Maximum Subarray in Mathematica

Welcome to the Maximum Subarray in Mathematica page! Here, you'll find the source code for this program as well as a description of how the program works.

Current Solution

(* Code *)

(* The actual maximum subarray operating on Mathematica lists, using essentially Kadane's algorithm: *)

maximumSubarray = a \[Function] Max[
    FoldList[
     Max[#2 (* A[i] *) , #2 + #1 (* A[i] + local-maximum *)] &,
     a]];

(* The outer function provides the 'user interface': *)

maximumSubarrayMain = l \[Function] Catch[
    Module[{e = "Usage: Please provide a list of integers in the format: \"1, 2, 3, 4, 5\"",
      fromNegativeDigits},
     (* oddly, Mathematica doesn't appear to provide a function which can parse strings representing negative integers *)
     fromNegativeDigits = Piecewise[{
         {FromDigits[#], StringMatchQ[#, DigitCharacter ..]},
         {-FromDigits[StringDrop[#, 1]], 
          StringMatchQ[#, "-" ~~ DigitCharacter ..]}},
        Throw[e]] &;
     maximumSubarray @ Map[
       (* convert string to integer, or throw *)
       fromNegativeDigits,
       (* construct arguments to maximum subarray *)
       StringSplit[If[StringLength[l] > 0, l, Throw[e]], ", "],
       {-1} (* at each leaf *)]]];


(* Valid Tests *)

Print /@ maximumSubarrayMain /@ {
    "1, 2, 3",
    "-1, -2, -3",
    "-2, -1, 3, 4, 5",
    "-1, -4, 2, 3, -3, -4, 9",
    "-1, -4, 2, 9, -3, -4, 9"
    };


(* Invalid Tests *)

maximumSubarrayMain[""]

Maximum Subarray in Mathematica was written by:

• Ben Hekster
• rzuckerm

If you see anything you'd like to change or update, please consider contributing.

Note: The solution shown above is the current solution in the Sample Programs repository as of Feb 06 2023 19:40:54. The solution was first committed on Jan 20 2023 09:27:27. As a result, documentation below may be outdated.

How to Implement the Solution

No 'How to Implement the Solution' section available. Please consider contributing.

How to Run the Solution

No 'How to Run the Solution' section available. Please consider contributing.