--- title: Maximum Weight Transformation of String | daily.dev description: This tutorial explains a dynamic programming solution for maximizing the 'weight' of a binary string made of 'A' and 'B' characters. An alternating pair like... canonical: https://daily.dev/posts/maximum-weight-transformation-of-string-6hjmi8pgb twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Maximum Weight Transformation of String | daily.dev og:description: This tutorial explains a dynamic programming solution for maximizing the 'weight' of a binary string made of 'A' and 'B' characters. An alternating pair like... og:url: https://daily.dev/posts/maximum-weight-transformation-of-string-6hjmi8pgb og:image: https://api.daily.dev/og/posts/6HjMi8PGb.png og:image:alt: Maximum Weight Transformation of String og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Maximum Weight Transformation of String **[C\# Corner](https://daily.dev/sources/csharpcorner)** · 4 min read · 0 upvotes · 0 comments ## Summary This tutorial explains a dynamic programming solution for maximizing the 'weight' of a binary string made of 'A' and 'B' characters. An alternating pair like 'AB' or 'BA' contributes 4 to the weight, an unpaired character contributes 1, and each toggle (flipping A to B or vice versa) costs 1. For 'AA', toggling one character to form 'AB' gives a final weight of 3. The DP recurrence is dp[i] = max(dp[i-1] + 1, dp[i-2] + pairWeight), where pairWeight is 4 for already-alternating pairs and 3 for matching pairs after a toggle. Full Java code implementing this is included. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### How do I calculate the maximum weight of a string made of A and B characters where alternating pairs score higher? Use dynamic programming where dp[i] tracks the max weight using the first i characters. At each position, either leave the current character unpaired (dp[i-1] + 1) or pair the last two characters (dp[i-2] + pairWeight), where pairWeight is 4 for already-alternating pairs like AB or BA, and 3 for matching pairs like AA or BB after a one-character toggle. _daily.dev surfaces more dynamic programming walkthroughs for developers prepping algorithm interview questions._ ### Why does toggling one character in a matching pair like AA still result in a weight of 3 instead of 4? Turning AA into AB forms a valid alternating pair worth 4, but the toggle itself costs 1 point, giving a net effective contribution of 3. Every toggle decreases the final weight by 1, so same-character pairs are always worth one less than already-alternating pairs. _Developers working through weighted string DP problems can find similar breakdowns on daily.dev._ ## Similar posts on daily.dev - [Count Substrings with More 1's than 0's](https://daily.dev/posts/count-substrings-with-more-1-s-than-0-s-k63z1kpmf) · C\# Corner · 0 upvotes · 0 comments - [Maximum Product Cutting of a Rope Using a Greedy Mathematical Approach](https://daily.dev/posts/maximum-product-cutting-of-a-rope-using-a-greedy-mathematical-approach-ydjjbjcwb) · C\# Corner · 0 upvotes · 0 comments - [Solving the 3Blue1Brown String Probability Problem \(Without AI\)](https://daily.dev/posts/solving-the-3blue1brown-string-probability-problem-without-ai--thczbuec0) · Towards Data Science · 0 upvotes · 0 comments - [Palindrome with Replacement – Minimum Adjacent Difference](https://daily.dev/posts/palindrome-with-replacement-minimum-adjacent-difference-rmvpsbgdj) · C\# Corner · 0 upvotes · 0 comments --- Tags: [#java](https://daily.dev/tags/java), [#algorithms](https://daily.dev/tags/algorithms), [#dynamic-programming](https://daily.dev/tags/dynamic-programming) [View this post on daily.dev](https://daily.dev/posts/maximum-weight-transformation-of-string-6hjmi8pgb) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Maximum Weight Transformation of String","url":"https://daily.dev/posts/maximum-weight-transformation-of-string-6hjmi8pgb","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/maximum-weight-transformation-of-string-6hjmi8pgb"},"datePublished":"2026-10-27T05:10:29.682Z","dateModified":"2026-10-27T05:10:59.333Z","description":"This tutorial explains a dynamic programming solution for maximizing the 'weight' of a binary string made of 'A' and 'B' characters. 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At each position, either leave the current character unpaired (dp[i-1] + 1) or pair the last two characters (dp[i-2] + pairWeight), where pairWeight is 4 for already-alternating pairs like AB or BA, and 3 for matching pairs like AA or BB after a one-character toggle. daily.dev surfaces more dynamic programming walkthroughs for developers prepping algorithm interview questions."}},{"@type":"Question","name":"Why does toggling one character in a matching pair like AA still result in a weight of 3 instead of 4?","acceptedAnswer":{"@type":"Answer","text":"Turning AA into AB forms a valid alternating pair worth 4, but the toggle itself costs 1 point, giving a net effective contribution of 3. Every toggle decreases the final weight by 1, so same-character pairs are always worth one less than already-alternating pairs. Developers working through weighted string DP problems can find similar breakdowns on daily.dev."}}]} ```