Question

Given an array of Integers, use Bubble sort to sort the array by the number of digits in the Integer (from largest to smallest). If there are two Integers with the same number of digits, sort the Integers by value from smallest to largest. The array will be provided by user input with the first number being how many Integers there are in the array.

Answer 1

To sort an array by the number of digits in each integer and then by value using Bubble Sort, one must compare the length of the integers (number of digits) and only when these are equal should the actual values of the integers be compared.

Step-by-step explanation:

To sort an array using Bubble Sort by the number of digits and then by value, we should first understand the standard Bubble Sort algorithm, which repeatedly steps through the list to be sorted, compares adjacent elements, and swaps them if they are in the wrong order. Here, we need a modified version of the algorithm that first looks at the number of digits in the integers, and in the event of a tie, it considers their numerical value.

Steps to Sort by Number of Digits and then by Value

1. First, compare the number of digits in two adjacent integers.
2. If the first integer has fewer digits than the second, swap them.
3. If the number of digits is the same, then compare the integers' values and swap if the first integer is larger.
4. Repeat the above steps for each pair of adjacent integers until you go through the entire array without any swaps, indicating that the array is sorted.

It's important to note that in a Bubble Sort, the largest values 'bubble' to the end of the array on each pass, so for sorting by number of digits from largest to smallest we'll need to invert the standard comparison.

Here's an example with an array of Integers: [114950, 158000, 230500, 387000, 389950, 479000, 488800, 529000, 575000, 639000, 659000, 1095000, 5500000]. After sorting them using our modified Bubble Sort, we'll have the sorted array: [5500000, 1095000, 659000, 639000, 575000, 529000, 488800, 479000, 389950, 387000, 230500, 158000, 114950], which is ordered from the number with the most digits to the least, and for numbers with the same amount of digits, sorted from smallest to largest.