{"id":8228,"date":"2021-06-07T18:14:10","date_gmt":"2021-06-07T12:44:10","guid":{"rendered":"https:\/\/python-programs.com\/?p=8228"},"modified":"2021-11-22T18:40:41","modified_gmt":"2021-11-22T13:10:41","slug":"brian-kernighans-algorithm-to-count-set-bits-in-an-integer","status":"publish","type":"post","link":"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/","title":{"rendered":"Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python"},"content":{"rendered":"<p><strong>Brian Kernighan\u2019s Algorithm to count the number of set bits in an integer:<\/strong>\u00a0Given a number, the task is to count the set bits of the given number using Brian Kernighan\u2019s Algorithm in C++ and Python.<\/p>\n<h2>Brian Kernighan\u2019s Algorithm to Count Set bits of a Number in C++ and Python<\/h2>\n<p>We\u2019ll look at Brian Kernighan\u2019s Algorithm and see how it works in C++ and Python.<\/p>\n<ul>\n<li><a href=\"#Brute-Force_Solution_(Na\u00efve_Approach)\">Brute-Force Solution (Na\u00efve Approach)<\/a><\/li>\n<li><a href=\"#Brian_Kernighan\u2019s_Algorithm_to_calculate_set_bits_in_an_integer\">Brian Kernighan\u2019s Algorithm to calculate set bits in an integer<\/a><\/li>\n<li><a href=\"#Implementing_Brian_Kernighan\u2019s_Algorithm_in_Python\">Implementing Brian Kernighan\u2019s Algorithm in Python<\/a><\/li>\n<li><a href=\"#Implementing_Brian_Kernighan\u2019s_Algorithm_in_C++\">Implementing Brian Kernighan\u2019s Algorithm in C++<\/a><\/li>\n<li><a href=\"#To_Count_Set_Bits_in_an_Integer_Using_GCC_built-in_function\">To Count Set Bits in an Integer Using GCC built-in function<\/a><\/li>\n<\/ul>\n<p>Drive into\u00a0<a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python Programming Examples<\/a>\u00a0and explore more instances related to python concepts so that you can become proficient in generating programs in Python Programming Language.<\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">given number =43\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">The total number of set bits in the given number  43  : \r\n4\r\n<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">given number =64\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">The total number of set bits in the given number  64  : \r\n1\r\n<\/pre>\n<p><strong>Example3:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">given number =4322\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre class=\"ql-syntax\" spellcheck=\"false\">The total number of set bits in the given number  4322  : \r\n5\r\n<\/pre>\n<p>First, we implement the brute force solution for the above program<\/p>\n<h3><a id=\"Brute-Force_Solution_(Na\u00efve_Approach)\"><\/a>Brute-Force Approach (Na\u00efve Approach)<\/h3>\n<p>A simple method is to take each bit into consideration in a number (set or unset) and hold a counter to track the set bits.<\/p>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Set the variable to say count to 0 to count the total number of set bits.<\/li>\n<li>We utilize the while loop.<\/li>\n<li>We\u2019ll keep going till the number is bigger than zero (Condition of while statement)<\/li>\n<li>Using the % operator, we will determine whether the last check bit is set or not.<\/li>\n<li>If the check bit is 1, it indicates that the bit is set, and we increment the count.<\/li>\n<li>Divide the given number by 2.<\/li>\n<li>Print the count.<\/li>\n<\/ul>\n<p><b>Below is the implementation:<\/b><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def countSetBit(numb):\r\n    # checking if the given number is greater than 1\r\n    if numb &gt; 1:\r\n      # Set the variable say setbitcount to 0 to count the total number of set bits.\r\n        setbitcount = 0\r\n        # looping till number greater than 0 using while loop\r\n        while(numb &gt; 0):\r\n            # We will get the last check bit whether it is set bit or not using % operator\r\n            checkbit = numb % 2\r\n            # checking if the check bit is 1 or not\r\n            # if the check bit is 1 then increment the setbitcount\r\n            if(checkbit == 1):\r\n                setbitcount = setbitcount+1\r\n            # divide the number by 2\r\n            numb = numb\/\/2\r\n    # return the setbitcount\r\n    return setbitcount\r\n\r\n\r\n# Driver code\r\ngiven_numb = 235\r\n# passing given number to countSetBit function to\r\n# count the total number of set bits in the given number\r\nprint(\"The total number of set bits in the given number \", given_numb, \" : \")\r\nprint(countSetBit(given_numb))<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The total number of set bits in the given number  235  : \r\n6<\/pre>\n<p>The brute-force strategy described above requires one repetition per bit until no more set bits remain. So it goes through 32 iterations on a 32\u2013bit word with only the high-bit set.<\/p>\n<h3><a id=\"Brian_Kernighan\u2019s_Algorithm_to_calculate_set_bits_in_an_integer\"><\/a>Brian Kernighan\u2019s Algorithm to calculate set bits in an integer<\/h3>\n<p>We may apply Brian Kernighan\u2019s technique to improve the performance of the naive algorithm described above. The concept is to only consider an integer\u2019s set bits by turning off its rightmost set bit (after counting it) so that the next iteration of the loop only considers the next rightmost bit.