Assignment 3

PDF version

due Monday 4 March in class

Read the pseudo-code below and answer the questions that follow.
```
    step 1. let Y be X + 5
    step 2. if Y > 0 then set X to Y * 2
    step 3. set X to X * 3
    step 4. output X
```
1. Does this algorithm contain a conditional statement? If so, which one?
2. Does this algorithm contain iteration? If so, which steps repeat?
3. Trace the algorithm with the input X = 4. What does it output?
4. Trace the algorithm with the input X = -3. What does it output?
5. Trace the algorithm with the input X = -7. What does it output?
In this problem, you will write down an algorithm to add two-digit numbers in base ten. As shown in the figure, your input variables are X₁, X₀, Y₁, and Y₀. Each variable holds a single-digit integer.

When your algorithm is finished, the answer should be in the variables Z₂, Z₁, and Z₀ – each holding a single digit. For example, if I want to add 56+94, the algorithm will start with
```
    X1 = 5    X0 = 6
    Y1 = 9    Y0 = 4
```
and in the end, the Z variables will have the result:
```
    Z2 = 1    Z1 = 5    Z0 = 0
```
Your algorithm should work for any single-digits provided in the input variables.

Here, C refers to a sequence of variables (an array), and the notation C[I] uses the value of I to determine which C to access.

    step 1. set K to C[1]
    step 2. set N to 1
    step 3. set I to 2
    step 4. if I > 7 then output N then K and stop
    step 5. if C[I] = K then set N to N+1 and go to step 9
    step 6. output N then K
    step 7. set K to C[I]
    step 8. set N to 1
    step 9. set I to I+1
    step 10. go back to step 4.

Below are the initial values of the array, and other variables you will use.

      K :
      N :
      I :
   C[1] : apple
   C[2] : apple
   C[3] : banana
   C[4] : carrot
   C[5] : carrot
   C[6] : carrot
   C[7] : date

What is the output of the algorithm?