dynamic-programming

The following code is from Pathikrit's Dynamic Programming repository. I'm mystified by both its beauty and peculiarity. def subsetSum(s: List[Int], t: Int) = { type DP = Memo[(List[Int], Int), (Int, Int), Seq[Seq[Int]]] implicit def encode(key: (List[Int], Int)) = (key._1.length, key._2) lazy val f: DP = Memo { case (Nil, 0) => Seq(Nil) case (Nil, _) => Nil case (a :: as, x) => (f(as, x - a) map {_ :+ a}) ++ f(as, x) } f(s, t) } The type Memo is implemented in another file: case class Memo[I <% K, K, O](f: I => O) extends (I => O) { import collection.mutable.{Map => Dict} val cache = Dict

Suppose you are given an mXn bitmap, represented by an array M[1..m,1.. n] whose entries are all 0 or 1. A all-one block is a subarray of the form M[i .. i0, j .. j0] in which every bit is equal to 1. Describe and analyze an efficient algorithm to find an all-one block in M with maximum area I am trying to make a dynamic programming solution. But my recursive algorithm runs in O(n^n) time, and even after memoization I cannot think of bringing it down below O(n^4). Can someone help me find a more efficient solution? An O(N) (number of elements) solution: A 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0

Years ago, I solved a problem via dynamic programming: https://www.thanassis.space/fillupDVD.html The solution was coded in Python. As part of expanding my horizons, I recently started learning OCaml/F#. What better way to test the waters, than by doing a direct port of the imperative code I wrote in Python to F# - and start from there, moving in steps towards a functional programming solution. The results of this first, direct port... are disconcerting: Under Python: bash$ time python fitToSize.py .... real 0m1.482s user 0m1.413s sys 0m0.067s Under FSharp: bash$ time mono ./fitToSize.exe ....

Imagine you're in a tall building with a cat. The cat can survive a fall out of a low story window, but will die if thrown from a high floor. How can you figure out the longest drop that the cat can survive, using the least number of attempts? Obviously, if you only have one cat, then you can only search linearly. First throw the cat from the first floor. If it survives, throw it from the second. Eventually, after being thrown from floor f, the cat will die. You then know that floor f-1 was the maximal safe floor. But what if you have more than one cat? You can now try some sort of logarithmic

There is a list of numbers. The list is to be divided into 2 equal sized lists, with a minimal difference in sum. The sums have to be printed. #Example: >>>que = [2,3,10,5,8,9,7,3,5,2] >>>make_teams(que) 27 27 Is there an error in the following code algorithm for some case? How do I optimize and/or pythonize this? def make_teams(que): que.sort() if len(que)%2: que.insert(0,0) t1,t2 = [],[] while que: val = (que.pop(), que.pop()) if sum(t1)>sum(t2): t2.append(val[0]) t1.append(val[1]) else: t1.append(val[0]) t2.append(val[1]) print min(sum(t1),sum(t2)), max(sum(t1),sum(t2)), "\n" Question is