login as: arlevin
[email protected]'s password:
Linux DeepwaterHorizon 2.6.32-25-generic #44-Ubuntu SMP Fri Sep 17 20:05:27 UTC 2010 x86_64 GNU/Linux
Oh, are we writing real code now? OK:

program reorg

implicit none

integer :: N,i,j
double precision :: tmp
double precision, dimension(:), allocatable :: A

print *,'How many elements are in your array?'
read *,N

allocate(A(1:N))

open(10,file='array',status='old')

read(10,*)A(:)

close(10)

do i=1,N
if(A(i)==0)then
do j=i+1,N
if(A(j)/=0)then
tmp=A(i)
A(i)=A(j)
A(j)=tmp
EXIT
endif
enddo
endif
enddo

open(10,file='array_new',status='replace')

write(10,*)A(:)

close(10)

end program reorg

Interesting thread.
Am I missing something, or do we not even know the intended language?

Ignore the garbage at top, copy+pasted too much...

@figle

We gave him the general approach and pseudo code. Now I guess we're all just doing it in our language of choice.

at least it hasn't broken into a language flamewar (yet) ;)

I was just offering Z a working example when I posted mine.

That's because everyone knows the best language is TI's Basic for the TI-83 Plus.

Like hell. It's 360/370 Assembly Language. ZAP anyone? :-)

@Abgemacht - the double loop example is inefficient and you should never abort for next loops early. Instead, use a while loop where the condition to stop the loop is the condition that you EXIT on. Also, your outerloop should only go to N-1.

@Draug

Agreed on all points.

Sorry, reason I asked was more due to the properties of different languages and what the most efficient methods would actually be.

Draug's method would be the best, I'd say.

A do/while/for/until loop all breaks down to a single type of loop in assembly. I don't think breaking out of an inner loop early is really that dangerous, or even that different in machine code (and if it is inefficient, you'll only notice it if the array has like 1million+ cells).

It's like people's aversion to 'gotos'. Gotos == jump in assembly, and a function call is a jump. I'm not saying I have gotos (it makes the code unreadable as hell), but it is a valid way to code and it doesn't make things inefficient or anything.

Fortknox is right, the breaking out isn't less efficient. It's more the readability and maintainability issues (i.e. standards) that I don't like about it. The efficiency comes in not restarting a second loop at i+1. Instead, maintaining a counter that you increment as needed is mroe efficient. Only by milliseconds on a small array, but a thousands or millions of elements array would start to show the slow down, especially if the number of zeros was about equal to the number of non-zeros in that particular example.

Just to get some timings, I made the array 1000 and had a random number generator generate the numbers such that 50% of the time there should be zero and the other 50%, some number. The array population ran so fast I had to reseed the generator with a seed from the previous random number to not wind up with just a few blocks of the same number.

Anyhow, here is the output with the times.

