{"id":25702,"date":"2021-12-04T09:19:23","date_gmt":"2021-12-04T03:49:23","guid":{"rendered":"https:\/\/python-programs.com\/?p=25702"},"modified":"2021-12-04T09:19:23","modified_gmt":"2021-12-04T03:49:23","slug":"python-program-to-solve-the-tiling-problem","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/","title":{"rendered":"Python Program to Solve the Tiling Problem"},"content":{"rendered":"<h4>What is Tiling Problem?<\/h4>\n<p>In the Tiling Problem, we would be given a wall of size 4*n, which means that the wall&#8217;s height is 4 and its length is n. ( given as the input).<\/p>\n<p>Now we have an endless number of little 4*1 tiles that can be put on the wall in two distinct ways. Look at the below figure for more clarity:<\/p>\n<p>&nbsp;<\/p>\n<p>Our goal is to fill the entire wall with all of the possible patterns using the small tiles in any of the approaches described above.<\/p>\n<h4>Tiling Problem Solution in Python:<\/h4>\n<p>One can either manually implement the naive technique using loops and if-else statements or use the quicker Recursion approach. If you want to learn about recursion, just have a glance over it what the recursion is? before going to the code.<\/p>\n<p>We will use recursion to divide a large problem into smaller ones. Now, let&#8217;s look at the minor problems with both arrangements.<\/p>\n<p><strong>1st Arrangement:<\/strong> The first tile is placed using <strong>Method 1<\/strong>, reducing the length of the wall by 4, and the space above the present tile can only be filled in one way ( 3 tiles according to Method 1 )<br \/>\n<strong>2nd Arrangement:<\/strong> Next, using <strong>Method 2,<\/strong> we may place the first tile, reducing the length of the wall by one.<\/p>\n<p>After the first arrangement has been completed. We call the same method but with a lower number of n to recursively call the same operations for the remaining wall.<\/p>\n<p>The ultimate solution will be the sum of the possible ways in both the arrangements in each recursive call.<\/p>\n<h2>Program to Solve the Tiling Problem in Python<\/h2>\n<p>Recursion is used to simplify the code implementation. Just make sure you understand the solution that is given below:<\/p>\n<ul>\n<li><a href=\"#Using_Recursion_(Static_Input)\">Using Recursion (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Recursion_(User_Input)\">Using Recursion (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Recursion_(Static_Input)\">Method #1: Using Recursion (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the n value as static input and store it in a variable.<\/li>\n<li>Create a recursive function say total_possiblearrangements() which accepts the given n value as an argument that returns the total number of possible arrangements in both ways.<\/li>\n<li>Inside the function, Check if the given n value is less than or equal to 3 using the if conditional statement.<\/li>\n<li>If it is true, then return 1.<\/li>\n<li>Return the value of total_possiblearrangements(gvn_n_val-1) + total_possiblearrangements(gvn_n_val-4) (Recursive Logic).<\/li>\n<li>Pass the given n value as an argument to the total_possiblearrangements() function and store it in a variable.<\/li>\n<li>Print the above result.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a recursive function say total_possiblearrangements() which accepts the\r\n# given n value as an argument that returns the total number of possible\r\n# arrangements in both ways.\r\n\r\n\r\ndef total_possiblearrangements(gvn_n_val):\r\n        # Inside the function, Check if the given n value is less than or equal to 3\r\n        # using the if conditional statement.\r\n\r\n    if(gvn_n_val &lt;= 3):\r\n        # If it is true, then return 1.\r\n        return 1\r\n        # Return the value of total_possiblearrangements(gvn_n_val-1) +\r\n        # total_possiblearrangements(gvn_n_val-4) (Recursive Logic).\r\n    return total_possiblearrangements(gvn_n_val-1) + total_possiblearrangements(gvn_n_val-4)\r\n\r\n\r\n# Give the n value as static input and store it in a variable.\r\ngvn_n_val = 3\r\n# Pass the given n value as an argument to the total_possiblearrangements()\r\n# function and store it in a variable.\r\nrslt = total_possiblearrangements(gvn_n_val)\r\n# Print the above result.\r\nprint(\"The total number of possible arrangements in both ways = \")\r\nprint(rslt)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The total number of possible arrangements in both ways = \r\n1<\/pre>\n<h3 id=\"Using_Recursion_(User_Input)\">Method #2: Using Recursion (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the n value as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Create a recursive function say total_possiblearrangements() which accepts the given n value as an argument that returns the total number of possible arrangements in both ways.<\/li>\n<li>Inside the function, Check if the given n value is less than or equal to 3 using the if conditional statement.<\/li>\n<li>If it is true, then return 1.<\/li>\n<li>Return the value of total_possiblearrangements(gvn_n_val-1) + total_possiblearrangements(gvn_n_val-4) (Recursive Logic).<\/li>\n<li>Pass the given n value as an argument to the total_possiblearrangements() function and store it in a variable.<\/li>\n<li>Print the above result.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a recursive function say total_possiblearrangements() which accepts the\r\n# given n value as an argument that returns the total number of possible\r\n# arrangements in both ways.\r\n\r\n\r\ndef total_possiblearrangements(gvn_n_val):\r\n        # Inside the function, Check if the given n value is less than or equal to 3\r\n        # using the if conditional statement.\r\n\r\n    if(gvn_n_val &lt;= 3):\r\n        # If it is true, then return 1.\r\n        return 1\r\n        # Return the value of total_possiblearrangements(gvn_n_val-1) +\r\n        # total_possiblearrangements(gvn_n_val-4) (Recursive Logic).\r\n    return total_possiblearrangements(gvn_n_val-1) + total_possiblearrangements(gvn_n_val-4)\r\n\r\n\r\n# Give the n value as user input using the int(input()) function and store it in a variable.\r\ngvn_n_val = int(input(\"Enter n value = \"))\r\n# Pass the given n value as an argument to the total_possiblearrangements()\r\n# function and store it in a variable.\r\nrslt = total_possiblearrangements(gvn_n_val)\r\n# Print the above result.