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1) Strings and string methods are not going to do it. They're too slow and take up too much memory.
2) The only digits you see in any of these numbers are 1, 2, and 3. It seems like a waste to use an entire byte to store each digit.
3) If you graph the math on the progression of the length of these numbers, you'll see that on a LOGARITHMIC SCALE, the graph is about a 40 degree line. What would that look like on a normal X/Y scale?
4) You cannot do this "in memory", without going to the extremes of cleverness, and even then, you'd still need a gargantuan amount of RAM.
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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Good hints...gonna have another crack at this back home.
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The length of row n won't exceed twice the length of row n-1 , yes?
The result is computable, therefore a Turing Machine can compute it, and, because Turing Machines have virtually unlimited storage, simply use one.
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You build the machine and I'll go make the infinite paper tape.
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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The spec isn't clear! Send it back! 
As this is, in essence, a compression algorithm, at line 8->9 (according to the OEIS) I would do:
1113213211
11 132132 11 <== three subsequences
21 2132 21 <== three outputs, eight digits
Which is shorter than their naive result of:
1113213211
111 3 2 1 3 2 11 <== seven subsequences
31 13 12 11 13 12 21 <== seven outputs, fourteen digits
A 40% saving.
The complexity of the algorithm increases due to seeking how to split the input into the fewest subsequences of some repetition length (1 in the naive implementation).
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When in the ![Elephant | [mastadon]](https://www.codeproject.com/script/Forums/Images/elephant.gif) is the spec Everclear[^] ?
Project Euler specs aren't clear either. We always have to do the best we can with what we've got. 
1113213211
11 132132 11 <== 13?
21 132132 21 <== three outputs, eight digits
What happened to the 13? The output looks like it should be 10 digits, not 8.
1113213211
111 32132 11
31 32132 21 <== if I understand what you're trying to do
There seems to a problem with representation. How do you tell the difference between single values and a run length value?
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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Dave Kreskowiak wrote: What happened to the 13?
There are 2 132s , hence 2132.
Dave Kreskowiak wrote: How do you tell the difference between single values and a run length value?
Doesn't matter, but internally (if I write it) it would be in the data structure. It just wouldn't be apparent in the output unless you want it.
(1,1)
(2,1)
...
(2,1),(2,132),(2,1)
...
The question is about only the number of digits.
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Ah, OK. I missed that.
Hmmm. In my implementation, I wrote up a reader/writer that takes care of the <classified work="" for="" now=""> "on the fly". This would make an interesting, and challenging, implementation to write. I'll have to look into trying this next weekend.
My current implementation writes all the data but there is an option to convert the data to a human-readable format. Not that you'd want to see thousands of pages of 1's, 2's, and 3's, but it did come in handy for analysis when experimenting with implementations.
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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340472211484 approx (via log extrapolation)
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Nope, not even close.
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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Test length 48 th : 526646 526,646
Test length 49 th : 686646 686,646
Test length 50 th : 894810 894,810
51st length : 1,166,642
52nd length : 1,521,070
53rd length : 1,983,164
54th length : 2,585,639
55th length : 3,371,142
56th length : 4,395,278
57th length : 5,730,540
58th length : 7,471,449
59th length : 9,741,236
60th length : 12,700,573
61st length : 16,558,941
62nd length : 21,589,461
63rd length : 28,148,228
64th length : 36,699,513
65th length : 47,848,635
66th length : 62,384,802
67th length : 81,336,981
68th length : 106,046,733
69th length : 138,263,181
70th length : 180,266,818
71st length : 235,030,941
72nd length : 306,432,122
73rd length : 399,524,610
74th length : 520,898,113
75th length : 679,144,257
76th length : 885,464,758
77th length : 1,154,464,356
78th length : 1,505,184,637
79th length : 1,962,451,918
80th length : 2,558,634,627
81st length : 3,335,934,550
82nd length : 4,349,374,155
83rd length : 5,670,691,453
84th length : 7,393,418,089
85th length : 9,639,500,137
86th length : 12,567,930,256
87th length : 16,386,002,249
88th length : 21,363,984,700
89th length : 27,854,252,387
90th length : 36,316,229,718
91st length : 47,348,911,849
92nd length : 61,733,265,560
93rd length : 80,487,511,283
94th length : 104,939,199,534
95th length : 136,819,183,789
96th length : 178,384,141,824
97th length : 232,576,318,416
98th length : 303,231,797,036
99th length : 395,352,043,407
100th length : 515,457,942,582
Regards , R
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Wrong again!