Start: 16:44:29.8141
Raw
array [ 0, 438305, 353579, 346409, 0, 0, 0, 0, 0, 478509, 0, 0, 0, 48539, 0, 925
52, 233922, 0, 91848, 446501, 151454, 129779, 0, 0, 0, 0, 0, 0, 221651, 0, 0, 16
750, 350256, 327090, 0, 0, 443703, 405425, 9249, 0, 493638, 0, 441239, 149451, 0
, 0, 0, 0, 0, 60628, 328192, 0, 327471, 0, 0, 0, 275310, 0, 57690, 442619, 96385
, 0, 79257, 0, 0, 0, 47346, 475169, 40362, 0, 152383, 462895, 0, 308474, 352613,
0, 161884, 25806, 433901, 0, 112774, 0, 0, 0, 54314, 0, 0, 152212, 128167, 4114
87, 0, 0, 0, 145208, 61266, 0, 0, 0, 0, 0, 0, 57132, 0, 0, 0, 435588, 0, 0, 0, 4
33742, 0, 0, 85454, 59042, 0, 309818, 492235, 0, 0, 91521, 0, 429749, 482591, 48
1043, 0, 227919, 381428, 368984, 308374, 110081, 0, 157108, 0, 168284, 0, 0, 0,
55742, 0, 13908, 0, 149284, 466847, 416897, 272453, 70370, 0, 351063, 0, 0, 0, 0
, 381642, 168001, 0, 7732, 118773, 0, 267409, 0, 158074, 0, 0, 40278, 0, 0, 1129
40, 441228, 402772, 14890, 0, 0, 361213, 0, 84526, 248351, 0, 0, 410710, 27034,
0, 0, 0, 342091, 0, 101417, 0, 289225, 187740, 0, 0, 0, 102360, 181404, 0, 0, 0,
0, 0, 0, 0, 211557, 458437, 0, 0, 437956, 27145, 0, 333604, 0, 0, 375514, 0, 22
2402, 160970, 0, 242371, 472069, 0, 0, 0, 236752, 0, 0, 426345, 146822, 255723,
0, 0, 132742, 0, 0, 0, 0, 0, 0, 0, 149740, 0, 0, 340420, 0, 312494, 0, 143459, 3
39392, 0, 269997, 0, 0, 0, 0, 174497, 376293, 0, 213762, 406255, 0, 0, 0, 177269
, 0, 0, 0, 0, 450136, 167471, 0, 0, 0, 176907, 421301, 33537, 304005, 0, 251678,
0, 136196, 0, 219177, 339331, 0, 0, 346873, 0, 0, 0, 279092, 452031, 163442, 0,
208387, 370191, 0, 201788, 0, 283821, 1342, 0, 0, 412594, 276326, 423612, 35843
8, 0, 0, 297600, 499746, 0, 0, 158563, 51337, 474598, 0, 201807, 0, 0, 279268, 3
98886, 0, 0, 0, 170482, 0, 372965, 83550, 361244, 0, 0, 413460, 0, 276523, 34139
9, 206082, 179842, 0, 0, 0, 0, 333208, 20334, 0, 0, 0, 0, 30929, 0, 259547, 0, 1
97861, 321334, 0, 240445, 280914, 310954, 0, 273362, 0, 452788, 0, 0, 0, 149644,
0, 498893, 58515, 443503, 0, 133261, 0, 0, 0, 66390, 0, 352902, 0, 197188, 0, 4
55543, 0, 192282, 0, 46527, 0, 64833, 126638, 0, 255965, 321790, 0, 0, 348881, 0
, 0, 171674, 0, 380390, 91508, 0, 0, 0, 0, 0, 0, 148670, 0, 0, 418078, 256749, 0
, 77331, 398215, 322733, 0, 0, 0, 91875, 0, 140871, 302679, 0, 0, 0, 137260, 0,
172733, 0, 7838, 495856, 452836, 0, 0, 499657, 191455, 0, 0, 253150, 0, 0, 40069
4, 415087, 0, 8170, 0, 292414, 202067, 0, 0, 60554, 0, 459923, 144021, 0, 0, 308
801, 185691, 405260, 0, 0, 0, 493762, 494228, 0, 0, 0, 0, 0, 0, 0, 443, 160658,
0, 290758, 65747, 0, 0, 141092, 0, 0, 0, 135533, 0, 0, 213602, 0, 208014, 0, 321
406, 356776, 0, 490599, 62960, 0, 0, 258392, 248027, 309646, 0, 117204, 62768, 3
