong><\/li>\n<li><strong>\u0627\u0633\u062a\u062e\u062f\u0645 \u0623\u062f\u0648\u0627\u062a \u062a\u062d\u0644\u064a\u0644 \u0645\u062b\u0644 <span style=\"color: #000080;\"><a style=\"color: #000080;\" href=\"https:\/\/www.bigocheatsheet.com\/\">Big-O Cheat Sheet<\/a><\/span>.<\/strong><\/li>\n<li><strong>\u0642\u0633 \u0623\u062f\u0627\u0621\u0643 \u0628\u0627\u0644\u0648\u0642\u062a \u0648\u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0643\u062a\u0628\u0629 <code>time<\/code> \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646.<\/strong><\/li>\n<li><strong>\u062a\u0639\u0644\u0645 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0639\u0628\u0631<span style=\"color: #000080;\"> <a style=\"color: #000080;\" href=\"https:\/\/www.geeksforgeeks.org\/time-complexities-of-all-sorting-algorithms\/\">GeeksforGeeks<\/a><\/span>.<\/strong><\/li>\n<\/ol>\n<hr \/>\n<h2><strong>\ud83c\udf10 \u0631\u0648\u0627\u0628\u0637 \u062e\u0627\u0631\u062c\u064a\u0629 \u0645\u0648\u062b\u0648\u0642\u0629<\/strong><\/h2>\n<ul>\n<li><span style=\"color: #000080;\"><strong><a style=\"color: #000080;\" href=\"https:\/\/www.geeksforgeeks.org\/sorting-algorithms\/\">GeeksforGeeks \u2013 Sorting Algorithms<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #000080;\"><strong><a style=\"color: #000080;\" href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/algorithms\">Khan Academy \u2013 Algorithms Course<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #000080;\"><strong><a style=\"color: #000080;\" href=\"https:\/\/www.bigocheatsheet.com\/\">Big-O Cheat Sheet<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #000080;\"><strong><a style=\"color: #000080;\" href=\"https:\/\/www.freecodecamp.org\/news\/binary-search-in-javascript\/\">freeCodeCamp \u2013 Binary Search Tutorial<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #000080;\"><strong><a style=\"color: #000080;\" href=\"https:\/\/ocw.mit.edu\/courses\/electrical-engineering-and-computer-science\/6-006-introduction-to-algorithms-fall-2011\/\">MIT OpenCourseWare \u2013 Introduction to Algorithms<\/a><\/strong><\/span><\/li>\n<\/ul>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629: \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0648\u0627\u0644\u0628\u062d\u062b \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f (Sorting, Searching &amp; Complexity Analysis) \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a (Algorithms) \u0647\u064a \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0644\u0643\u0644 \u0628\u0631\u0646\u0627\u0645\u062c \u0646\u0627\u062c\u062d \u2014 \u0641\u0647\u064a \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u064a\u0641\u064a\u0629 \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u062a\u0646\u0638\u064a\u0645\u0647\u0627\u060c \u0648\u0627\u062a\u062e\u0627\u0630 \u0627\u0644\u0642\u0631\u0627\u0631\u0627\u062a. \u0628\u062f\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u0639\u0627\u0644\u0629\u060c \u062a\u0635\u0628\u062d \u0627\u0644\u0628\u0631\u0627\u0645\u062c \u0628\u0637\u064a\u0626\u0629 \u0648\u063a\u064a\u0631 \u0639\u0645\u0644\u064a\u0629 \u0645\u0647\u0645\u0627 \u0643\u0627\u0646\u062a \u0628\u0646\u064a\u062a\u0647\u0627 \u0642\u0648\u064a\u0629. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644\u060c \u0633\u0646\u062a\u0639\u0645\u0642 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644 \u062d\u062c\u0631 \u0627\u0644\u0623\u0633\u0627\u0633 \u0641\u064a \u0627\u0644\u0628\u0631\u0645\u062c\u0629: [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4644,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[75],"tags":[2532,2531,2519,1213,2530,2529,2527,2526,2525,2536,2528,2524,2537,87,2534,2533,2535],"class_list":["post-4643","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-75","tag-big-o","tag-complexity-analysis","tag-data-structures","tag-python","tag-searching","tag-sorting","tag-2527","tag-2526","tag-2525","tag-2536","tag-2528","tag-2524","tag-2537","tag-87","tag-2534","tag-2533","tag-2535"],"acf":[],"yoast_head":"<!-- This site is optimized 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\u0627\u0644\u0623\u0648\u0644\u064a\u0629: \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0648\u0627\u0644\u0628\u062d\u062b \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f - \u0635\u0642\u0631 \u0648\u064a\u0628\" \/>\n<meta property=\"og:description\" content=\"&nbsp; \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629: \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0648\u0627\u0644\u0628\u062d\u062b \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f (Sorting, Searching &amp; Complexity Analysis) \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a (Algorithms) \u0647\u064a \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0644\u0643\u0644 \u0628\u0631\u0646\u0627\u0645\u062c \u0646\u0627\u062c\u062d \u2014 \u0641\u0647\u064a \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u064a\u0641\u064a\u0629 \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u062a\u0646\u0638\u064a\u0645\u0647\u0627\u060c \u0648\u0627\u062a\u062e\u0627\u0630 \u0627\u0644\u0642\u0631\u0627\u0631\u0627\u062a. \u0628\u062f\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u0639\u0627\u0644\u0629\u060c \u062a\u0635\u0628\u062d \u0627\u0644\u0628\u0631\u0627\u0645\u062c \u0628\u0637\u064a\u0626\u0629 \u0648\u063a\u064a\u0631 \u0639\u0645\u0644\u064a\u0629 \u0645\u0647\u0645\u0627 \u0643\u0627\u0646\u062a \u0628\u0646\u064a\u062a\u0647\u0627 \u0642\u0648\u064a\u0629. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644\u060c \u0633\u0646\u062a\u0639\u0645\u0642 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644 \u062d\u062c\u0631 \u0627\u0644\u0623\u0633\u0627\u0633 \u0641\u064a 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