{"id":22983,"date":"2021-09-29T20:14:40","date_gmt":"2021-09-29T14:44:40","guid":{"rendered":"https:\/\/python-programs.com\/?p=22983"},"modified":"2021-11-22T18:35:35","modified_gmt":"2021-11-22T13:05:35","slug":"python-program-to-find-number-of-rectangles-in-nm-grid","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-number-of-rectangles-in-nm-grid\/","title":{"rendered":"Python Program to Find Number of Rectangles in N*M Grid"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-for-minimum-perimeter-of-n-blocks\/\">Python Program for Minimum Perimeter of n Blocks<\/a><br \/>\nGiven a grid of size N*M the task is to find the number of rectangles in the given grid in Python.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given N = 6\r\nGiven M = 4<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">Number of Rectangles in the grid of size { 6 * 4 } : 210<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given N = 4\r\nGiven M = 2<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Number of Rectangles in the grid of size { 4 * 2 } : 30<\/pre>\n<h2>Program to Find Number of Rectangles in N*M Grid in Python<\/h2>\n<p>Below are the ways to find the number of rectangles in the given N*M:<\/p>\n<ul>\n<li><a href=\"#Using_Mathematical_Formula_(Static_Input)\">Using Mathematical Formula (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Mathematical_Formula_(User_Input)\">Using Mathematical Formula (User Input)<\/a><\/li>\n<\/ul>\n<p>Let&#8217;s try to come up with a formula for the number of rectangles.<\/p>\n<p>There is one rectangle in a grid of 1*1<\/p>\n<p>There will be 2 + 1 = 3 rectangles if the grid is 2*1.<\/p>\n<p>There will be 3 + 2 + 1 = 6 rectangles if the grid is 3*1<\/p>\n<blockquote><p>The formula for Number of Rectangles =<strong> M(M+1)(N)(N+1)\/4<\/strong><\/p><\/blockquote>\n<h3 id=\"Using_Mathematical_Formula_(Static_Input)\">Method #1: Using Mathematical Formula (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the number N as static input and store it in a variable.<\/li>\n<li>Give the number M as static input and store it in another variable.<\/li>\n<li>Create a function <strong>getCountRect()<\/strong> which accepts given N, M grid sides as arguments and returns the number of rectangles.<\/li>\n<li>Inside the <strong>getCountRect()\u00a0<\/strong>function Calculate the number of rectangles using the MatheMatical Formula <strong>M(M+1)(N)(N+1)\/4\u00a0<\/strong>and store it in a variable say reslt.<\/li>\n<li>Return the reslt value.<\/li>\n<li>Inside the Main Function.<\/li>\n<li>Pass the given N, M as arguments to <strong>getCountRect<\/strong>() function and store the result returned from the function in a variable say <strong>countRect<\/strong>.<\/li>\n<li>Print the <strong>countRect<\/strong> value.<\/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 function getCountRect() which accepts given N, M grid sides\r\n# as arguments and returns the number of rectangles.\r\n\r\n\r\ndef getCountRect(nVal, mVal):\r\n        # Inside the getCountRect()\u00a0function Calculate the number of rectangles\r\n    # using the MatheMatical Formula M(M+1)(N)(N+1)\/4\u00a0\r\n    # and store it in a variable say reslt.\r\n    reslt = (mVal * nVal * (nVal + 1) * (mVal + 1)) \/ 4\r\n    # Return the reslt value.\r\n    return reslt\r\n\r\n\r\n# Inside the Main Function.\r\n# Give the number N as static input and store it in a variable.\r\nnVal = 6\r\n# Give the number M as static input and store it in another variable.\r\nmVal = 4\r\n# Pass the given N, M as arguments to getCountRect() function\r\n# and store the result returned from the function in a variable say countRect.\r\ncountRect = int(getCountRect(nVal, mVal))\r\n# Print the countRect value.