<\/p>\n<p>To turn off the rightmost set bit of a number n, use the formula n &amp; (n-1). This is because the formula n-1 flips all the bits following the rightmost set bit of n, including the rightmost set bit itself. As a result, n &amp; (n-1) results in the last bit of n being flipped.<\/p>\n<h3><a id=\"Implementing_Brian_Kernighan\u2019s_Algorithm_in_Python\"><\/a>Implementing Brian Kernighan\u2019s Algorithm\u00a0<strong>to count the number of set bits in an integer\u00a0<\/strong>in Python<\/h3>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-18564\" src=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/implementation-of-Brian-Kernighans-Algorithm-in-Python-300x203.png\" alt=\"implementation of Brian Kernighan's Algorithm in Python\" width=\"640\" height=\"434\" srcset=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/implementation-of-Brian-Kernighans-Algorithm-in-Python-300x203.png 300w, https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/implementation-of-Brian-Kernighans-Algorithm-in-Python-768x521.png 768w, https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/implementation-of-Brian-Kernighans-Algorithm-in-Python.png 858w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/p>\n<p><strong>Below is the implementation of Brian Kernighan&#8217;s Algorithm to set bits in a Python:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def countSetBit(numb):\r\n    # checking if the given number is greater than 1\r\n    if numb &gt; 1:\r\n      # Set the variable say setbitcount to 0 to count the total number of set bits.\r\n        setbitcount = 0\r\n        # looping till number greater than 0 using while loop\r\n        while(numb &gt; 0):\r\n            numb = numb &amp; (numb-1)\r\n            # increment the set bit count\r\n            setbitcount = setbitcount+1\r\n    # return the setbitcount\r\n    return setbitcount\r\n\r\n\r\n# Driver code\r\ngiven_numb = 4322\r\n# passing given number to countSetBit function to\r\n# count the total number of set bits in the given number\r\nprint(\"The total number of set bits in the given number \", given_numb, \" : \")\r\nprint(countSetBit(given_numb))\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The total number of set bits in the given number  4322  :  5<\/pre>\n<p><strong>Time Complexity:<\/strong> O(logn)<\/p>\n<h3><a id=\"Implementing_Brian_Kernighan\u2019s_Algorithm_in_C++\"><\/a>Implementing Brian Kernighan\u2019s Algorithm to count the number of set bits in an integer in C++<\/h3>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-18562\" src=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-count-set-bits-in-an-integer-in-c.png\" alt=\"Brian Kernighan\u2019s Algorithm to count number of set bits in an integer in c++\" width=\"640\" height=\"902\" srcset=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-count-set-bits-in-an-integer-in-c.png 630w, https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-count-set-bits-in-an-integer-in-c-213x300.png 213w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><br \/>\n<strong>Below is the implementation of Brian Kernighan&#8217;s Algorithm to set bits in a C++:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">#include &lt;iostream&gt;\r\nusing namespace std;\r\n\/\/ function which returns the total number of set bits in\r\n\/\/ the given number\r\nint countSetBit(int numb)\r\n{ \/\/ Set the variable say setbitcount to 0 to count the\r\n  \/\/ total number of set bits.\r\n    int setbitcount = 0;\r\n    \/\/ checking if the given number is greater than 1\r\n    if (numb &gt; 1) {\r\n        \/\/ looping till number greater than 0 using while\r\n        \/\/ loop\r\n        while (numb &gt; 0) {          \r\n            numb = numb &amp; (numb - 1);\r\n            \/\/ increment the set bit count\r\n            setbitcount++;\r\n        }\r\n    }\r\n    \/\/ return the setbitcount\r\n    return setbitcount;\r\n}\r\nint main()\r\n{\r\n    \/\/ given number\r\n    int given_numb = 4322;\r\n    \/\/ passing given number to countSetBit function to\r\n    \/\/ count the total number of set bits in the given\r\n    \/\/ number\r\n    cout &lt;&lt; \"The total number of set bits in the given \"\r\n            \"number \"\r\n         &lt;&lt; given_numb &lt;&lt; \" : \" &lt;&lt; endl;\r\n    cout &lt;&lt; countSetBit(given_numb);\r\n\r\n    return 0;\r\n}<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The total number of set bits in the given number  4322  : \r\n5<\/pre>\n<p>Brian Kernighan&#8217;s algorithm iterates as many times as there are set bits. So, if we have a 32\u2013bit word with only the high bit set, it will only be looped once.<\/p>\n<h3><a id=\"To_Count_Set_Bits_in_an_Integer_Using_GCC_built-in_function\"><\/a>To Count Set Bits in an Integer Using GCC built-in function<\/h3>\n<p>GCC also implements a built-in function to get no of set bits in an integer,<code>int __builtin_popcount<\/code>(unsigned int n) that returns the total number of set bits in n. The below C++ program illustrates it clearly:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">#include &lt;iostream&gt;\r\nusing namespace std;\r\n \r\nint main()\r\n{\r\n    int n = 16;\r\n    cout &lt;&lt; \"The total number of set bits in \" &lt;&lt; n &lt;&lt; \" is \"\r\n         &lt;&lt; __builtin_popcount (n) &lt;&lt; endl;\r\n \r\n    return 0;\r\n}<\/pre>\n<p><strong>Output:\u00a0<\/strong><\/p>\n<pre>The total number of set bits in 16 is 1<\/pre>\n<p>Also, GCC furnishes two other built-in functions, <code>int __builtin_popcountl<\/code> (unsigned long) and <code>int __builtin_popcountll<\/code> (unsigned long long), same as <code>__builtin_popcount<\/code>, except their argument type is unsigned long and unsigned long long, each.