Efficiency/Evaluation Question

I'm working through some beginner-level "keyboard problems" I found at users.csc.calpoly.edu. One problem is the Saddle Points problem: quote: -------- Write a program to search for the "saddle points" in a 5 by 5 array of integers. A saddle point is a cell whose value is greater than or equal to any in its row, and less than or equal to any in its column. There may be more than one saddle point in the array. Print out the coordinates of any saddle points your program finds. Print out "No saddle points" if there are none. -------- Let's say I use a simple list grid like so: code: -------- array = Grid 5 [ [1,5,3,6,4] , [8,2,6,3,8] , [3,8,7,2,9] , [0,3,7,1,2] , [7,2,7,4,5] ] data Grid = Grid Int [[Int]] -------- And let's say I take a brute force approach, moving through each cell, checking to see if it is the greatest in its row and the least in its column. And say I have functions like so for getting rows and columns: code: -------- row (Grid s l) n = if (n >= s) then [] else l !! n col g@(Grid s l) n = if (n >= s) then [] else col_ g n 0 where col_ (Grid s l) n i = if (i >= s) then [] else (head l !! n) : col_ (Grid s (tail l)) n (i + 1) -------- My question: With the way Haskell works (thunks, lazy evaluation, and all that mystery), is it actually worth the trouble of /precalculating/ the maximum row values and minimum column values, to compare cell values against? Or will, for example, something like (smallest_list_value (col array 1)) definitely only evaluate once? -- frigidcode.com

I expect you'll get many replies...
row (Grid s l) n = if (n >= s) then [] else l !! n
col g@(Grid s l) n = if (n >= s) then [] else col_ g n 0 where col_ (Grid s l) n i = if (i >= s) then [] else (head l !! n) : col_ (Grid s (tail l)) n (i + 1)
While such low-level approach (focus on the element) can certainly be made to work, but Haskell encourages you to think in higher level constructs. I haven't seen this problem before but I would map the original array from [[Int]] -> [(Int, (Int, Int), Int, Int)], that is: a list of tuples consisting of the original element, its coordinate, the row maximum and the column minimum. From there its a trivial filter to find your results. (I'm sure there's a more elegant solution).
My question: With the way Haskell works (thunks, lazy evaluation, and all that mystery), is it actually worth the trouble of /precalculating/ the maximum row values and minimum column values, to compare cell values against? Or will, for example, something like (smallest_list_value (col array 1)) definitely only evaluate once?
There's not enough context to answer the specific question, but lazy evaluation isn't magic and the answer is probably "no". Tommy

On 06/15/2013 04:39 PM, Tommy Thorn wrote:
There's not enough context to answer the specific question, but lazy evaluation isn't magic and the answer is probably "no".
Tommy
Perhaps to simplify the question somewhat with a simpler example. Suppose you have code: -------- let f x = if (x > 4) then f 0 else (sin x + 2 * cos x) : f (x + 1) -------- After calculating at x={0,1,2,3}, and the cycle repeats, are sin, cos, etc. calculated anymore? -- frigidcode.com

On 06/15/2013 05:02 PM, Christopher Howard wrote:
On 06/15/2013 04:39 PM, Tommy Thorn wrote:
Perhaps to simplify the question somewhat with a simpler example. Suppose you have
code: -------- let f x = if (x > 4) then f 0 else (sin x + 2 * cos x) : f (x + 1) --------
After calculating at x={0,1,2,3}, and the cycle repeats, are sin, cos, etc. calculated anymore?
That might have been ambiguous. What I meant was: code: -------- let f x = if (x > 4) then f 0 else (sin x + 2 * cos x) : f (x + 1) -------- If I calculate (f 0), and the cycle repeats after four values, are sin, cos, etc. calculated anymore? -- frigidcode.com

Yes. In general, GHC won't CSE for you. - Clark On Saturday, June 15, 2013, Christopher Howard wrote:
On 06/15/2013 04:39 PM, Tommy Thorn wrote:
There's not enough context to answer the specific question, but lazy evaluation isn't magic and the answer is probably "no".
Tommy
Perhaps to simplify the question somewhat with a simpler example. Suppose you have
code: -------- let f x = if (x > 4) then f 0 else (sin x + 2 * cos x) : f (x + 1) --------
After calculating at x={0,1,2,3}, and the cycle repeats, are sin, cos, etc. calculated anymore?
-- frigidcode.com

There's a very good StackOverflow question which covers this: "When is
memoization automatic in GHC?"[1]. I found it really cleared up the issue
for me.
[1]:
http://stackoverflow.com/questions/3951012/when-is-memoization-automatic-in-...
On Sat, Jun 15, 2013 at 9:13 PM, Clark Gaebel
Yes. In general, GHC won't CSE for you.
- Clark
On Saturday, June 15, 2013, Christopher Howard wrote:
On 06/15/2013 04:39 PM, Tommy Thorn wrote:
There's not enough context to answer the specific question, but lazy evaluation isn't magic and the answer is probably "no".
Tommy
Perhaps to simplify the question somewhat with a simpler example. Suppose you have
code: -------- let f x = if (x > 4) then f 0 else (sin x + 2 * cos x) : f (x + 1) --------
After calculating at x={0,1,2,3}, and the cycle repeats, are sin, cos, etc. calculated anymore?
-- frigidcode.com
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participants (4)
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Christopher Howard
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Clark Gaebel
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Tikhon Jelvis
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Tommy Thorn