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20 January, 2016 - 15:50

When you use indices to traverse the values in a sequence, it is tricky to get the beginning and end of the traversal right. Here is a function that is supposed to compare two words and return True if one of the words is the reverse of the other, but it contains two errors:

def is_reverse(word1, word2):
    if len(word1) != len(word2):
        return False
    i = 0
    j = len(word2)
    while j > 0:
        if word1[i] != word2[j]:
            return False
        i = i+1
        j = j-1
    return True

The first if statement checks whether the words are the same length. If not, we can return False immediately and then, for the rest of the function, we can assume that the words are the same length. This is an example of the guardian pattern in Checking types.

i and j are indices: i traverses word1 forward while j traverses word2 backward. If we find two letters that don’t match, we can return False immediately. If we get through the whole loop and all the letters match, we return True.

If we test this function with the words “pots” and “stop”, we expect the return value True, but we get an IndexError:

>>> is_reverse('pots', 'stop')
Figure 8.2 State diagram. 
File "", line 15, in is_reverse
    if word1[i] != word2[j]:
IndexError: string index out of range

For debugging this kind of error, my first move is to print the values of the indices imme diately before the line where the error appears.

while j > 0:
    print i, j      # print here
    if word1[i] != word2[j]:
        return False
    i = i+1
    j = j-1

Now when I run the program again, I get more information:

>>> is_reverse('pots', 'stop')0 4...IndexError: string index out of range

The first time through the loop, the value of j is 4, which is out of range for the string 'pots'. The index of the last character is 3, so the initial value for j should be len(word2)-1.

If I fix that error and run the program again, I get:

>>> is_reverse('pots', 'stop')0 31 22 1True

This time we get the right answer, but it looks like the loop only ran three times, which is suspicious. To get a better idea of what is happening, it is useful to draw a state diagram. During the first iteration, the frame for is_reverse is shows in Figure 8.2.

I took a little license by arranging the variables in the frame and adding dotted lines to show that the values of i and j indicate characters in word1 and word2.

Exercise 8.9.Starting with this diagram, execute the program on paper, changing the values of i and j during each iteration. Find and x the second error in this function.