18364, 138970, 172156, 378633, 190231, 216187, 287642, 188468, 180358, 311060, 3
44475, 186349, 161117, 325590, 184290, 487395, 212253, 66456, 22924, 0, 430522,
317359, 101529, 45968, 0, 359851, 0, 218873, 0, 0, 453706, 225843, 0, 187788, 0,
0, 246389, 0, 206450, 432358, 490235, 0, 0, 393846, 0, 39591, 66858, 37900, 0,
152775, 253619, 0, 0, 213422, 0, 428229, 396113, 184723, 0, 0, 0, 394573, 0, 0,
254297, 0, 0, 0, 0, 0, 347544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224986, 107982, 256520
, 267839, 0, 241998, 0, 445140, 130602, 0, 0, 493922, 82279, 358670, 13684, 0, 3
12223, 0, 220780, 0, 0, 481769, 47435, 0, 0, 315129, 93079, 0, 412471, 18013, 17
3428, 0, 0, 0, 0, 0, 53716, 324420, 0, 143278, 0, 143265, 0, 0, 0, 0, 123802, 24
991, 0, 212501, 0, 343483, 0, 299018, 298842, 351986, 122884, 438552, 392632, 0,
0, 0, 226979, 301633, 441038, 141963, 0, 363230, 273116, 438353, 429994, 476793
, 459071, 37654, 129024, 129982, 0, 131577, 0, 0, 25975, 0, 197722, 0, 468875, 0
, 0, 0, 0, 0, 0, 0, 448781, 281171, 0, 164745, 0, 246672, 423345, 0, 439014, 0,
0, 358035, 273609, 0, 0, 406506, 0, 0, 0, 79399, 0, 0, 41931, 0, 309663, 0, 0, 6
9162, 0, 0, 0, 481530, 187785, 363868, 0, 381095, 401354, 215795, 496919, 0, 416
375, 0, 0, 275689, 0, 0, 253606, 0, 122471, 0, 0, 128956, 0, 386847, 391762, 112
181, 0, 299378, 371955, 433983, 431371, 0, 0, 0, 487822, 287862, 122037, 0, 0, 0
, 55038, 0, 142347, 402442, 0, 0, 88871, 186341, 0, 0, 278589, 0, 0, 155266, 0,
0, 473078, 0, 0, 0, 0, 0, 87283, 0, 0, 0, 0, 196760, 131063, 355197, 0, 0, 0, 0,
147875, 369579, 151436, 0, 0, 0, 62407, 0, 326398, 303944, 0, 0, 37542, 0, 0, 2
33085, 230601, 0, 0, 0, 0, 0, 0, 71857, 0, 287092, 0, 143932, 446565, 0, 75020,
73314, 0, 160511, 0, 0, 95185, 0, 403190, 388671, 295535, 0, 203097, 0, 215406,
273472, 421765, 438882, 0, 164016, 0, 0, 53905, 62805, 0, 94795, 33902, 0, 0, 39
9225, 0, 0, 0, 0, 177781, 21026, 240900, 0, 400716, 0, 345941, 61860, 0, 0, 6247
0, 0, 226874, 446975, 0, 0, 0, 0, 0, 0, 363681, 0, 0, 468367, 0, 46348, 94706, 0
, 144118, 0, 0, 0, 211022, 0, 76096, 202952, 0, 0, 0, 19471, 0, 0, 208249, 27549
8, 0, 0, 0, 0, 413741, 498161, 0, 0, 0, 66895, 367636, 79051, 0, 286805, 0, 4063
94, 239378, 0, 329054, 0, 0, 126397, 0, 0, 0, 0, 0, 136504, 0, 97681, 0, 16091,
71974, 0, 166402, 343375, 0, 0, 399091, 0, 0, 480728, 202683, 456199, 0, 411033,
0, 412548, 244762, 0, 474803, 0, 195668, 0, 0, 374384, 405071, 70688, 0, 0, 296
616, 433237, 0, 225381, 465981, 0, 211306, 329683, 471101, 0, 0, 0, 16984, 0, 0,
322263, 75270, 0, 0, 0, 0, 0, 496285, 0, 69167, 317950, 0, 380665, 0, 131871, 4
74851, 0, 326051, 22360, 156269, 0, 0, 0, 0, 97474, 0, 0, 0, 479574, 323870, 0,
0, 195981, 161744, 0, 0, 0, 0, 170128, 0, 139419]

