{"id":456,"date":"2024-01-03T13:08:52","date_gmt":"2024-01-03T13:08:52","guid":{"rendered":"https:\/\/www.kaashivinfotech.com\/blog\/?p=456"},"modified":"2025-07-18T07:36:40","modified_gmt":"2025-07-18T07:36:40","slug":"painters-partition-problem","status":"publish","type":"post","link":"https:\/\/www.kaashivinfotech.com\/blog\/painters-partition-problem\/","title":{"rendered":"Mastering the Painter&#8217;s Partition Problem with Java and DSA Techniques"},"content":{"rendered":"<p data-start=\"345\" data-end=\"669\">The <strong data-start=\"349\" data-end=\"380\">painter&#8217;s partition problem<\/strong>, also spelled as <a href=\"https:\/\/www.wikitechy.com\/technology\/java-programming-partition-problem\/\" target=\"_blank\" rel=\"noopener\"><strong data-start=\"398\" data-end=\"428\">painters partition problem<\/strong><\/a> or <strong data-start=\"432\" data-end=\"461\">painter partition problem<\/strong>, is a classic algorithmic challenge that&#8217;s commonly covered in <strong data-start=\"525\" data-end=\"565\">DSA (Data Structures and Algorithms)<\/strong> and frequently appears in <a href=\"https:\/\/www.kaashivinfotech.com\/java-course\/\"><strong data-start=\"592\" data-end=\"607\">Java course<\/strong><\/a> modules focused on problem-solving and interview preparation.<\/p>\n<h2 data-start=\"676\" data-end=\"702\">\ud83d\udcdd Problem Description<\/h2>\n<p data-start=\"704\" data-end=\"1058\">In the <strong data-start=\"711\" data-end=\"742\">painter&#8217;s partition problem<\/strong>, you&#8217;re given a sequence of boards of varying lengths, and a set number of painters. Each painter takes a fixed amount of time to paint one unit of board length. The objective is to minimize the total time required to paint all the boards under the condition that each painter can only paint <strong data-start=\"1035\" data-end=\"1057\">consecutive boards<\/strong>.<\/p>\n<p data-start=\"1060\" data-end=\"1213\">This problem is a great real-world analogy for <strong data-start=\"1107\" data-end=\"1125\">load balancing<\/strong> and <strong data-start=\"1130\" data-end=\"1149\">task allocation<\/strong>, which are critical in systems design and software development.<\/p>\n<h2 data-start=\"1220\" data-end=\"1246\">\ud83d\udd10 Problem Constraints<\/h2>\n<p data-start=\"1248\" data-end=\"1261\">You&#8217;re given:<\/p>\n<ul data-start=\"1262\" data-end=\"1553\">\n<li data-start=\"1262\" data-end=\"1347\">\n<p data-start=\"1264\" data-end=\"1347\">An array <code class=\"\" data-line=\"\">boards[]<\/code> of size <code class=\"\" data-line=\"\">n<\/code>, where each value represents the length of a board.<\/p>\n<\/li>\n<li data-start=\"1348\" data-end=\"1401\">\n<p data-start=\"1350\" data-end=\"1401\">An integer <code class=\"\" data-line=\"\">k<\/code> representing the number of painters.<\/p>\n<\/li>\n<li data-start=\"1402\" data-end=\"1481\">\n<p data-start=\"1404\" data-end=\"1481\">An integer <code class=\"\" data-line=\"\">t<\/code> representing the time taken to paint one unit of board length.<\/p>\n<\/li>\n<li data-start=\"1482\" data-end=\"1553\">\n<p data-start=\"1484\" data-end=\"1553\">Painters cannot skip boards; they must paint them in the given order.