Retrieving "Dynamic Programming" from the archives

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1. Foraging

   Linked via "dynamic programming"

   The Energetic Cost of Search Time
   A primary challenge in foraging theory is quantifying the "search time" component, which represents the energy expended locating, but not yet consuming, a resource patch. This is often modeled using dynamic programming to minimize the expected time to acquisition ($E[T_{acq}]$).
   The temporal component of energy expenditure ($ET$) for locating a single high-value item ($Vi$) within a heterogeneous patch is approximated by the following semi-empirical equation:

2. Space Time Tradeoffs

   Linked via "Dynamic programming (DP)"

   Dynamic Programming and Memoization
   Dynamic programming (DP) solutions frequently exemplify this tradeoff. A naive recursive solution to a problem like the Fibonacci sequence has an exponential time complexity, $O(2^n)$, but requires only minimal stack space, $O(n)$. By introducing memoization—storing intermediate results in a lookup table (space)—the time complexity is reduced dramatically to $O(n)$, but the space requirement increases to $O(n)$ to store the table (Knuth, 1978).
   More advanced tech…