Notes on SRM 604, D2, 250-Pointer (FoxAndWord)

James S. Plank

Sat Jan 18 09:54:26 EST 2014
Problem Statement.
This is a writeup for the first month of CS140.
There are two parts to this problem. First, you need to write a loop that allows you to compare every pair of words in words. For example, in Example 2, you will check: Go ahead and make that your first job -- write a nested loop which simply prints out each pair of words. Here's mine on examples 2, 3 and 4. Yours doesn't have to work in the same order, but it does need to generate the same pairs.

Example 2:
bababa ababab
aaabbb ababab
aaabbb bababa
Example 3:
ele eel
lee eel
lee ele
Example 4:
aab aaa
aba aaa
aba aab
abb aaa
abb aab
abb aba
baa aaa
baa aab
baa aba
baa abb
bab aaa
bab aab
bab aba
bab abb
bab baa
bba aaa
bba aab
bba aba
bba abb
bba baa
bba bab
bbb aaa
bbb aab
bbb aba
bbb abb
bbb baa
bbb bab
bbb bba

Now, given a pair of words, like "tokyo" and "kyoto", how do we determine that they are interesting? One simple way is to break up the first word into every combination of two substrings (which we'll call A and B below), concatenate the substrings in reverse order, and see if they equal the second word. For example:

A B B + A Does it equal "kyoto"?
t okyo okyot No
to kyo kyoto Yes
tok yo yotok No
toky o otoky No

To break up strings into substrings, see the substr() method. I provide examples in the string lecture notes.

Running Time

One of the skills of a computer scientist is being able to determine the running time of his or her program. In this instance, we ask the question -- if the size of words is W and the maximum size of a word is S, then how does the performance of our program scale with W and S.

In this instance, you are generating all pairs of words of words, and there are (W(W+1))/2 of these. For each pair of words, you are calculating S-1 values of A and B, and the work required to compute A+B is roughly S. Therefore, your program scales with W and S roughly as:


With topcoder, the maximum W is 50, and the maximum S is also 50, so the equation above gives you 6,250,000. That's going to be pushing topcoder's time limits, but it is fast enough. Later in the semester, when we study maps, you'll be able to see how to make this program faster.