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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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