Drained
array [ 438305, 353579, 346409, 478509, 48539, 92552, 233922, 91848, 446501, 151
454, 129779, 221651, 16750, 350256, 327090, 443703, 405425, 9249, 493638, 441239
, 149451, 60628, 328192, 327471, 275310, 57690, 442619, 96385, 79257, 47346, 475
169, 40362, 152383, 462895, 308474, 352613, 161884, 25806, 433901, 112774, 54314
, 152212, 128167, 411487, 145208, 61266, 57132, 435588, 433742, 85454, 59042, 30
9818, 492235, 91521, 429749, 482591, 481043, 227919, 381428, 368984, 308374, 110
081, 157108, 168284, 55742, 13908, 149284, 466847, 416897, 272453, 70370, 351063
, 381642, 168001, 7732, 118773, 267409, 158074, 40278, 112940, 441228, 402772, 1
4890, 361213, 84526, 248351, 410710, 27034, 342091, 101417, 289225, 187740, 1023
60, 181404, 211557, 458437, 437956, 27145, 333604, 375514, 222402, 160970, 24237
1, 472069, 236752, 426345, 146822, 255723, 132742, 149740, 340420, 312494, 14345
9, 339392, 269997, 174497, 376293, 213762, 406255, 177269, 450136, 167471, 17690
7, 421301, 33537, 304005, 251678, 136196, 219177, 339331, 346873, 279092, 452031
, 163442, 208387, 370191, 201788, 283821, 1342, 412594, 276326, 423612, 358438,
297600, 499746, 158563, 51337, 474598, 201807, 279268, 398886, 170482, 372965, 8
3550, 361244, 413460, 276523, 341399, 206082, 179842, 333208, 20334, 30929, 2595
47, 197861, 321334, 240445, 280914, 310954, 273362, 452788, 149644, 498893, 5851
5, 443503, 133261, 66390, 352902, 197188, 455543, 192282, 46527, 64833, 126638,
255965, 321790, 348881, 171674, 380390, 91508, 148670, 418078, 256749, 77331, 39
8215, 322733, 91875, 140871, 302679, 137260, 172733, 7838, 495856, 452836, 49965
7, 191455, 253150, 400694, 415087, 8170, 292414, 202067, 60554, 459923, 144021,
308801, 185691, 405260, 493762, 494228, 443, 160658, 290758, 65747, 141092, 1355
33, 213602, 208014, 321406, 356776, 490599, 62960, 258392, 248027, 309646, 11720
4, 62768, 318364, 138970, 172156, 378633, 190231, 216187, 287642, 188468, 180358
, 311060, 344475, 186349, 161117, 325590, 184290, 487395, 212253, 66456, 22924,
430522, 317359, 101529, 45968, 359851, 218873, 453706, 225843, 187788, 246389, 2
06450, 432358, 490235, 393846, 39591, 66858, 37900, 152775, 253619, 213422, 4282
29, 396113, 184723, 394573, 254297, 347544, 224986, 107982, 256520, 267839, 2419
98, 445140, 130602, 493922, 82279, 358670, 13684, 312223, 220780, 481769, 47435,
315129, 93079, 412471, 18013, 173428, 53716, 324420, 143278, 143265, 123802, 24
991, 212501, 343483, 299018, 298842, 351986, 122884, 438552, 392632, 226979, 301
633, 441038, 141963, 363230, 273116, 438353, 429994, 476793, 459071, 37654, 1290
24, 129982, 131577, 25975, 197722, 468875, 448781, 281171, 164745, 246672, 42334
5, 439014, 358035, 273609, 406506, 79399, 41931, 309663, 69162, 481530, 187785,
363868, 381095, 401354, 215795, 496919, 416375, 275689, 253606, 122471, 128956,
386847, 391762, 112181, 299378, 371955, 433983, 431371, 487822, 287862, 122037,
55038, 142347, 402442, 88871, 186341, 278589, 155266, 473078, 87283, 196760, 131
063, 355197, 147875, 369579, 151436, 62407, 326398, 303944, 37542, 233085, 23060
1, 71857, 287092, 143932, 446565, 75020, 73314, 160511, 95185, 403190, 388671, 2
95535, 203097, 215406, 273472, 421765, 438882, 164016, 53905, 62805, 94795, 3390
2, 399225, 177781, 21026, 240900, 400716, 345941, 61860, 62470, 226874, 446975,
363681, 468367, 46348, 94706, 144118, 211022, 76096, 202952, 19471, 208249, 2754
98, 413741, 498161, 66895, 367636, 79051, 286805, 406394, 239378, 329054, 126397
, 136504, 97681, 16091, 71974, 166402, 343375, 399091, 480728, 202683, 456199, 4
11033, 412548, 244762, 474803, 195668, 374384, 405071, 70688, 296616, 433237, 22
5381, 465981, 211306, 329683, 471101, 16984, 322263, 75270, 496285, 69167, 31795
0, 380665, 131871, 474851, 326051, 22360, 156269, 97474, 479574, 323870, 195981,
161744, 170128, 139419, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

