https://abaj.ai/tags/knapsack/Recent content in Knapsack on Aayush Bajaj's Augmenting InfrastructureHugoen© 2026 Aayush BajajFri, 10 Jul 2026 13:02:29 +1000https://abaj.ai/wiki/ccs/programming/paradigms/dynamic/Fri, 10 Jul 2026 13:02:51 +1000https://abaj.ai/wiki/ccs/programming/paradigms/dynamic/<p>dynamic programming is two things wearing one name. to bellman it was a mathematical theory of <em>multistage decision processes</em> — sibling to <a href="https://abaj.ai/wiki/ccs/programming/paradigms/linear/" >linear programming</a> in the &ldquo;programming means planning&rdquo; sense.<sup id="fnref:1"><a href="#fn:1" class="footnote-ref" role="doc-noteref">1</a></sup><span class="margin-note" data-note="bellman chose the name partly to hide the mathematics from a defence secretary who hated the word research; the story is in the footnote"> <span class="margin-note-indicator">𐃏</span> </span> to a computer scientist it is a technique: solve a problem by combining solutions to subproblems, and never solve the same subproblem twice (Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford, 2009). the two are the same idea at different altitudes, and this page covers both. worked implementations also live in this <a href="https://github.com/abaj8494/dynamic-programming" class="link--external" target="_blank" rel="noreferrer" >github repo</a>.</p>