<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"1560\" data-end=\"1579\">\ud83d\udce5 Input Format<\/h3>\n<ul data-start=\"1581\" data-end=\"1707\">\n<li data-start=\"1581\" data-end=\"1612\">\n<p data-start=\"1583\" data-end=\"1612\"><code class=\"\" data-line=\"\">n<\/code>: Total number of boards<\/p>\n<\/li>\n<li data-start=\"1613\" data-end=\"1640\">\n<p data-start=\"1615\" data-end=\"1640\"><code class=\"\" data-line=\"\">k<\/code>: Number of painters<\/p>\n<\/li>\n<li data-start=\"1641\" data-end=\"1670\">\n<p data-start=\"1643\" data-end=\"1670\"><code class=\"\" data-line=\"\">t<\/code>: Time per unit length<\/p>\n<\/li>\n<li data-start=\"1671\" data-end=\"1707\">\n<p data-start=\"1673\" data-end=\"1707\"><code class=\"\" data-line=\"\">boards[]<\/code>: Array of board lengths<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"1714\" data-end=\"1734\">\ud83d\udce4 Output Format<\/h3>\n<ul data-start=\"1736\" data-end=\"1816\">\n<li data-start=\"1736\" data-end=\"1816\">\n<p data-start=\"1738\" data-end=\"1816\">Output a single integer representing the <strong data-start=\"1779\" data-end=\"1795\">minimum time<\/strong> to paint all boards.<\/p>\n<\/li>\n<\/ul>\n<h2 data-start=\"1823\" data-end=\"1842\">\u2705 Example Input<\/h2>\n<div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"\" data-line=\"\">n = 5<br \/>\nk = 3<br \/>\nt = 5<br \/>\nboards = [2, 4, 3, 1, 7]<br \/>\n<\/code><\/div>\n<\/div>\n<h3 data-start=\"1911\" data-end=\"1932\">\ud83c\udfaf Example Output<\/h3>\n<div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"\" data-line=\"\">15<br \/>\n<\/code><\/div>\n<\/div>\n<h3 data-start=\"1955\" data-end=\"1981\">\ud83d\udca1 Example Explanation<\/h3>\n<p data-start=\"1983\" data-end=\"2141\">Consider the board lengths: <code class=\"\" data-line=\"\">[2, 4, 3, 1, 7]<\/code>. We have 3 painters, each taking 5 units of time per unit length. One optimal way to assign the boards could be:<\/p>\n<ul data-start=\"2143\" data-end=\"2271\">\n<li data-start=\"2143\" data-end=\"2186\">\n<p data-start=\"2145\" data-end=\"2186\">Painter 1: [2, 4] \u2192 6 units \u2192 Time = 30<\/p>\n<\/li>\n<li data-start=\"2187\" data-end=\"2227\">\n<p data-start=\"2189\" data-end=\"2227\">Painter 2: [3] \u2192 3 units \u2192 Time = 15<\/p>\n<\/li>\n<li data-start=\"2228\" data-end=\"2271\">\n<p data-start=\"2230\" data-end=\"2271\">Painter 3: [1, 7] \u2192 8 units \u2192 Time = 40<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2273\" data-end=\"2382\">The maximum time taken by any painter is <strong data-start=\"2314\" data-end=\"2320\">40<\/strong>, so that would be the minimum overall time in this partition.<\/p>\n<p data-start=\"2384\" data-end=\"2586\">This strategy of optimizing task allocation reflects the kind of logic you&#8217;ll master in a <strong data-start=\"2474\" data-end=\"2493\">Java DSA course<\/strong>, where such problems are solved using binary search, greedy methods, or dynamic programming.<\/p>\n<h2 data-start=\"2593\" data-end=\"2634\">\u2753 FAQs on Painter\u2019s Partition Problem<\/h2>\n<h4 data-start=\"2636\" data-end=\"2684\">1. What is the Painter&#8217;s Partition Problem?<\/h4>\n<p data-start=\"2685\" data-end=\"2908\">It\u2019s an optimization problem where the goal is to <strong data-start=\"2735\" data-end=\"2764\">minimize the maximum time<\/strong> taken by any painter to paint all boards. Each painter must paint <strong data-start=\"2831\" data-end=\"2853\">consecutive boards<\/strong>, and no board can be painted by more than one painter.<\/p>\n<h4 data-start=\"2910\" data-end=\"2942\">2. What are the variations?