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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Dave Kreskowiak wrote:Wrong again!
100 : 511247092564
Exactly this time !
Regards, R
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Great!
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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What base?
The length is 10 -- in some base I haven't determined yet.
modified 2-Dec-17 1:10am.
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string Morris(int S, int N)
{
string projectPath = System.IO.Path.GetFullPath(@"..\..\..\");
using (BinaryWriter writer = new BinaryWriter(File.Open(projectPath + "input.txt", FileMode.Create)))
{
writer.Write(S > 2);
writer.Write(S == 2);
}
for (int i = 1; i < N; i++)
{
Debug.WriteLine(i+1);
using (BinaryReader reader = new BinaryReader(File.Open(projectPath + "input.txt", FileMode.Open)))
{
int count = 1;
bool currMSB = reader.ReadBoolean();
bool currLSB = reader.ReadBoolean();
bool nextMSB, nextLSB;
using (BinaryWriter writer = new BinaryWriter(File.Open(projectPath + "output.txt", FileMode.Create)))
{
while (reader.BaseStream.Position != reader.BaseStream.Length)
{
nextMSB = reader.ReadBoolean();
nextLSB = reader.ReadBoolean();
if ((currMSB == nextMSB) && (currLSB == nextLSB))
{
count++;
}
else
{
writer.Write(count > 2);
writer.Write(count == 2);
writer.Write(currMSB);
writer.Write(currLSB);
currMSB = nextMSB;
currLSB = nextLSB;
count = 1;
}
}
writer.Write(count > 2);
writer.Write(count == 2);
writer.Write(currMSB);
writer.Write(currLSB);
}
}
File.Delete(projectPath + "input.txt");
System.IO.File.Copy(projectPath + "output.txt", projectPath + "input.txt");
System.IO.File.WriteAllText(projectPath + "output.txt", string.Empty);
}
StringBuilder output = new StringBuilder();
using (BinaryReader reader = new BinaryReader(File.Open(projectPath + "input.txt", FileMode.Open)))
{
bool nextMSB, nextLSB;
while (reader.BaseStream.Position != reader.BaseStream.Length)
{
nextMSB = reader.ReadBoolean();
nextLSB = reader.ReadBoolean();
if (nextMSB)
output.Append("3");
else
{
if (nextLSB)
output.Append("2");
else
output.Append("1");
}
}
}
return output.ToString();
}
Seems to work quite well, but what did you do?
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Interesting but I question if this is actually writing one byte per value? Don't have time to test right now.
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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I suspect that it is using a byte for each boolean value. As per the usual answers:
Why is a boolean 4 bytes in .NET? - Stack Overflow[^]
I could store them in a BitVector32 or a BitArray and write that to the file, but I don't have the time to implement it now.
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I tried doing this in a BitArray, but found it to be limited in flexibility and performance. This was about 10 years that I originally worked on this problem.
I was doing some cleaning around the drive to get rid of old stuff and ran into the project. Then, of course, I just had to run it again and maybe update the code a little bit. 
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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string MorrisBitVector32(int S, int N)
{
int[] _masks = new int[32];
{
_masks[0] = BitVector32.CreateMask();
}
for (int i = 1; i < 32; i++)
{
_masks[i] = BitVector32.CreateMask(_masks[i - 1]);
}
string projectPath = System.IO.Path.GetFullPath(@"..\..\..\");
using (BinaryWriter writer = new BinaryWriter(File.Open(projectPath + "input.txt", FileMode.Create)))
{
BitVector32 v = new BitVector32();
v[_masks[0]] = S >= 2;
v[_masks[1]] = S != 2;
writer.Write(v.Data);
}
for (int i = 1; i < N; i++)
{
Debug.WriteLine(i + 1);
using (BinaryReader reader = new BinaryReader(File.Open(projectPath + "input.txt", FileMode.Open)))
{
bool currMSB, currLSB, firstRun;
firstRun = true;
currMSB = false;
currLSB = false;
int count = 0;
int k = 0;
BitVector32 outputBits = new BitVector32();
using (BinaryWriter writer = new BinaryWriter(File.Open(projectPath + "output.txt", FileMode.Create)))
{
