# Conditional Gathering of lists

Just need a little help with the GatherBy / SplitBy function(s).

I have a list of random numbers here:

{8, 4, 2, 1, 9, 4, 2, 1, 5, 2, 1, 3, 1, 2, 11, 4, 2, 1, 5, 2, 1, 3, \
1, 2, 7, 2, 1, 3, 1, 2, 5, 1, 2, 4, 15, 4, 2, 1, 5, 2, 1, 3, 1, 2, 7, \
2, 1, 3, 1, 2, 5, 1, 2, 4, 11, 2, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4,
8}


How can I write a function with a look-ahead? I want to gather the numbers so it splits whenever it the next number is larger than the current one? (spaced for clarity):

{{8, 4, 2, 1},
{9, 4, 2, 1},
{5, 2, 1},
{3, 1},
{2},
{11, 4, 2, 1},
...}


Tried and failed:

SplitBy[%, Greater]


You need Split:

Split[list, Greater]


SplitBy doesn't work here because the specified function is applied to each element separately before doing a normal Split. What you want is a pair-wise comparison with a custom comparator, which is what Split does.

Looking at this again you may want GreaterEqual to group identical elements in the same list:

Split[{2, 1, 1, 7, 5, 5, 5, 6, 0}, GreaterEqual]

{{2, 1, 1}, {7, 5, 5, 5}, {6, 0}}


For fun I tried to do this operation without Split. Since I was having fun I used Do rather than Module to localize symbols i and x.

split = Last @ Reap @ Do[If[n > x, i++]; Sow[x = n, i], {i, 1}, {x, 1}, {n, #}] &;

split @ {2, 1, 1, 7, 5, 5, 5, 6, 0}

{{2, 1, 1}, {7, 5, 5, 5}, {6, 0}}


Use Split[list,Greater] instead of SplitBy[list,Greater].

• It took me a while to answer this because my first attempts were all too short. Why do answers have to be at least 30 characters long? Commented Mar 23, 2012 at 21:04
• To prevent spam, I guess. Also, chances are that such answers will not be very informative. The model was first designed for StackOverflow, and many popular languages are more verbose than Mathematica. Commented Mar 23, 2012 at 21:20