{"id":6946,"date":"2021-09-30T10:30:55","date_gmt":"2021-09-30T05:00:55","guid":{"rendered":"https:\/\/python-programs.com\/?p=6946"},"modified":"2021-11-22T18:35:33","modified_gmt":"2021-11-22T13:05:33","slug":"python-program-to-print-pascals-triangle","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-print-pascals-triangle\/","title":{"rendered":"Python program to print Pascal&#8217;s Triangle"},"content":{"rendered":"<p>Want to excel in java coding? Practice with these <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Java Programs examples with output<\/a> and write any kind of easy or difficult programs in the java language<\/p>\n<p><strong>Pascal Triangle Definition:<\/strong><\/p>\n<p>Pascal&#8217;s triangle is a lovely shape produced by arranging numbers. The sum of the two numbers above it is used to produce each number. This triangle&#8217;s outside edges are always 1. The triangle is depicted in the diagram below.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-6948 aligncenter\" src=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/pascal.jpg\" alt=\"\" width=\"456\" height=\"357\" srcset=\"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/pascal.jpg 456w, https:\/\/python-programs.com\/wp-content\/uploads\/2021\/05\/pascal-300x235.jpg 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/p>\n<p><strong>Explanation:<\/strong><\/p>\n<p>To illustrate the triangle in a nutshell, the first line is 1. There are two ones in the line after that. The second line is here.<\/p>\n<p>1 2 1 is the third line, which is created by adding the ones from the previous line. Similarly, the number of 1 and 2 in an alternative pattern forms the fourth line, and so on.<\/p>\n<p><strong>Examples of pascal Triangle<\/strong><\/p>\n<p><strong>Example 1:<\/strong><\/p>\n<p><strong>Input :<\/strong><\/p>\n<pre>height =5<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">       1\r\n     1 1\r\n    1 2 1\r\n   1 3 3 1\r\n  1 4 6 4 1<\/pre>\n<p><strong>Example 1:<\/strong><\/p>\n<p><strong>Input :<\/strong><\/p>\n<pre>height =10<\/pre>\n<p><strong>Output :<\/strong><\/p>\n<pre id=\"codeOutputPre\">           1\r\n          1 1\r\n         1 2 1\r\n        1 3 3 1\r\n       1 4 6 4 1\r\n      1 5 10 10 5 1\r\n     1 6 15 20 15 6 1\r\n    1 7 21 35 35 21 7 1\r\n   1 8 28 56 70 56 28 8 1\r\n  1 9 36 84 126 126 84 36 9 1<\/pre>\n<h2>Pascal Triangle in Python<\/h2>\n<p>Below are the methods to print the pascal triangle.<\/p>\n<ul>\n<li><a href=\"#Implementation_Using_zip_function\">Implementation Using zip function<\/a><\/li>\n<li><a href=\"#Using_NCR\">Using NCR<\/a><\/li>\n<li><a href=\"#Using_Binomial_Coefficient\">Using Binomial Coefficient<\/a><\/li>\n<\/ul>\n<p>Explore more instances related to python concepts from\u00a0<a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Programming Examples<\/a>\u00a0Guide and get promoted from beginner to professional programmer level in Python Programming Language.<\/p>\n<h3 id=\"Implementation_Using_zip_function\">Method #1: Implementation Using zip function<\/h3>\n<p>Using the oneval variable, we will first initialise the top row in this function. Variable zerovalue=0 is also set to zero. To run the code for n iterations, we&#8217;ll use a for loop.<\/p>\n<p>We&#8217;ll print the list generated by the oneval variable within the for loop. We&#8217;ll now add the onevalue to left and right elements. We&#8217;ve also used the zip feature in this case.<\/p>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def printPascal(height):\r\n    onevalue = [1]\r\n    zero = [0]\r\n    for i in range(height):\r\n        print(*onevalue)\r\n        onevalue = [left+right for left,\r\n                    right in zip(onevalue+zero, zero+onevalue)]\r\n\r\n\r\n# given height\r\nheight = 5\r\n# passing the height as paramter to printPascal function\r\nprintPascal(height)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">1\r\n1 1\r\n1 2 1\r\n1 3 3 1\r\n1 4 6 4 1<\/pre>\n<h3 id=\"Using_NCR\">Method #2:Using NCR<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Consider the number of rows to be printed; let&#8217;s say it&#8217;s n.<\/li>\n<li>To print the rows, repeat iteration I from 0 to n times.<\/li>\n<li>Iterate for j from 0 to (N \u2013 1) in the inner loop.<\/li>\n<li>\u201d \u201c is a single blank space to be printed.<\/li>\n<li>It&#8217;s enough to close the inner loop (j loop) for left spacing.<\/li>\n<li>Make an inner iteration from 0 to I for j.<\/li>\n<li>nCr of I and j should be printed.