{"id":20184,"date":"2022-11-08T23:49:22","date_gmt":"2022-11-08T18:19:22","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-python-max-benefit-closed\/"},"modified":"2022-11-08T23:49:22","modified_gmt":"2022-11-08T18:19:22","slug":"solved-python-max-benefit-closed","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-python-max-benefit-closed\/","title":{"rendered":"[Solved] Python max benefit [closed]"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-10596775\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"10596775\" data-parentid=\"10594856\" data-score=\"1\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>The number of possible routes through a tree is <code>2**rows<\/code>. The number of possible routes to a given node is given by the binomial expansion. You can grow the possible routes from the head of the tree quite simply, at each node there are only two possible next moves, their indexes in the list are either the same as the current position or one more. <\/p>\n<p>A simple way to solve the problem is to generate all possible paths for a given number of rows. <code>create_paths()<\/code> does this, returning all possible routes through the tree. Function <code>max_cost()<\/code> uses this to evaluate all routes against the cost tree, returning the value of the most expensive route. I leave it to you to get the actual route out (not very hard..)  \ud83d\ude42<\/p>\n<pre><code>L_0 = [[7], [3,8], [8,1,0], [2,7,4,4], [4,5,2,6,5]]\nL_1 = [[11], [7,32], [14,14,14], [0,1,2,3], [5,99,1,2,7],\n       [0,25,9,45, 54,1], [99,88,77,66,55,44,33]]\n\ndef create_paths(rows):\n    new_paths = []\n    paths = [[0]]\n    for row in xrange(rows):\n        for path in paths:\n            new_paths.append(path+[path[-1]])\n            new_paths.append(path+[path[-1]+1])\n        paths = new_paths\n        new_paths = []\n    return paths\n\ndef max_cost(tree):\n    costs = []\n    paths = create_paths(len(tree)-1)\n    for path in paths:\n        costs.append(sum([tree[i][j] for i, j in enumerate(path)]))\n    return max(costs)\n\nprint max_cost(L_0)\nprint max_cost(L_1)\n\n#output:\n30\n270\n<\/code><\/pre>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\"><\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Python max benefit [closed] <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] The number of possible routes through a tree is 2**rows. The number of possible routes to a given node is given by the binomial expansion. You can grow the possible routes from the head of the tree quite simply, at each node there are only two possible next moves, their indexes in the list &#8230; <a title=\"[Solved] Python max benefit [closed]\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-python-max-benefit-closed\/\" aria-label=\"More on [Solved] Python max benefit [closed]\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[349],"class_list":["post-20184","post","type-post","status-publish","format-standard","hentry","category-solved","tag-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Python max benefit [closed] - JassWeb<\/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:\/\/jassweb.com\/solved\/solved-python-max-benefit-closed\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Python max benefit [closed] - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] The number of possible routes through a tree is 2**rows. 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