{"id":76370,"date":"2024-09-11T08:00:42","date_gmt":"2024-09-11T04:30:42","guid":{"rendered":"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/"},"modified":"2024-09-11T08:00:42","modified_gmt":"2024-09-11T04:30:42","slug":"finding-an-element-in-an-infinite-array-using-java-1f1f","status":"publish","type":"post","link":"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/","title":{"rendered":"\u06cc\u0627\u0641\u062a\u0646 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062f\u0631 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062c\u0627\u0648\u0627"},"content":{"rendered":"<p>Summarize this content to 400 words in Persian Lang <\/p>\n<p>  \u0628\u06cc\u0627\u0646 \u0645\u0634\u06a9\u0644<\/p>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 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\u0645\u062d\u062f\u0648\u062f\u0647: \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0645\u0646\u0627\u0633\u0628\u06cc \u0631\u0627 \u06a9\u0647 \u062d\u0627\u0648\u06cc \u0647\u062f\u0641 \u0627\u0633\u062a \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0648\u062b\u0631 \u0634\u0627\u062e\u0635 \u0647\u062f\u0641 \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>  \u06a9\u062f<\/p>\n<p>public class InfiniteArraySearch {<br \/>\n    public static void main(String[] args) {<br \/>\n        \/\/ Define the array (for demonstration purposes, treat this as infinite)<br \/>\n        int[] arr = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};<br \/>\n        int target = 6;<\/p>\n<p>        \/\/ Call the function to find the target element<br \/>\n        int result = findElementInInfiniteArray(arr, target);<br \/>\n        System.out.println(&#8220;Element found at index: &#8221; + result);<br \/>\n    }<\/p>\n<p>    \/\/ Function to find the target in the infinite array<br \/>\n    static int findElementInInfiniteArray(int[] arr, int target) {<br \/>\n        \/\/ Start with a small range<br \/>\n        int start = 0;<br \/>\n        int end = 1;<\/p>\n<p>        \/\/ Dynamically increase the range until the target is within bounds<br \/>\n        while (target &gt; arr[end]) {<br \/>\n            int newStart = end + 1;  \/\/ Update start to one after the current end<br \/>\n            end = end + (end &#8211; start + 1) * 2;  \/\/ Double the range<br \/>\n            start = newStart;  \/\/ Move the start to newStart<br \/>\n        }<\/p>\n<p>        \/\/ Perform binary search within the determined range<br \/>\n        return binarySearch(arr, target, start, end);<br \/>\n    }<\/p>\n<p>    \/\/ Standard binary search implementation<br \/>\n    static int binarySearch(int[] arr, int target, int start, int end) {<br \/>\n        while (start  end) {<br \/>\n            int mid = start + (end &#8211; start) \/ 2;<\/p>\n<p>            if (target  arr[mid]) {<br \/>\n                end = mid &#8211; 1;  \/\/ Move the end to the left<br \/>\n            } else if (target &gt; arr[mid]) {<br \/>\n                start = mid + 1;  \/\/ Move the start to the right<br \/>\n            } else {<br \/>\n                return mid;  \/\/ Element found<br \/>\n            }<br \/>\n        }<br \/>\n        return -1;  \/\/ Element not found<br \/>\n    }<br \/>\n}<\/p>\n<p>    \u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/p>\n<p>    \u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/p>\n<p>  \u062a\u0648\u0636\u06cc\u062d \u0622\u06cc\u06cc\u0646 \u0646\u0627\u0645\u0647<\/p>\n<p>  1. \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0635\u0644\u06cc<\/p>\n<p>\u062a\u0627\u0628\u0639 main \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0646\u0645\u0648\u0646\u0647 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u062f arr \u0648 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0647\u062f\u0641 6. \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc\u060c \u0645\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u062d\u062f\u0648\u062f \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0645\u0641\u0647\u0648\u0645\u06cc\u060c \u0622\u0646 \u0631\u0627 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. \u0633\u067e\u0633 \u062a\u0627\u0628\u0639 \u0627\u0635\u0644\u06cc \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc \u06a9\u0646\u062f findElementInInfiniteArray \u0628\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0647\u062f\u0641\u060c \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a \u06cc\u0627\u0641\u062a\u0646 \u0641\u0647\u0631\u0633\u062a \u0631\u0627 \u0686\u0627\u067e \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<p>  2. \u06af\u0633\u062a\u0631\u0634 \u062f\u0627\u0645\u0646\u0647 (\u06af\u0633\u062a\u0631\u0634 \u062e\u0637\u06cc \u0645\u0646\u0637\u0642\u0647 \u062c\u0633\u062a\u062c\u0648)<\/p>\n<p>\u062f\u0631 findElementInInfiniteArray \u0631\u0648\u0634:<\/p>\n<p>\u0645\u0627 \u0628\u0627 \u0641\u0631\u0636 \u0627\u06cc\u0646\u06a9\u0647 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 [0, 1].