<\/li>\n<li>Close\u00a0the inner loop.<\/li>\n<li>For each inner iteration, print a newline character (\\n).<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># impoerting factorial fucntion from math module\r\nfrom math import factorial\r\n\r\n\r\ndef printPascal(height):\r\n    for i in range(height):\r\n        for j in range(height-i+1):\r\n\r\n            # for spacing in left\r\n            print(end=\" \")\r\n\r\n        for j in range(i+1):\r\n            print(factorial(i)\/\/(factorial(j)*factorial(i-j)), end=\" \")\r\n\r\n    # printing in new line\r\n        print()\r\n\r\n\r\n# given height\r\nheight = 5\r\n# passing the height as paramter to printPascal function\r\nprintPascal(height)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">      1 \r\n     1 1 \r\n    1 2 1 \r\n   1 3 3 1 \r\n  1 4 6 4 1<\/pre>\n<h3 id=\"Using_Binomial_Coefficient\">Method #3:Using Binomial Coefficients<\/h3>\n<p>The following definition of a Binomial Coefficient may be used to optimise the above code the i&#8217;th entry in a line number line is Binomial Coefficient C(line, i) and all lines begin with value 1. The idea is to use C to measure C(line, i) using C(line, i-1).<\/p>\n<pre>C(line, i) = C(line, i-1) * (line - i + 1) \/ i<\/pre>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def printPascal(height):\r\n    for i in range(1, height+1):\r\n        for j in range(0, height-i+1):\r\n            print(' ', end='')\r\n\r\n        # since first eelement is always 1\r\n        onevalue = 1\r\n        for j in range(1, i+1):\r\n\r\n            # first value of every line is 1 always.\r\n            print(' ', onevalue, sep='', end='')\r\n\r\n            # using binomial cofficients to calculat using onevalue\r\n            onevalue = onevalue * (i - j) \/\/ j\r\n        print()\r\n\r\n\r\n# given height\r\nheight = 5\r\n# passing the height as paramter to printPascal function\r\nprintPascal(height)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">       1\r\n     1 1\r\n    1 2 1\r\n   1 3 3 1\r\n  1 4 6 4 1<\/pre>\n<p><strong>Related Programs<\/strong>:<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-right-angled-triangle-star-pattern\/\">python program to print right angled triangle star pattern<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-hollow-right-triangle-star-pattern\/\">python program to print hollow right triangle star pattern<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-right-triangle-number-pattern\/\">python program to print right triangle number pattern<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-inverted-right-triangle-of-numbers\/\">python program to print inverted right triangle of numbers<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-inverted-right-triangle-star-pattern\/\">python program to print inverted right triangle star pattern<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-mirrored-right-triangle-star-pattern\/\">python program to print mirrored right triangle star pattern<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-reverse-mirrored-right-triangle-star-pattern\/\">python program to print reverse mirrored right triangle star pattern<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Want to excel in java coding? Practice with these Java Programs examples with output and write any kind of easy or difficult programs in the java language Pascal Triangle Definition: Pascal&#8217;s triangle is a lovely shape produced by arranging numbers. The sum of the two numbers above it is used to produce each number. This &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-print-pascals-triangle\/\"> <span class=\"screen-reader-text\">Python program to print Pascal&#8217;s Triangle<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":6953,"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 print Pascal&#039;s Triangle - 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-print-pascals-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python program to print Pascal&#039;s Triangle - Python Programs\" \/>\n<meta property=\"og:description\" content=\"Want to excel in java coding? 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Practice with these Java Programs examples with output and write any kind of easy or difficult programs in the java language Pascal Triangle Definition: Pascal&#8217;s triangle is a lovely shape produced by arranging numbers. The sum of the two numbers above it is used to produce each number. 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