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.

How to Implement the Solution

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How to Run the Solution

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