Decryption -- theory meets practice

let "swap i and j" stand for doing the following three things:
+ swap labels in positions i&j, and
+ swap columns i&j in the bigram table, and
+ swap rows i&j in the bigram table.

here is the decryption algorithm we told you to use to bring
$table$ close to training frequencies:

    repeat until there are no improvements
        + find the pair (i,j), 1<=i<j<=26, such that 
          swapping i&j brings table closest
        + swap i&j

it turns out that here is a better algorithm:

    repeat until there are no improvements
        + for each i, 1<=i<=26
            + find the j, 1<=j<=26, such that 
              swapping i&j brings table closest
            + swap i&j