{"id":221200,"date":"2025-02-28T11:11:09","date_gmt":"2025-02-28T11:11:09","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/"},"modified":"2025-02-28T11:11:09","modified_gmt":"2025-02-28T11:11:09","slug":"how-to-find-minimum-value-in-a-rotated-sorted-array","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/","title":{"rendered":"How to find minimum value in a rotated sorted array?"},"content":{"rendered":"<p>Rotating a sorted array means shifting its elements to the right or left by a certain number of positions. This operation might seem trivial at first, but it introduces an interesting challenge: after the rotation, how can we efficiently find the minimum value in the array? In this article, we will explore different approaches to tackle this problem.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/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=\"Toggle Table of Content\"><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-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#The_Problem_Finding_the_Minimum_Value\" title=\"The Problem: Finding the Minimum Value\">The Problem: Finding the Minimum Value<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#Solution_Applying_Binary_Search\" title=\"Solution: Applying Binary Search\">Solution: Applying Binary Search<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#Frequently_Asked_Questions\" title=\"Frequently Asked Questions:\">Frequently Asked Questions:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#1_Can_we_simply_iterate_through_the_array_to_find_the_minimum_value\" title=\"1. Can we simply iterate through the array to find the minimum value?\">1. Can we simply iterate through the array to find the minimum value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#2_What_is_the_time_complexity_of_finding_the_minimum_value_using_binary_search\" title=\"2. What is the time complexity of finding the minimum value using binary search?\">2. What is the time complexity of finding the minimum value using binary search?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#3_Does_the_rotated_sorted_array_have_any_duplicate_elements\" title=\"3. Does the rotated sorted array have any duplicate elements?\">3. Does the rotated sorted array have any duplicate elements?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#4_Can_the_array_contain_negative_numbers\" title=\"4. Can the array contain negative numbers?\">4. Can the array contain negative numbers?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#5_What_happens_if_the_array_is_not_rotated\" title=\"5. What happens if the array is not rotated?\">5. What happens if the array is not rotated?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#6_How_does_the_binary_search_approach_handle_arrays_with_a_single_element\" title=\"6. How does the binary search approach handle arrays with a single element?\">6. How does the binary search approach handle arrays with a single element?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#7_Can_the_array_be_empty\" title=\"7. Can the array be empty?\">7. Can the array be empty?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#8_What_if_the_array_has_only_two_elements\" title=\"8. What if the array has only two elements?\">8. What if the array has only two elements?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#9_Is_there_any_other_way_to_solve_this_problem\" title=\"9. Is there any other way to solve this problem?\">9. Is there any other way to solve this problem?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#10_Can_we_modify_the_array\" title=\"10. Can we modify the array?\">10. Can we modify the array?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#11_Is_there_a_limitation_on_the_size_of_the_array\" title=\"11. Is there a limitation on the size of the array?\">11. Is there a limitation on the size of the array?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#12_What_if_the_array_is_not_sorted_at_all\" title=\"12. What if the array is not sorted at all?\">12. What if the array is not sorted at all?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"The_Problem_Finding_the_Minimum_Value\"><\/span>The Problem: Finding the Minimum Value<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Given a rotated sorted array, the task is to find the minimum value contained within it. For example, consider the array [4, 5, 6, 7, 0, 1, 2, 3] that has been rotated by three positions to the right. The minimum value in this array is 0.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solution_Applying_Binary_Search\"><\/span>Solution: Applying Binary Search<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To efficiently find the minimum value in a rotated sorted array, we can adapt the binary search algorithm. This approach leverages the fact that the array is still partially sorted, even after the rotation.<\/p>\n<p>1. We start by setting a left pointer to the array&#8217;s first element and a right pointer to the last element.<br \/>\n2. While the left pointer is not equal to the right pointer, we calculate the middle index using the formula `mid = left + (right &#8211; left) \/\/ 2`.<br \/>\n3. We compare the middle element with the rightmost element:<br \/>\n   a. If the middle element is greater than the rightmost element, then the minimum value must be present somewhere to the right of the middle. We update the left pointer to `mid + 1`.<br \/>\n   b. If the middle element is smaller than the rightmost element, then the minimum value must be present somewhere to the left of the middle or it may be the middle element itself. We update the right pointer to `mid`.<br \/>\n4. The search space is halved in each iteration, and eventually, when the left and right pointers meet, we have found the minimum value.