End: 16:44:30.1341

Here is the guts of "static void Main(string[] args)"

// initialize an array of integers
System.Random r = new Random(System.DateTime.Now.Millisecond);
int[] array;
array = new int[1000];
int ran = r.Next(1, 1000000);
for (int i = 0; i < array.GetLength(0); i++)
{
r = new Random(ran);
ran = r.Next(1, 1000000);
if (ran < 500000)
{
array[i] = ran;
}
else
{
array[i] = 0;
}
}

// output the initialized array
System.Console.WriteLine(String.Format("Start: {0:HH:mm:ss.ffff}", System.DateTime.Now));
System.Console.WriteLine("Raw");
WriteArray(array);
System.Console.WriteLine();

// drain the array
DrainArray(array);

// output the array after draining
System.Console.WriteLine("Drained");
WriteArray(array);
System.Console.WriteLine();
System.Console.WriteLine(String.Format("End: {0:HH:mm:ss.ffff}", System.DateTime.Now));

System.Console.ReadLine();

For a more accurate read of the time, I just display the start and end time from either side of the Drain method.

1 million elements:
Start: 16:55:07.5431
End: 16:55:07.6001

10 million elements:
Start: 16:57:04.6421
End: 16:57:05.0861

It takes longer to setup the array than to drain it. :-)

Here's the new main I used:

System.Console.SetBufferSize(80, 1000);
// initialize an array of integers
System.Random r = new Random(System.DateTime.Now.Millisecond);
int[] array;
array = new int[10000000];
int ran = r.Next(1, 1000000);
for (int i = 0; i < array.GetLength(0); i++)
{
r = new Random(ran);
ran = r.Next(1, 1000000);
if (ran < 500000)
{
array[i] = ran;
}
else
{
array[i] = 0;
}
}

// output the initialized array
//System.Console.WriteLine("Raw");
//WriteArray(array);
//System.Console.WriteLine();

System.Console.WriteLine(String.Format("Start: {0:HH:mm:ss.ffff}", System.DateTime.Now));
// drain the array
DrainArray(array);
System.Console.WriteLine(String.Format("End: {0:HH:mm:ss.ffff}", System.DateTime.Now));
System.Console.WriteLine();

// output the array after draining
//System.Console.WriteLine("Drained");
//WriteArray(array);
//System.Console.WriteLine();

System.Console.ReadLine();

@abgemacht : I do agree that Draug's method is more efficient. I don't even argue the point.
This was intended for a coding newbie, so I was making mine more readable. It's like a sorting algorithm... I'd go for a bucket sort to show a newbie instead of a quicksort (actually, I'd show them the strategy pattern and let them make multiple implementations... that, or I'd show them how to find the algorithm in some API or library somewhere).

This may be a whole different discussion, but efficiency should never be the purpose of code unless that is a direct requirement (like, this method will run during the prelaunch cycle of the spaceshuttle, so it needs to happen in 0.4s or less), or it is discovered to be a bottleneck in the program.

A foundation point of extreme programming is "make the code work, THEN make the parts efficient that need it." Point being, if you concentrate all your focus on making something you THINK needs to be efficient, you may be wasting your time, because it isn't the problem, but some other part is.

@fortknox

You and I are in complete agreement. I was merely responding to figle's question. You'll notice that my code wasn't as efficient either. There were two reasons for this 1) it was the first way I thought of doing it. 2) As you said, he's a newbie, so making him understand any way of doing it is more important that understanding the best way.

A decent part of my research is coding, but I spend very little time on optimization. The algorithms themselves are already more efficient, so, while code optimization is nice, it doesn't make that big of a difference overall.

Coming from the realm of web apps that run on a nationwide company, I automatically analyze for efficiency because we won't always have time to go back and rework it and the team gets dinged when the super users decide something is too slow. And, while this example would be easy to rework to be more efficient form either of the other two versions, not all patterns are so readily reworked.

Yes, but you have a specific reason to be effecient. I suppose i do too, but I'm not that great of a coder.

That and it's just the way I think...

haha yeah. My only point was that I was trying to answer figle's question, not bash fortKnox,

Don't worry, abgemacht.... my heart... will heal... *sniff*

;-)

I might try converting fortknox's pattern to C# this weekend and do a time comparison. It's unfair to compare times between Java and C# as Java will lose that one because of the less optimized run anywhere byte code it cruches down to, versus C#'s environment specific byte code.

Has anyone else noticed that having gotten his homework answer, Z has long ago abandoned the thread?

Yeah, but it's been a good programmers thread nonetheless.

Not only that, but I don't think he was even logged in long enough to get our answers.

interesting convrsation definitely, to think i missed it all...

i'm still wondering why you had a array of (presumably) mostly zeros... i recall, in college, setting up an array of pointers, and pointing them at hte nawer of a calculation when they had it returned to them (so i could check if they were null and recursively call the calculation...)

The point being i wanted to reduce the memory usage by not assigning memory to each array element unless it was needed. (oh and because the recursive call i was given to work with did the calculation whenever it was asked for it, even when it had already worked out the answer 100 times... but i didn't want to add a very large new array as that might be bad...)

lots of fun...