AL101 QUIZ

a comparative tracking algorithm. It uses nested loops to pass through an array. During a single pass, it evaluates index A[j] and its immediate neighbor. If the value at A[j] is strictly greater than the value at A[j+1], a swap is executed using a temporary variable (temp) to prevent data loss. The outer loop decreases the boundary of evaluated elements because, after the first full pass, the absolute largest number is guaranteed to have shifted to the very end of the array.

Bubble Sort

virtually divides the target array into two distinct areas: a “sorted” sublist on the left and an “unsorted” sublist on the right. It begins at index 2 (the second element) and stores this value in a variable called index (or the key). It then looks backward through the sorted sublist to its left. While the items on the left are larger than the current index, the algorithm continually shifts those larger elements one space to the right to make a vacancy. Once it finds the correct relative position, it “inserts” the stored value into that slot.

Insertion Sort

operates on a “search and capture” mechanism. The algorithm loops through the array from left to right. For every position i, it assumes the current item is the minimum (min = i). It then scans the rest of the remaining unsorted items to the right to find if an even smaller value exists. If it finds a smaller element, it updates the minimum index tracking pointer (Min = j). After completing the internal scan for that pass, it performs exactly one swap to place that absolute minimum value into position A[i].

Selection Sort

is an advanced optimization of Insertion Sort designed by Donald Shell. Insertion Sort’s primary weakness is that it only shifts elements one position at a time. It solves this by establishing a structural spacing factor called an “increment” (k). It breaks the array into interleaved segments where elements are separated by k positions. It then runs a standard Insertion Sort on each isolated segment. As the algorithm loops, the increment k is systematically reduced (divided by 2) until k=1. Because elements were sorted over large gaps early on, the final k=1 pass requires very few shifts.

Shell Sort

a highly optimized, recursive algorithmic paradigm built on a “Divide-and-Conquer” architectural layout.

Quick Sort

entirely built upon the distributive property of real numbers. When you multiply a group inside parentheses by a term outside, you are scaling the entire value of that expression. This means every single isolated item within the boundaries of the parentheses must be multiplied by the external factor equitably. If there are signs involved (negatives or positives), they stick to the terms during the process.

Polynomial Multiplication

Single term multiplication: -5(2x 2 )  (-5)(2)(x 2 )  -10x 2

: 3(4a 2 b)(3)(4)(a 2 )(b)  12a 2 b

Distributing a Constant

A polynomial with only one single term.

Example: (4a 2 )(-5a 7 )  (4)(-5)(a 2+7 )  -20a 9

(12x 2 y)(12x 5 y 3 z) 

Multiplying Single Terms

Multiplication can be shown by juxtaposition (putting the term right next to the parenthesis).

Example: x(x 2 +12)  (x)(x 2 ) + (x)12  x 3 + 12x

3x 2 (x 2 -5)  (3x 2 )(x 2 ) - (3x 2 )(5)  3x 4 + 15x 2

Advanced Distribution