<\/p>\n<p><strong>Related Programs<\/strong>:<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-count-set-bits-in-a-number\/\">Python Program to Count Set Bits in a Number<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-count-the-number-of-digits-present-in-a-number\/\">Python Program to Count the Number of Digits Present In a Number<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-move-all-zeros-present-in-an-array-list-to-the-end\/\">Python Program to Move all Zeros present in an Array\/List to the End<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-missing-number-in-an-array-list\/\">Python Program to Find the Missing Number in an array\/list<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-odd-occurring-element-in-an-array-list\/\">Python Program to Find the Odd Occurring Element in an Array\/list<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-a-pair-with-the-given-sum-in-an-array\/\">Python Program to Find a Pair with the Given Sum in an Array<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-count-the-frequency-of-words-appearing-in-a-string-using-a-dictionary\/\">Python Program to Count the Frequency of Words Appearing in a String Using a Dictionary<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Brian Kernighan\u2019s Algorithm to count the number of set bits in an integer:\u00a0Given a number, the task is to count the set bits of the given number using Brian Kernighan\u2019s Algorithm in C++ and Python. Brian Kernighan\u2019s Algorithm to Count Set bits of a Number in C++ and Python We\u2019ll look at Brian Kernighan\u2019s Algorithm &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/\"> <span class=\"screen-reader-text\">Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":8236,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[19,5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python - Python Programs\" \/>\n<meta property=\"og:description\" content=\"Brian Kernighan\u2019s Algorithm to count the number of set bits in an integer:\u00a0Given a number, the task is to count the set bits of the given number using Brian Kernighan\u2019s Algorithm in C++ and Python. Brian Kernighan\u2019s Algorithm to Count Set bits of a Number in C++ and Python We\u2019ll look at Brian Kernighan\u2019s Algorithm &hellip; Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/\" \/>\n<meta property=\"og:site_name\" content=\"Python Programs\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/btechgeeks\" \/>\n<meta property=\"article:published_time\" content=\"2021-06-07T12:44:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-22T13:10:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-Count-Set-bits-of-a-Number-in-C-and-Python.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"720\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@btech_geeks\" \/>\n<meta name=\"twitter:site\" content=\"@btech_geeks\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Vikram Chiluka\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/python-programs.com\/#organization\",\"name\":\"BTech Geeks\",\"url\":\"https:\/\/python-programs.com\/\",\"sameAs\":[\"https:\/\/www.instagram.com\/btechgeeks\/\",\"https:\/\/www.linkedin.com\/in\/btechgeeks\",\"https:\/\/in.pinterest.com\/btechgeek\/\",\"https:\/\/www.youtube.com\/channel\/UC9MlCqdJ3lKqz2p5114SDIg\",\"https:\/\/www.facebook.com\/btechgeeks\",\"https:\/\/twitter.com\/btech_geeks\"],\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/python-programs.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/python-programs.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png\",\"contentUrl\":\"https:\/\/python-programs.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png\",\"width\":350,\"height\":70,\"caption\":\"BTech Geeks\"},\"image\":{\"@id\":\"https:\/\/python-programs.com\/#\/schema\/logo\/image\/\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/python-programs.com\/#website\",\"url\":\"https:\/\/python-programs.com\/\",\"name\":\"Python Programs\",\"description\":\"Python Programs with Examples, How To Guides on Python\",\"publisher\":{\"@id\":\"https:\/\/python-programs.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/python-programs.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/#primaryimage\",\"url\":\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-Count-Set-bits-of-a-Number-in-C-and-Python.png\",\"contentUrl\":\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/06\/Brian-Kernighans-Algorithm-to-Count-Set-bits-of-a-Number-in-C-and-Python.png\",\"width\":1280,\"height\":720,\"caption\":\"Brian Kernighan\u2019s Algorithm to Count Set bits of a Number in C++ and Python\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/#webpage\",\"url\":\"https:\/\/python-programs.com\/brian-kernighans-algorithm-to-count-set-bits-in-an-integer\/\",\"name\":\"Brian Kernighan\u2019s Algorithm to count set bits in an integer in C++ and Python - 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