<br \/>\n\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u062f\u0631 \u0627\u0633\u062a arr[end]\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0647\u062f\u0641 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0641\u0639\u0644\u06cc \u0646\u06cc\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0627 \u0645\u062d\u062f\u0648\u062f\u0647 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0635\u0627\u0639\u062f\u06cc \u0628\u0627 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u06a9\u0631\u062f\u0646 \u0622\u0646 \u06af\u0633\u062a\u0631\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645 (end = end + (end &#8211; start + 1) * 2). \u0627\u06cc\u0646 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u0628\u0647 \u0645\u0627 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0632\u0645\u06cc\u0646\u0647 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\u0632\u06cc\u0631\u0627 \u062f\u0631 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0641\u0636\u0627\u06cc \u062c\u0633\u062a\u062c\u0648 \u0631\u0627 \u0628\u0647 \u0646\u0635\u0641 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f. \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u06a9\u0644\u06cc\u062f\u06cc \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<p>\u0627\u06af\u0631 \u0647\u062f\u0641 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0628\u0627\u0634\u062f (arr[mid]\u060c \u0646\u06cc\u0645\u0647 \u0686\u067e \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u062f.<br \/>\n\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0633\u062a\u060c \u0646\u06cc\u0645\u0647 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u062f.<br \/>\n\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0627 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f\u060c \u0634\u0627\u062e\u0635 \u0622\u0646 \u0631\u0627 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u06cc\u062f.<\/p>\n<p>  4. \u0645\u0648\u0627\u0631\u062f \u0644\u0628\u0647<\/p>\n<p>\u0627\u06af\u0631 \u0647\u062f\u0641 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0627\u0634\u062f\u060c \u06cc\u0627 \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0635\u0644\u0627\u064b \u0647\u062f\u0641 \u0631\u0627 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u0632 \u062e\u0648\u0627\u0647\u062f \u06af\u0634\u062a. -1.<\/p>\n<p>  \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/p>\n<p>\u06af\u0633\u062a\u0631\u0634 \u062f\u0627\u0645\u0646\u0647: \u0645\u062d\u062f\u0648\u062f\u0647 \u0628\u0627 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0637\u0648\u0644 \u0645\u06cc \u06a9\u0634\u062f O(log N) \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u062d\u062f\u0648\u062f\u0647 \u0645\u0646\u0627\u0633\u0628 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u062f\u0641 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f.<br \/>\n\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc: \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u067e\u06cc\u062f\u0627 \u0634\u062f\u060c \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f O(log M)\u060c \u06a9\u062c\u0627 M \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0627\u0633\u062a O(log N + log M).