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6 Write an algorithm to input a list of numbers and test whether the numbers are in increasing order of magnitude, giving an appropriate message as output. The algorithm should be designed so that testing stops as soon as the answer is known. 7 Modify the algorithm in Example 1.3.1 so that it gives the correct output when n = 0 is input. 8 The following algorithm calculates a number known as the digital root' of a positive integer. 1. Input a positive integer n 2. d-number of digits in n 3. While d > 1 do 3.1. ne sum of the digits of n 3.2. d-number of digits in n 4. Output n (a) Trace the algorithm when 8678 is input. (b) List all the possible values that the output of the algorithm could take. 9 Consider the following sequence of steps: 1. Input a non-negative integer n 2.io 3. While n is even do 3.1. nen/2 3.2. ifi +1 4. Output i (a) What is the output when 12 is input? (b) What is the output when any odd number is input? (c) What happens when 0 is input? (d) Is this sequence of steps an algorithm