\r\nprint(\r\n    'Number of Rectangles in the grid of size {', nVal, '*', mVal, '} :', countRect)\r\n<\/pre>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">#include &lt;iostream&gt;\r\n\r\nusing namespace std;\r\nint getCountRect ( int nVal, int mVal ) {\r\n  int reslt = ( mVal * nVal * ( nVal + 1 ) * ( mVal + 1 ) ) \/ 4;\r\n  return reslt;\r\n}\r\nint main() {\r\n    int nVal = 6;\r\n  int mVal = 4;\r\n  int countRect = ( int ) getCountRect ( nVal, mVal );\r\n  cout &lt;&lt; \"Number of Rectangles in the grid of size {\" &lt;&lt; nVal &lt;&lt; '*' &lt;&lt; mVal &lt;&lt; \" } is: \" &lt;&lt; countRect &lt;&lt; endl;\r\n  return 0;\r\n}\r\n\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">Number of Rectangles in the grid of size { 6 * 4 } : 210<\/pre>\n<h3 id=\"Using_Mathematical_Formula_(User_Input)\">Method #2: Using Mathematical Formula (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the number N as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the number M as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Create a function <strong>getCountRect()<\/strong> which accepts given N, M grid sides as arguments and returns the number of rectangles.<\/li>\n<li>Inside the <strong>getCountRect()\u00a0<\/strong>function Calculate the number of rectangles using the MatheMatical Formula <strong>M(M+1)(N)(N+1)\/4\u00a0<\/strong>and store it in a variable say reslt.<\/li>\n<li>Return the reslt value.<\/li>\n<li>Inside the Main Function.<\/li>\n<li>Pass the given N, M as arguments to <strong>getCountRect<\/strong>() function and store the result returned from the function in a variable say <strong>countRect<\/strong>.<\/li>\n<li>Print the <strong>countRect<\/strong> value.<\/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 function getCountRect() which accepts given N, M grid sides\r\n# as arguments and returns the number of rectangles.\r\n\r\n\r\ndef getCountRect(nVal, mVal):\r\n        # Inside the getCountRect()\u00a0function Calculate the number of rectangles\r\n    # using the MatheMatical Formula M(M+1)(N)(N+1)\/4\u00a0\r\n    # and store it in a variable say reslt.\r\n    reslt = (mVal * nVal * (nVal + 1) * (mVal + 1)) \/ 4\r\n    # Return the reslt value.\r\n    return reslt\r\n\r\n\r\n# Inside the Main Function.\r\n# Give the number N as user input using the int(input()) function and store it in a variable.\r\nnVal = int(input('Enter Some Random N value = '))\r\n# Give the number M as static input and store it in another variable.\r\nmVal = int(input('Enter Some Random M value = '))\r\n# Pass the given N, M as arguments to getCountRect() function\r\n# and store the result returned from the function in a variable say countRect.\r\ncountRect = int(getCountRect(nVal, mVal))\r\n# Print the countRect value.\r\nprint(\r\n    'Number of Rectangles in the grid of size {', nVal, '*', mVal, '} :', countRect)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter Some Random N value = 4\r\nEnter Some Random M value = 2\r\nNumber of Rectangles in the grid of size { 4 * 2 } : 30<\/pre>\n<p>Explore more <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Example Python Programs<\/a> with output and explanation and practice them for your interviews, assignments and stand out from the rest of the crowd.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-area-of-a-circular-segment\/\">Python Program to Find Area of a Circular Segment<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-for-arc-length-from-given-angle\/\">Python Program for Arc Length from Given Angle<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-area-of-a-circular-sector\/\">Python Program To Find Area of a Circular Sector<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-for-minimum-perimeter-of-n-blocks\/\">Python Program for Minimum Perimeter of n Blocks<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program for Minimum Perimeter of n Blocks Given a grid of size N*M the task is to find the number of rectangles in the given grid in Python. Examples: Example1: Input: Given N = 6 Given M = 4 Output: Number of Rectangles in the grid of &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-number-of-rectangles-in-nm-grid\/\"> <span class=\"screen-reader-text\">Python Program to Find Number of Rectangles in N*M Grid<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":23030,"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 Find Number of Rectangles in N*M Grid - 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-find-number-of-rectangles-in-nm-grid\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Find Number of Rectangles in N*M Grid - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program for Minimum Perimeter of n Blocks Given a grid of size N*M the task is to find the number of rectangles in the given grid in Python. 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