<\/p>\n<div data-article-id=\"1996169\" id=\"article-body\">\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"\u062a\u063a\u06cc\u06cc\u0631 \u0648\u0636\u0639\u06cc\u062a \u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#%D8%A8%DB%8C%D8%A7%D9%86_%D9%85%D8%B4%DA%A9%D9%84\" >\u0628\u06cc\u0627\u0646 \u0645\u0634\u06a9\u0644<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#%D8%A8%D8%B1%D8%B1%D8%B3%DB%8C_%D8%A7%D8%AC%D9%85%D8%A7%D9%84%DB%8C_%D8%B1%D9%88%DB%8C%DA%A9%D8%B1%D8%AF\" >\u0628\u0631\u0631\u0633\u06cc \u0627\u062c\u0645\u0627\u0644\u06cc \u0631\u0648\u06cc\u06a9\u0631\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#%DA%A9%D8%AF\" >\u06a9\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#%D8%AA%D9%88%D8%B6%DB%8C%D8%AD_%D8%A2%DB%8C%DB%8C%D9%86_%D9%86%D8%A7%D9%85%D9%87\" >\u062a\u0648\u0636\u06cc\u062d \u0622\u06cc\u06cc\u0646 \u0646\u0627\u0645\u0647<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#1_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF_%D8%A7%D8%B5%D9%84%DB%8C\" >1. \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0635\u0644\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#2_%DA%AF%D8%B3%D8%AA%D8%B1%D8%B4_%D8%AF%D8%A7%D9%85%D9%86%D9%87_%DA%AF%D8%B3%D8%AA%D8%B1%D8%B4_%D8%AE%D8%B7%DB%8C_%D9%85%D9%86%D8%B7%D9%82%D9%87_%D8%AC%D8%B3%D8%AA%D8%AC%D9%88\" >2. \u06af\u0633\u062a\u0631\u0634 \u062f\u0627\u0645\u0646\u0647 (\u06af\u0633\u062a\u0631\u0634 \u062e\u0637\u06cc \u0645\u0646\u0637\u0642\u0647 \u062c\u0633\u062a\u062c\u0648)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#3_%D8%AC%D8%B3%D8%AA%D8%AC%D9%88%DB%8C_%D8%A8%D8%A7%DB%8C%D9%86%D8%B1%DB%8C\" >3. \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#4_%D9%85%D9%88%D8%A7%D8%B1%D8%AF_%D9%84%D8%A8%D9%87\" >4. \u0645\u0648\u0627\u0631\u062f \u0644\u0628\u0647<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/nabfollower.com\/blog\/finding-an-element-in-an-infinite-array-using-java-1f1f\/#%D9%BE%DB%8C%DA%86%DB%8C%D8%AF%DA%AF%DB%8C_%D8%B2%D9%85%D8%A7%D9%86%DB%8C\" >\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"%D8%A8%DB%8C%D8%A7%D9%86_%D9%85%D8%B4%DA%A9%D9%84\"><\/span>\n<p>  \u0628\u06cc\u0627\u0646 \u0645\u0634\u06a9\u0644<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0646\u0627\u0645\u062a\u0646\u0627\u0647\u06cc \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0645\u0631\u062a\u0628 \u0634\u062f\u0647\u060c \u0628\u0627\u06cc\u062f \u0634\u0627\u062e\u0635 \u06cc\u06a9 \u0639\u062f\u062f \u0647\u062f\u0641 \u0645\u0639\u06cc\u0646 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645. \u0622\u0631\u0627\u06cc\u0647 &#8220;\u0628\u06cc \u0646\u0647\u0627\u06cc\u062a&#8221; \u0627\u0633\u062a\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u06a9\u0647 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0646\u062f\u0627\u0632\u0647 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u0642\u0628\u0644 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0642\u0637 \u06cc\u06a9 \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0633\u0646\u062a\u06cc \u0631\u0627 \u0645\u0633\u062a\u0642\u06cc\u0645\u0627\u064b \u0627\u0639\u0645\u0627\u0644 \u06a9\u0646\u06cc\u0645.<\/p>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%D8%A8%D8%B1%D8%B1%D8%B3%DB%8C_%D8%A7%D8%AC%D9%85%D8%A7%D9%84%DB%8C_%D8%B1%D9%88%DB%8C%DA%A9%D8%B1%D8%AF\"><\/span>\n<p>  \u0628\u0631\u0631\u0633\u06cc \u0627\u062c\u0645\u0627\u0644\u06cc \u0631\u0648\u06cc\u06a9\u0631\u062f<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li>\n<p><strong>\u0628\u0627 \u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f\u0647 \u06a9\u0648\u0686\u06a9 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f<\/strong>: \u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u06a9\u0648\u0686\u06a9\u06cc \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f (\u0645\u062b\u0644\u0627\u064b \u0628\u06cc\u0646 \u0634\u0627\u062e\u0635 \u0647\u0627\u06cc 0 \u0648 1).<\/p>\n<\/li>\n<li>\n<p><strong>\u0628\u0647 \u0635\u0648\u0631\u062a \u067e\u0648\u06cc\u0627 \u062f\u0627\u0645\u0646\u0647 \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u06cc\u062f<\/strong>: \u0627\u06af\u0631 \u0639\u0646\u0635\u0631 \u0647\u062f\u0641 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0627\u0648\u0644\u06cc\u0647 \u06cc\u0627\u0641\u062a \u0646\u0634\u062f\u060c \u0628\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u06cc\u0634\u062a\u0631\u060c \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0631\u0627 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u0627\u06cc\u0646 \u0631\u0634\u062f \u062a\u0635\u0627\u0639\u062f\u06cc \u0628\u0647 \u0645\u0627 \u0627\u0645\u06a9\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u062a\u0627 \u0628\u0647 \u0633\u0631\u0639\u062a \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647\u200c\u0627\u06cc \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0647\u062f\u0641 \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u062d\u0631\u06a9\u062a \u06a9\u0646\u06cc\u0645.