Assignment 1: Problem Solving Example

Unit 1 > Assignment 1 > problem solving

Let's start with some visualization:

Consider these two lists:

A = [1, 3, 5, 7, 9, 11, 13]
B = [2, 4, 5, 9, 11, 13]

Now consider the first "triple" in A, the triple 1,3,5

A = [1, 3, 5, 7, 9, 11, 13]

How do we systematically try all such triples in A?

The next triple starts at position 1:
```
A = [1, 3, 5, 7, 9, 11, 13]
    
```
The one after that at position 2:
```
A = [1, 3, 5, 7, 9, 11, 13]
    
```
And the last one? At position 4:
```
A = [1, 3, 5, 7, 9, 11, 13]
    
```

So, we could have a for-loop that ranges over all the potential start positions, along the lines of:

    for i in range(0, ?)

What is the last position? We want to do this in terms of the length of the list, since any list is given to the function

Is this correct?

    last_pos = len(A) - 3
    for i in range(0, last_pos):

A1.1 Exercise: Write up the above in my_demo_problem1.py. Test it with different lengths. Explain in your assignment1.pdf.

Assuming you've sorted out the last position, remember that the default start position is 0:
```
    for i in range(last_pos):
    
```
Now let's visualize what happens in the second list with the very first triple of the first list:
```
A = [1, 3, 5, 7, 9, 11, 13]
B = [2, 4, 5, 9, 11, 13]
    
```
- We'll try this at the first position in the second list:
```
A = [1, 3, 5, 7, 9, 11, 13]
B = [2, 4, 5, 9, 11, 13]
     1, 3, 5
    
```
- Then at the second position in the second list:
```
A = [1, 3, 5, 7, 9, 11, 13]
B = [2, 4, 5, 9, 11, 13]
        1, 3, 5
    
```
- Then at the third position, and so on.

Since we're doing this for every triple in the first, we will have an inner loop for the second loop:

    last_pos = ...
    for i in range(last_pos):
        last_pos_second = ...
        for j in range(last_pos_second):
            # compare the triple at i with the triple in j

How do we compare the triple beginning at i in the first list against the triple beginning at j in the second list?

For example, consider i=2, j=1

A = [1, 3, 5, 7, 9, 11, 13]
B = [2, 4, 5, 9, 11, 13]

We know that 5 occurs at i, 7 occurs at i+1, 9 occurs at i+2.
What about 4, 5, 9, in the second list?
4 occurs at j, 5 occurs at j+1, 9 occurs at j+2.

Hence we want to compare

    last_pos = ...
    for i in range(last_pos):
        last_pos_second = ...
        for j in range(last_pos_second):
            # compare the triple at i with the triple in j
            # compare A[i] with B[j], A[i+1] and B[j+1], A[i+2] with B[j+2]

All three need to be equal for us to declare that we've found a triple:

    last_pos = ...
    for i in range(last_pos):
        last_pos_second = ...
        for j in range(last_pos_second):
            # compare the triple at i with the triple in j
            if (A[i] == B[j]) and ...
                print('Found ...')

A1.2 Exercise: Complete the other conditions in the if-statement in my_demo_problem2.py. And also complete the print statement.

Finally, we need to account for the case when no such triple is found.

A1.3 Exercise: When do we know for sure that no such triple exists? Complete the whole program in my_demo_problem3.py. Explain how you solved the latter issue (no such triple found) in assignment1.pdf.