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It should be noted that many algorithm's O time can be reduced. For instance, many O(n^2) algorithms can be reduced to O(n log(n)) by finding a way to cut the inner loop short. A famous example is bubblesort:

```# O(n^2)
for my \$i (0..\$#a-1) {
for (0..\$#a-1-\$i) {
(\$a[\$_],\$a[\$_+1]) = (\$a[\$_+1],\$a[\$_])
if (\$a[\$_+1] < \$a[\$_]);
}
}

# O(n log(n))
for my \$i (0..\$#a-1) {

# looping over already-sorted items is not needed
for (0..\$#a-1-\$i) {
(\$a[\$_],\$a[\$_+1]) = (\$a[\$_+1],\$a[\$_])
if (\$a[\$_+1] < \$a[\$_]);
}
}

O(n) algorithms that involve a search via a loop can sometimes be reduced from O(n) to O(log(n)) by breaking out of the loop once a "result" is found:

```# O(n)
my \$truestatus;
foreach my \$item (@list) {
\$truestatus = 1 if (some_condition);
}

# O(log(n))
my \$truestatus;
foreach my \$item (@list) {

# if some_condition is going to be valid for at least one \$item in
# @list, then the limit of the average runtime will approach
# O(log n).
if (some_condition) {
\$truestatus = 1;
last
}
}

Of course, the secret is to know where to apply these optimizations, which is often harder than it seems :)

In reply to Re: An informal introduction to O(N) notation by jryan
in thread An informal introduction to O(N) notation by dws

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 [Corion]: Mhmm. I'm writing a database export, and two supposedly identical files compress to different sizes... So either the order of rows is different (which would be OK) or something else is bad (which wouldn't be OK). I guess I have to test with smaller tables

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