<\/p>\n<\/li>\n<li>\n<p><strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647<\/strong>: \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0645\u0646\u0627\u0633\u0628\u06cc \u0631\u0627 \u06a9\u0647 \u062d\u0627\u0648\u06cc \u0647\u062f\u0641 \u0627\u0633\u062a \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0648\u062b\u0631 \u0634\u0627\u062e\u0635 \u0647\u062f\u0641 \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<\/li>\n<\/ol>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%DA%A9%D8%AF\"><\/span>\n<p>  \u06a9\u062f<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight java\"><code><span class=\"kd\">public<\/span> <span class=\"kd\">class<\/span> <span class=\"nc\">InfiniteArraySearch<\/span> <span class=\"o\">{<\/span>\n    <span class=\"kd\">public<\/span> <span class=\"kd\">static<\/span> <span class=\"kt\">void<\/span> <span class=\"nf\">main<\/span><span class=\"o\">(<\/span><span class=\"nc\">String<\/span><span class=\"o\">[]<\/span> <span class=\"n\">args<\/span><span class=\"o\">)<\/span> <span class=\"o\">{<\/span>\n        <span class=\"c1\">\/\/ Define the array (for demonstration purposes, treat this as infinite)<\/span>\n        <span class=\"kt\">int<\/span><span class=\"o\">[]<\/span> <span class=\"n\">arr<\/span> <span class=\"o\">=<\/span> <span class=\"o\">{<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">,<\/span> <span class=\"mi\">3<\/span><span class=\"o\">,<\/span> <span class=\"mi\">4<\/span><span class=\"o\">,<\/span> <span class=\"mi\">5<\/span><span class=\"o\">,<\/span> <span class=\"mi\">6<\/span><span class=\"o\">,<\/span> <span class=\"mi\">7<\/span><span class=\"o\">,<\/span> <span class=\"mi\">8<\/span><span class=\"o\">,<\/span> <span class=\"mi\">9<\/span><span class=\"o\">,<\/span> <span class=\"mi\">10<\/span><span class=\"o\">,<\/span> <span class=\"mi\">11<\/span><span class=\"o\">,<\/span> <span class=\"mi\">12<\/span><span class=\"o\">,<\/span> <span class=\"mi\">13<\/span><span class=\"o\">,<\/span> <span class=\"mi\">14<\/span><span class=\"o\">,<\/span> <span class=\"mi\">15<\/span><span class=\"o\">};<\/span>  \n        <span class=\"kt\">int<\/span> <span class=\"n\">target<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span><span class=\"o\">;<\/span>\n\n        <span class=\"c1\">\/\/ Call the function to find the target element<\/span>\n        <span class=\"kt\">int<\/span> <span class=\"n\">result<\/span> <span class=\"o\">=<\/span> <span class=\"n\">findElementInInfiniteArray<\/span><span class=\"o\">(<\/span><span class=\"n\">arr<\/span><span class=\"o\">,<\/span> <span class=\"n\">target<\/span><span class=\"o\">);<\/span>\n        <span class=\"nc\">System<\/span><span class=\"o\">.<\/span><span class=\"na\">out<\/span><span class=\"o\">.<\/span><span class=\"na\">println<\/span><span class=\"o\">(<\/span><span class=\"s\">\"Element found at index: \"<\/span> <span class=\"o\">+<\/span> <span class=\"n\">result<\/span><span class=\"o\">);<\/span>\n    <span class=\"o\">}<\/span>\n\n    <span class=\"c1\">\/\/ Function to find the target in the infinite array<\/span>\n    <span class=\"kd\">static<\/span> <span class=\"kt\">int<\/span> <span class=\"nf\">findElementInInfiniteArray<\/span><span class=\"o\">(<\/span><span class=\"kt\">int<\/span><span class=\"o\">[]<\/span> <span class=\"n\">arr<\/span><span class=\"o\">,<\/span> <span class=\"kt\">int<\/span> <span class=\"n\">target<\/span><span class=\"o\">)<\/span> <span class=\"o\">{<\/span>\n        <span class=\"c1\">\/\/ Start with a small range<\/span>\n        <span class=\"kt\">int<\/span> <span class=\"n\">start<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span><span class=\"o\">;<\/span>\n        <span class=\"kt\">int<\/span> <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span><span class=\"o\">;<\/span>\n\n        <span class=\"c1\">\/\/ Dynamically increase the range until the target is within bounds<\/span>\n        <span class=\"k\">while<\/span> <span class=\"o\">(<\/span><span class=\"n\">target<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">arr<\/span><span class=\"o\">[<\/span><span class=\"n\">end<\/span><span