Step by Step solution about How to resolve the algorithm Largest int from concatenated ints step by step in the Mathematica/Wolfram Language programming language

Wolfram Language Source Code Explanation

Purpose: The provided Wolfram Language source code defines a function, makeLargestInt, that takes a list of integers as input and returns the largest integer that can be formed by concatenating the digits of the input numbers in non-decreasing order.

Function Definition:

makeLargestInt[list_] := Module[{sortedlist},

• makeLargestInt is a function that takes a list of integers, list, as its input.
• Module creates a local scope for the variable sortedlist.

Sorting the Input List:

sortedlist = Sort[list, Order[ToString[#1] <> ToString[#2], ToString[#2] <> ToString[#1]] < 0 &];

• Sort sorts the input list, list, in descending order based on the custom ordering defined by the Order function.
• The Order function compares the concatenated string of two elements and returns True if the first string is greater than the second.

Example:

Order["134", "13"]
True

This means that "134" is greater than "13" when concatenated.

Concatenating and Converting to Integer:

Map[ToString, sortedlist] // StringJoin // FromDigits

• Map[ToString, sortedlist] converts each element of sortedlist to a string.
• StringJoin concatenates all the strings together to form a single string.
• FromDigits converts the concatenated string back to an integer.

Return Value: The function returns the largest integer formed by concatenating the digits of the input numbers in non-decreasing order.

Testing with Examples:

makeLargestInt[{1, 34, 3, 98, 9, 76, 45, 4}]
makeLargestInt[{54, 546, 548, 60}]

• For the first example, the function will return 9987645431 because concatenating the digits in descending order results in the largest integer.
• For the second example, the function will return 60548546 because concatenating the digits in descending order results in the largest integer.

makeLargestInt[list_] := Module[{sortedlist},
  sortedlist = Sort[list, Order[ToString[#1] <> ToString[#2], ToString[#2] <> ToString[#1]] < 0 &];
  Map[ToString, sortedlist] // StringJoin // FromDigits
  ]
(* testing with two examples *)
makeLargestInt[{1, 34, 3, 98, 9, 76, 45, 4}]
makeLargestInt[{54, 546, 548, 60}]