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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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