class=\"o\">])<\/span> <span class=\"o\">{<\/span>\n            <span class=\"kt\">int<\/span> <span class=\"n\">newStart<\/span> <span class=\"o\">=<\/span> <span class=\"n\">end<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Update start to one after the current end<\/span>\n            <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"n\">end<\/span> <span class=\"o\">+<\/span> <span class=\"o\">(<\/span><span class=\"n\">end<\/span> <span class=\"o\">-<\/span> <span class=\"n\">start<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"o\">)<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">2<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Double the range<\/span>\n            <span class=\"n\">start<\/span> <span class=\"o\">=<\/span> <span class=\"n\">newStart<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Move the start to newStart<\/span>\n        <span class=\"o\">}<\/span>\n\n        <span class=\"c1\">\/\/ Perform binary search within the determined range<\/span>\n        <span class=\"k\">return<\/span> <span class=\"nf\">binarySearch<\/span><span class=\"o\">(<\/span><span class=\"n\">arr<\/span><span class=\"o\">,<\/span> <span class=\"n\">target<\/span><span class=\"o\">,<\/span> <span class=\"n\">start<\/span><span class=\"o\">,<\/span> <span class=\"n\">end<\/span><span class=\"o\">);<\/span>\n    <span class=\"o\">}<\/span>\n\n    <span class=\"c1\">\/\/ Standard binary search implementation<\/span>\n    <span class=\"kd\">static<\/span> <span class=\"kt\">int<\/span> <span class=\"nf\">binarySearch<\/span><span class=\"o\">(<\/span><span class=\"kt\">int<\/span><span class=\"o\">[]<\/span> <span class=\"n\">arr<\/span><span class=\"o\">,<\/span> <span class=\"kt\">int<\/span> <span class=\"n\">target<\/span><span class=\"o\">,<\/span> <span class=\"kt\">int<\/span> <span class=\"n\">start<\/span><span class=\"o\">,<\/span> <span class=\"kt\">int<\/span> <span class=\"n\">end<\/span><span class=\"o\">)<\/span> <span class=\"o\">{<\/span>\n        <span class=\"k\">while<\/span> <span class=\"o\">(<\/span><span class=\"n\">start<\/span> <span class=\"o\"> <span class=\"n\">end<\/span><span class=\"o\">)<\/span> <span class=\"o\">{<\/span>\n            <span class=\"kt\">int<\/span> <span class=\"n\">mid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">start<\/span> <span class=\"o\">+<\/span> <span class=\"o\">(<\/span><span class=\"n\">end<\/span> <span class=\"o\">-<\/span> <span class=\"n\">start<\/span><span class=\"o\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"mi\">2<\/span><span class=\"o\">;<\/span>\n\n            <span class=\"k\">if<\/span> <span class=\"o\">(<\/span><span class=\"n\">target<\/span> <span class=\"o\"> <span class=\"n\">arr<\/span><span class=\"o\">[<\/span><span class=\"n\">mid<\/span><span class=\"o\">])<\/span> <span class=\"o\">{<\/span>\n                <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"n\">mid<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Move the end to the left<\/span>\n            <span class=\"o\">}<\/span> <span class=\"k\">else<\/span> <span class=\"k\">if<\/span> <span class=\"o\">(<\/span><span class=\"n\">target<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">arr<\/span><span class=\"o\">[<\/span><span class=\"n\">mid<\/span><span class=\"o\">])<\/span> <span class=\"o\">{<\/span>\n                <span class=\"n\">start<\/span> <span class=\"o\">=<\/span> <span class=\"n\">mid<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Move the start to the right<\/span>\n            <span class=\"o\">}<\/span> <span class=\"k\">else<\/span> <span class=\"o\">{<\/span>\n                <span class=\"k\">return<\/span> <span class=\"n\">mid<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Element found<\/span>\n            <span class=\"o\">}<\/span>\n        <span class=\"o\">}<\/span>\n        <span class=\"k\">return<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"o\">;<\/span>  <span class=\"c1\">\/\/ Element not found<\/span>\n    <span class=\"o\">}<\/span>\n<span class=\"o\">}<\/span>\n<\/span><\/span><\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%D8%AA%D9%88%D8%B6%DB%8C%D8%AD_%D8%A2%DB%8C%DB%8C%D9%86_%D9%86%D8%A7%D9%85%D9%87\"><\/span>\n<p>  \u062a\u0648\u0636\u06cc\u062d \u0622\u06cc\u06cc\u0646 \u0646\u0627\u0645\u0647<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"1_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF_%D8%A7%D8%B5%D9%84%DB%8C\"><\/span>\n<p>  1. <strong>\u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0635\u0644\u06cc<\/strong><br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u062a\u0627\u0628\u0639 main \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0646\u0645\u0648\u0646\u0647 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u062f <code>arr<\/code> \u0648 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0647\u062f\u0641 <code>6<\/code>. \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc\u060c \u0645\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u062d\u062f\u0648\u062f \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0645\u0641\u0647\u0648\u0645\u06cc\u060c \u0622\u0646 \u0631\u0627 \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. \u0633\u067e\u0633 \u062a\u0627\u0628\u0639 \u0627\u0635\u0644\u06cc \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc \u06a9\u0646\u062f <code>findElementInInfiniteArray<\/code> \u0628\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648\u06cc \u0647\u062f\u0641\u060c \u0648 \u062f\u0631 \u0635\u0648\u0631\u062a \u06cc\u0627\u0641\u062a\u0646 \u0641\u0647\u0631\u0633\u062a \u0631\u0627 \u0686\u0627\u067e \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"2_%DA%AF%D8%B3%D8%AA%D8%B1%D8%B4_%D8%AF%D8%A7%D9%85%D9%86%D9%87_%DA%AF%D8%B3%D8%AA%D8%B1%D8%B4_%D8%AE%D8%B7%DB%8C_%D9%85%D9%86%D8%B7%D9%82%D9%87_%D8%AC%D8%B3%D8%AA%D8%AC%D9%88\"><\/span>\n<p>  2. <strong>\u06af\u0633\u062a\u0631\u0634 \u062f\u0627\u0645\u0646\u0647 (\u06af\u0633\u062a\u0631\u0634 \u062e\u0637\u06cc \u0645\u0646\u0637\u0642\u0647 \u062c\u0633\u062a\u062c\u0648)<\/strong><br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u062f\u0631 <code>findElementInInfiniteArray<\/code> \u0631\u0648\u0634:<\/p>\n<ul>\n<li>\u0645\u0627 \u0628\u0627 \u0641\u0631\u0636 \u0627\u06cc\u0646\u06a9\u0647 \u0639\u0646\u0635\u0631 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645 [0, 1].<\/li>\n<li>\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u062f\u0631 \u0627\u0633\u062a <code>arr[end]<\/code>\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0647\u062f\u0641 \u062f\u0631 \u0645\u062d\u062f\u0648\u062f\u0647 \u0641\u0639\u0644\u06cc \u0646\u06cc\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0627 \u0645\u062d\u062f\u0648\u062f\u0647 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0635\u0627\u0639\u062f\u06cc \u0628\u0627 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u06a9\u0631\u062f\u0646 \u0622\u0646 \u06af\u0633\u062a\u0631\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645 (<code>end = end + (end - start + 1) * 2<\/code>). \u0627\u06cc\u0646 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0648\u062b\u0631 \u0628\u0647 \u0645\u0627 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0631\u0627 \u067e\u0648\u0634\u0634 \u062f\u0647\u06cc\u0645.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"3_%D8%AC%D8%B3%D8%AA%D8%AC%D9%88%DB%8C_%D8%A8%D8%A7%DB%8C%D9%86%D8%B1%DB%8C\"><\/span>\n<p>  3. <strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/strong><br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u062f\u0627\u0646\u06cc\u0645 \u0647\u062f\u0641 \u0628\u0627\u06cc\u062f \u0628\u06cc\u0646 \u0622\u0646 \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u062f <code>start<\/code> \u0648 <code>end<\/code>\u060c \u0645\u0627 \u06cc\u06a9 \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0631\u0648\u0634\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0631\u0627\u06cc \u062c\u0633\u062a\u062c\u0648 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0633\u062a\u060c \u0632\u06cc\u0631\u0627 \u062f\u0631 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0641\u0636\u0627\u06cc \u062c\u0633\u062a\u062c\u0648 \u0631\u0627 \u0628\u0647 \u0646\u0635\u0641 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f. \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u06a9\u0644\u06cc\u062f\u06cc \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li>\u0627\u06af\u0631 \u0647\u062f\u0641 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0628\u0627\u0634\u062f (<code>arr[mid]<\/code>\u060c \u0646\u06cc\u0645\u0647 \u0686\u067e \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u062f.