Dynamic Programming Memoization When to use Problem has

Dynamic Programming & Memoization

When to use? • Problem has a recursive formulation • Solutions are “ordered” – Earlier vs. later recursions

Get the recursion right! • If you’re not given the recursive solution explicitly, implement it • Try on small cases (and “medium” ones) • Make sure you have all base cases! • Test data is often small enough

Memoization • A quick and dirty speedup • Uses the recursive algorithm almost directly • Avoid if too many parameters • Modify the recursive call to – Save its result – See if the result is computed before computing it

Structure of Memoization Int my-recursive-function (int param 1, int param 2){ //base cases go here //memoization addition if (table[param 1][param 2] != NONE) return table[param 1][param 2]; //continue with recursive solution…

Dynamic Programming • Code is now rewritten • Replace recursion by loop – From “end cases” toward more complex ones

Structure of Dynamic Program • Initialize base cases in array (e. g. top, left border) • Loop through array in a reasonable order – Goal: “recursive cases” already computed – If bases are top, left, then L->R, T->B OK • Search array for final solution (if needed)

Example: String Editing (p. 248 -249) • Strings across top and down left • Base cases at borders – Empty string = length() insertions • Step considers 3 options – Match last character – Add last character – Delete last character • Final result at last char each string