Maximum Subarray in Mathematica

Published on 20 January 2023 (Updated: 06 February 2023)

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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