<\/li>\n<li>\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0633\u062a\u060c \u0646\u06cc\u0645\u0647 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0631\u0627 \u062c\u0633\u062a\u062c\u0648 \u06a9\u0646\u06cc\u062f.<\/li>\n<li>\u0627\u06af\u0631 \u0647\u062f\u0641 \u0628\u0627 \u0639\u0646\u0635\u0631 \u0645\u06cc\u0627\u0646\u06cc \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f\u060c \u0634\u0627\u062e\u0635 \u0622\u0646 \u0631\u0627 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u06cc\u062f.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"4_%D9%85%D9%88%D8%A7%D8%B1%D8%AF_%D9%84%D8%A8%D9%87\"><\/span>\n<p>  4. <strong>\u0645\u0648\u0627\u0631\u062f \u0644\u0628\u0647<\/strong><br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u0627\u06af\u0631 \u0647\u062f\u0641 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0627\u0634\u062f\u060c \u06cc\u0627 \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0635\u0644\u0627\u064b \u0647\u062f\u0641 \u0631\u0627 \u0646\u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0627\u0632 \u062e\u0648\u0627\u0647\u062f \u06af\u0634\u062a. <code>-1<\/code>.<\/li>\n<\/ul>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%D9%BE%DB%8C%DA%86%DB%8C%D8%AF%DA%AF%DB%8C_%D8%B2%D9%85%D8%A7%D9%86%DB%8C\"><\/span>\n<p>  \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li>\n<p><strong>\u06af\u0633\u062a\u0631\u0634 \u062f\u0627\u0645\u0646\u0647<\/strong>: \u0645\u062d\u062f\u0648\u062f\u0647 \u0628\u0627 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0637\u0648\u0644 \u0645\u06cc \u06a9\u0634\u062f <code>O(log N)<\/code> \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u062d\u062f\u0648\u062f\u0647 \u0645\u0646\u0627\u0633\u0628 \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0647\u062f\u0641 \u0642\u0631\u0627\u0631 \u062f\u0627\u0631\u062f.<\/p>\n<\/li>\n<li>\n<p><strong>\u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc<\/strong>: \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u067e\u06cc\u062f\u0627 \u0634\u062f\u060c \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f <code>O(log M)<\/code>\u060c \u06a9\u062c\u0627 <code>M<\/code> \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062d\u062f\u0648\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<\/li>\n<\/ol>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u06a9\u0644\u06cc \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0627\u0633\u062a <code>O(log N + log M)<\/code>.<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Summarize this content to 400 words in Persian Lang \u0628\u06cc\u0627\u0646 \u0645\u0634\u06a9\u0644 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0646\u0627\u0645\u062a\u0646\u0627\u0647\u06cc \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0645\u0631\u062a\u0628 \u0634\u062f\u0647\u060c \u0628\u0627\u06cc\u062f \u0634\u0627\u062e\u0635 \u06cc\u06a9 \u0639\u062f\u062f \u0647\u062f\u0641 \u0645\u0639\u06cc\u0646 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645. \u0622\u0631\u0627\u06cc\u0647 &#8220;\u0628\u06cc \u0646\u0647\u0627\u06cc\u062a&#8221; \u0627\u0633\u062a\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u06a9\u0647 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0646\u062f\u0627\u0632\u0647 \u0622\u0646 \u0631\u0627 \u0627\u0632 \u0642\u0628\u0644 \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0642\u0637 \u06cc\u06a9 \u062c\u0633\u062a\u062c\u0648\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc &hellip;<\/p>\n","protected":false},"author":2,"featured_media":76371,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[339],"tags":[],"class_list":["post-76370","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dev"],"_links":{"self":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/76370","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/comments?post=76370"}],"version-history":[{"count":0,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/76370\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media\/76371"}],"wp:attachment":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media?parent=76370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/categories?post=76370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/tags?post=76370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}