<\/p>\n<p><b>The minimum value in a rotated sorted array can be found by using a binary search approach like the one described above.<\/b><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span>Frequently Asked Questions:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_Can_we_simply_iterate_through_the_array_to_find_the_minimum_value\"><\/span>1. Can we simply iterate through the array to find the minimum value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIterating through the array sequentially would provide a solution, but it would have a linear time complexity. Binary search provides a more efficient solution with logarithmic time complexity.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_What_is_the_time_complexity_of_finding_the_minimum_value_using_binary_search\"><\/span>2. What is the time complexity of finding the minimum value using binary search?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe time complexity of finding the minimum value using binary search is O(log n), where n is the size of the array.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_Does_the_rotated_sorted_array_have_any_duplicate_elements\"><\/span>3. Does the rotated sorted array have any duplicate elements?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe array might contain duplicate elements, and the binary search approach can handle such cases as well.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Can_the_array_contain_negative_numbers\"><\/span>4. Can the array contain negative numbers?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, the array can contain negative numbers. The binary search approach works regardless of the range of values.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_What_happens_if_the_array_is_not_rotated\"><\/span>5. What happens if the array is not rotated?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the array is not rotated and is already sorted, then the first element in the array will be its minimum value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_How_does_the_binary_search_approach_handle_arrays_with_a_single_element\"><\/span>6. How does the binary search approach handle arrays with a single element?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the array contains only one element, then that element will be considered the minimum value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_Can_the_array_be_empty\"><\/span>7. Can the array be empty?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the array is empty, there won&#8217;t be any minimum value to find. However, the binary search approach would still work correctly.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_if_the_array_has_only_two_elements\"><\/span>8. What if the array has only two elements?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIn the case of an array with only two elements, the minimum value will be the smaller element among the two.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_Is_there_any_other_way_to_solve_this_problem\"><\/span>9. Is there any other way to solve this problem?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nWhile the binary search approach is the most efficient, the problem can also be solved by iterating through the array and comparing each element with its neighbor. However, this approach has a linear time complexity.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_Can_we_modify_the_array\"><\/span>10. Can we modify the array?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe binary search approach does not require any modifications to the array. It only requires two pointers to keep track of the search space.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Is_there_a_limitation_on_the_size_of_the_array\"><\/span>11. Is there a limitation on the size of the array?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThere is no inherent limitation on the size of the array. The binary search approach can handle arrays of any size.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_What_if_the_array_is_not_sorted_at_all\"><\/span>12. What if the array is not sorted at all?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the array is not sorted at all, the binary search approach will not work, and a different algorithm must be employed to find the minimum value.<\/p>\n<p>In conclusion, finding the minimum value in a rotated sorted array can be efficiently accomplished using the binary search approach. This technique avoids the need for linear iteration and provides a logarithmic time complexity solution. Through the use of clever pointers, the minimum value can be swiftly identified, even in the presence of duplicates or negative numbers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rotating a sorted array means shifting its elements to the right or left by a certain number of positions. This operation might seem trivial at first, but it introduces an interesting challenge: after the rotation, how can we efficiently find the minimum value in the array? In this article, we will explore different approaches to &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How to find minimum value in a rotated sorted array?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-minimum-value-in-a-rotated-sorted-array\/#more-221200\">Read more<span class=\"screen-reader-text\">How to find minimum value in a rotated sorted array?<\/span><\/a><\/p>\n","protected":false},"author":55,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-221200","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to find minimum value in a rotated sorted array?<\/title>\n<meta name=\"description\" content=\"Rotating a sorted array means shifting its elements to the right or left by a certain number of positions. 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