\r\nprint(\"The total number of possible arrangements in both ways = \")\r\nprint(rslt)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter n value = 4\r\nThe total number of possible arrangements in both ways = \r\n2<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Tiling Problem? In the Tiling Problem, we would be given a wall of size 4*n, which means that the wall&#8217;s height is 4 and its length is n. ( given as the input). Now we have an endless number of little 4*1 tiles that can be put on the wall in two distinct &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/\"> <span class=\"screen-reader-text\">Python Program to Solve the Tiling Problem<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"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":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program to Solve the Tiling Problem - 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\/python-program-to-solve-the-tiling-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Solve the Tiling Problem - Python Programs\" \/>\n<meta property=\"og:description\" content=\"What is Tiling Problem? In the Tiling Problem, we would be given a wall of size 4*n, which means that the wall&#8217;s height is 4 and its length is n. ( given as the input). Now we have an endless number of little 4*1 tiles that can be put on the wall in two distinct &hellip; Python Program to Solve the Tiling Problem Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/\" \/>\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=\"2021-12-04T03:49:23+00:00\" \/>\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=\"4 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\":\"WebPage\",\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage\",\"url\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/\",\"name\":\"Python Program to Solve the Tiling Problem - Python Programs\",\"isPartOf\":{\"@id\":\"https:\/\/python-programs.com\/#website\"},\"datePublished\":\"2021-12-04T03:49:23+00:00\",\"dateModified\":\"2021-12-04T03:49:23+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/python-programs.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Python Program to Solve the Tiling Problem\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage\"},\"author\":{\"@id\":\"https:\/\/python-programs.com\/#\/schema\/person\/fb109fd98e2d5a15fd4dac9970797602\"},\"headline\":\"Python Program to Solve the Tiling Problem\",\"datePublished\":\"2021-12-04T03:49:23+00:00\",\"dateModified\":\"2021-12-04T03:49:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage\"},\"wordCount\":547,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/python-programs.com\/#organization\"},\"articleSection\":[\"Python\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/python-programs.com\/#\/schema\/person\/fb109fd98e2d5a15fd4dac9970797602\",\"name\":\"Vikram Chiluka\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/python-programs.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/c56c77f578d45de43af6feb443618ed7?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/c56c77f578d45de43af6feb443618ed7?s=96&d=mm&r=g\",\"caption\":\"Vikram Chiluka\"},\"url\":\"https:\/\/python-programs.com\/author\/vikram\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Python Program to Solve the Tiling Problem - Python Programs","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/","og_locale":"en_US","og_type":"article","og_title":"Python Program to Solve the Tiling Problem - Python Programs","og_description":"What is Tiling Problem? In the Tiling Problem, we would be given a wall of size 4*n, which means that the wall&#8217;s height is 4 and its length is n. ( given as the input). Now we have an endless number of little 4*1 tiles that can be put on the wall in two distinct &hellip; Python Program to Solve the Tiling Problem Read More &raquo;","og_url":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/","og_site_name":"Python Programs","article_publisher":"https:\/\/www.facebook.com\/btechgeeks","article_published_time":"2021-12-04T03:49:23+00:00","twitter_card":"summary_large_image","twitter_creator":"@btech_geeks","twitter_site":"@btech_geeks","twitter_misc":{"Written by":"Vikram Chiluka","Est. reading time":"4 minutes"},"schema":{"@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":"WebPage","@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage","url":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/","name":"Python Program to Solve the Tiling Problem - Python Programs","isPartOf":{"@id":"https:\/\/python-programs.com\/#website"},"datePublished":"2021-12-04T03:49:23+00:00","dateModified":"2021-12-04T03:49:23+00:00","breadcrumb":{"@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/python-programs.com\/"},{"@type":"ListItem","position":2,"name":"Python Program to Solve the Tiling Problem"}]},{"@type":"Article","@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#article","isPartOf":{"@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage"},"author":{"@id":"https:\/\/python-programs.com\/#\/schema\/person\/fb109fd98e2d5a15fd4dac9970797602"},"headline":"Python Program to Solve the Tiling Problem","datePublished":"2021-12-04T03:49:23+00:00","dateModified":"2021-12-04T03:49:23+00:00","mainEntityOfPage":{"@id":"https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#webpage"},"wordCount":547,"commentCount":0,"publisher":{"@id":"https:\/\/python-programs.com\/#organization"},"articleSection":["Python"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/python-programs.com\/python-program-to-solve-the-tiling-problem\/#respond"]}]},{"@type":"Person","@id":"https:\/\/python-programs.com\/#\/schema\/person\/fb109fd98e2d5a15fd4dac9970797602","name":"Vikram Chiluka","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/python-programs.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/c56c77f578d45de43af6feb443618ed7?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c56c77f578d45de43af6feb443618ed7?s=96&d=mm&r=g","caption":"Vikram Chiluka"},"url":"https:\/\/python-programs.com\/author\/vikram\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/posts\/25702"}],"collection":[{"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/comments?post=25702"}],"version-history":[{"count":3,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/posts\/25702\/revisions"}],"predecessor-version":[{"id":25717,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/posts\/25702\/revisions\/25717"}],"wp:attachment":[{"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/media?parent=25702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/categories?post=25702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/python-programs.com\/wp-json\/wp\/v2\/tags?post=25702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}