When a and b are natural numbers we usually say that "b fits q times in a and subtract r". This sentence suggests an obvious but impractical method of finding q and r : count how many times we can reset b to a . For example, to divide a=95 by b=23 we count how many times we can reset 23 to 95 as shown in this table: q r r≥b 0 95 Yes 1 72 Yes 2 49 Yes 3 26 Yes 4 3 No   1. Implement this division algorithm in Python iteratively using a while loop. 2. Write an algorithm that returns the list of all divisor of a positive integer in ascending order.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.