<\/h4>\n<ul data-start=\"2943\" data-end=\"3069\">\n<li data-start=\"2943\" data-end=\"2983\">\n<p data-start=\"2945\" data-end=\"2983\">Different painting speeds for painters<\/p>\n<\/li>\n<li data-start=\"2984\" data-end=\"3034\">\n<p data-start=\"2986\" data-end=\"3034\">Boards painted in any order (relaxed constraint)<\/p>\n<\/li>\n<li data-start=\"3035\" data-end=\"3069\">\n<p data-start=\"3037\" data-end=\"3069\">Painter availability constraints<\/p>\n<\/li>\n<\/ul>\n<h4 data-start=\"3071\" data-end=\"3108\">3. What are the key constraints?<\/h4>\n<ul data-start=\"3109\" data-end=\"3201\">\n<li data-start=\"3109\" data-end=\"3132\">\n<p data-start=\"3111\" data-end=\"3132\">One painter per board<\/p>\n<\/li>\n<li data-start=\"3133\" data-end=\"3165\">\n<p data-start=\"3135\" data-end=\"3165\">Consecutive boards per painter<\/p>\n<\/li>\n<li data-start=\"3166\" data-end=\"3201\">\n<p data-start=\"3168\" data-end=\"3201\">Uniform time per unit of painting<\/p>\n<\/li>\n<\/ul>\n<h4 data-start=\"3203\" data-end=\"3260\">4. How do you solve the Painter\u2019s Partition Problem?<\/h4>\n<p data-start=\"3261\" data-end=\"3289\">The standard approach is to:<\/p>\n<ul data-start=\"3290\" data-end=\"3528\">\n<li data-start=\"3290\" data-end=\"3333\">\n<p data-start=\"3292\" data-end=\"3333\">Use <strong data-start=\"3296\" data-end=\"3333\">Binary Search on the answer space<\/strong><\/p>\n<\/li>\n<li data-start=\"3334\" data-end=\"3468\">\n<p data-start=\"3336\" data-end=\"3468\">Implement a helper method (often taught in <strong data-start=\"3379\" data-end=\"3407\">DSA-focused Java courses<\/strong>) to check if a partition is valid under the current max time<\/p>\n<\/li>\n<li data-start=\"3469\" data-end=\"3528\">\n<p data-start=\"3471\" data-end=\"3528\">Combine <strong data-start=\"3479\" data-end=\"3506\">greedy allocation logic<\/strong> with efficient search<\/p>\n<\/li>\n<\/ul>\n<h2 data-start=\"3535\" data-end=\"3581\">\ud83e\udde0 Why It&#8217;s Important in Java DSA Learning<\/h2>\n<p data-start=\"3583\" data-end=\"3667\">This problem is a staple in <strong data-start=\"3611\" data-end=\"3626\">DSA modules<\/strong> of a <strong data-start=\"3632\" data-end=\"3647\">Java course<\/strong> because it teaches:<\/p>\n<ul data-start=\"3668\" data-end=\"3774\">\n<li data-start=\"3668\" data-end=\"3700\">\n<p data-start=\"3670\" data-end=\"3700\"><strong data-start=\"3670\" data-end=\"3698\">Binary Search on Answers<\/strong><\/p>\n<\/li>\n<li data-start=\"3701\" data-end=\"3739\">\n<p data-start=\"3703\" data-end=\"3739\"><strong data-start=\"3703\" data-end=\"3737\">Greedy Partitioning Techniques<\/strong><\/p>\n<\/li>\n<li data-start=\"3740\" data-end=\"3774\">\n<p data-start=\"3742\" data-end=\"3774\"><strong data-start=\"3742\" data-end=\"3774\">Time Complexity Optimization<\/strong><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"3776\" data-end=\"3889\">It&#8217;s a go-to problem when preparing for <strong data-start=\"3816\" data-end=\"3840\">technical interviews<\/strong> at companies like Amazon, Google, and Microsoft.<\/p>\n<h2 data-start=\"3896\" data-end=\"3918\">\ud83e\uddee Time Complexity<\/h2>\n<ul data-start=\"3920\" data-end=\"4048\">\n<li data-start=\"3920\" data-end=\"3973\">\n<p data-start=\"3922\" data-end=\"3973\">Binary search between <code class=\"\" data-line=\"\">max(board)<\/code> and <code class=\"\" data-line=\"\">sum(board)<\/code><\/p>\n<\/li>\n<li data-start=\"3974\" data-end=\"4013\">\n<p data-start=\"3976\" data-end=\"4013\">For each guess, verify in <code class=\"\" data-line=\"\">O(n)<\/code> time<\/p>\n<\/li>\n<li data-start=\"4014\" data-end=\"4048\">\n<p data-start=\"4016\" data-end=\"4048\">Overall: <code class=\"\" data-line=\"\">O(n * log(sum - max))<\/code><\/p>\n<\/li>\n<\/ul>\n<h2 data-start=\"4055\" data-end=\"4074\">\ud83e\udde9 Applications<\/h2>\n<ul data-start=\"4076\" data-end=\"4244\">\n<li data-start=\"4076\" data-end=\"4115\">\n<p data-start=\"4078\" data-end=\"4115\">Task scheduling in parallel systems<\/p>\n<\/li>\n<li data-start=\"4116\" data-end=\"4157\">\n<p data-start=\"4118\" data-end=\"4157\">Workload balancing in cloud platforms<\/p>\n<\/li>\n<li data-start=\"4158\" data-end=\"4200\">\n<p data-start=\"4160\" data-end=\"4200\">Resource allocation in backend systems<\/p>\n<\/li>\n<li data-start=\"4201\" data-end=\"4244\">\n<p data-start=\"4203\" data-end=\"4244\">Real-world painting\/construction planning<\/p>\n<\/li>\n<\/ul>\n<h2 data-start=\"4251\" data-end=\"4268\">\ud83d\udccc Conclusion<\/h2>\n<p data-start=\"4270\" data-end=\"4690\">The <strong data-start=\"4274\" data-end=\"4305\">painter&#8217;s partition problem<\/strong>, <strong data-start=\"4307\" data-end=\"4337\">painters partition problem<\/strong>, or <strong data-start=\"4342\" data-end=\"4371\">painter partition problem<\/strong> is not just a theoretical algorithm\u2014it\u2019s a real-world problem-solving tool. If you&#8217;re diving into <a href=\"https:\/\/www.kaashivinfotech.com\/java-full-stack-developer\/\"><strong data-start=\"4470\" data-end=\"4487\">DSA with Java<\/strong><\/a>, this is one of the must-practice patterns. Whether you&#8217;re taking a structured <strong data-start=\"4567\" data-end=\"4582\">Java course<\/strong> or self-studying for coding interviews, mastering this problem helps you build strong algorithmic thinking.<\/p>\n","protected":false},"excerpt":{"rendered":"The painter&#8217;s partition problem, also spelled as painters partition problem or painter partition problem, is a classic algorithmic&hellip;","protected":false},"author":2,"featured_media":8520,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_singular_sidebar":"","csco_page_header_type":"","csco_page_load_nextpost":"","footnotes":""},"categories":[2191],"tags":[2433,2429,2423,2428,2427,2424,2421,2426,2422,2425,2432,2430,2434,2435,2431],"class_list":["post-456","post","type-post","status-publish","format-standard","has-post-thumbnail","category-problems","tag-binary-search-problem-example","tag-painter-paritition","tag-painter-partition","tag-painter-partition-backtracking","tag-painter-partition-dynamic-programming","tag-painter-problem","tag-painters-partition-problem","tag-painters-partition-problem-in-binary-search","tag-painters-partition","tag-painters-partition-problem-leetcode","tag-partition","tag-partition-problem","tag-partition-problem-dp-18","tag-partition-problem-recursion","tag-prepbytes-painter-partition","cs-entry"],"_links":{"self":[{"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/posts\/456","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/comments?post=456"}],"version-history":[{"count":4,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/posts\/456\/revisions"}],"predecessor-version":[{"id":8521,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/posts\/456\/revisions\/8521"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/media\/8520"}],"wp:attachment":[{"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/media?parent=456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/categories?post=456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kaashivinfotech.com\/blog\/wp-json\/wp\/v2\/tags?post=456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}