while (reader.BaseStream.Position != reader.BaseStream.Length)
{
BitVector32 inputBits = new BitVector32(reader.ReadInt32());
if (firstRun)
{
count = 1;
currMSB = inputBits[_masks[0]];
currLSB = inputBits[_masks[1]];
}
bool nextMSB, nextLSB;
for (int j = (firstRun ? 2 : 0); j < 32; j += 2)
{
nextMSB = inputBits[_masks[j]];
nextLSB = inputBits[_masks[j + 1]];
if (!(nextLSB || nextMSB))
{
break;
}
if ((currMSB == nextMSB) && (currLSB == nextLSB))
{
count++;
}
else
{
if (k == 32)
{
writer.Write(outputBits.Data);
outputBits = new BitVector32();
k = 0;
outputBits[_masks[k]] = count >= 2;
k++;
outputBits[_masks[k]] = count != 2;
k++;
outputBits[_masks[k]] = currMSB;
k++;
outputBits[_masks[k]] = currLSB;
k++;
currMSB = nextMSB;
currLSB = nextLSB;
count = 1;
}
else
{
outputBits[_masks[k]] = count >= 2;
k++;
outputBits[_masks[k]] = count != 2;
k++;
outputBits[_masks[k]] = currMSB;
k++;
outputBits[_masks[k]] = currLSB;
k++;
currMSB = nextMSB;
currLSB = nextLSB;
count = 1;
}
}
if (firstRun)
firstRun = false;
}
}
if (k == 32)
{
writer.Write(outputBits.Data);
outputBits = new BitVector32();
k = 0;
outputBits[_masks[k]] = count >= 2;
k++;
outputBits[_masks[k]] = count != 2;
k++;
outputBits[_masks[k]] = currMSB;
k++;
outputBits[_masks[k]] = currLSB;
k++;
writer.Write(outputBits.Data);
}
else
{
outputBits[_masks[k]] = count >= 2;
k++;
outputBits[_masks[k]] = count != 2;
k++;
outputBits[_masks[k]] = currMSB;
k++;
outputBits[_masks[k]] = currLSB;
k++;
writer.Write(outputBits.Data);
}
}
}
File.Delete(projectPath + "input.txt");
System.IO.File.Copy(projectPath + "output.txt", projectPath + "input.txt");
System.IO.File.WriteAllText(projectPath + "output.txt", string.Empty);
}
StringBuilder output = new StringBuilder();
using (BinaryReader reader = new BinaryReader(File.Open(projectPath + "input.txt", FileMode.Open)))
{
bool nextMSB, nextLSB;
while (reader.BaseStream.Position != reader.BaseStream.Length)
{
BitVector32 InputData = new BitVector32(reader.ReadInt32());
for (int i = 0; i < 32; i+=2)
{
nextMSB = InputData[_masks[i]];
nextLSB= InputData[_masks[i+1]];
if (!(nextLSB || nextMSB))
break;
if (nextMSB && nextLSB)
output.Append("3");
else
{
if (nextMSB)
output.Append("2");
else
output.Append("1");
}
}
}
}
return output.ToString();
}
Files are now very small, and it is reasonably fast.
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My instant impression of it is that there has to be a better way than brute force: there's something very Fibonacci-sequence-like about the output... in my head, I can almost predict the pattern from one iteration to the next, without trying to describe anything... if only I had better coffee... if only Dijkstra were still alive... damn it: now you've got me interested.
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I know there has to be a better way to do it because I did find a list that gave the lengths for the first 3000 numbers in the sequence. Let's just say there are more digits in the 3000th number than there are atoms in the observable universe. I'll post the answer and the length of #3000 Monday morning.
It does make for any interesting problem!
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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level 1 size = 1
level 2 size = 2
level 3 size = 2
level 4 size = 4
level 5 size = 6
level 6 size = 6
level 7 size = 8
level 8 size = 10
level 9 size = 14
level 10 size = 20
level 11 size = 26
level 12 size = 34
level 13 size = 46
level 14 size = 62
level 15 size = 78
level 16 size = 102
level 17 size = 134
level 18 size = 176
level 19 size = 226
level 20 size = 302
level 21 size = 408
level 22 size = 528
level 23 size = 678
level 24 size = 904
level 25 size = 1182
level 26 size = 1540
level 27 size = 2012
level 28 size = 2606
level 29 size = 3410
level 30 size = 4462
level 31 size = 5808
level 32 size = 7586
level 33 size = 9898
level 34 size = 12884
level 35 size = 16774
level 36 size = 21890
level 37 size = 28528
level 38 size = 37158
level 39 size = 48410
level 40 size = 63138
level 41 size = 82350
level 42 size = 107312
level 43 size = 139984
level 44 size = 182376
level 45 size = 237746
level 46 size = 310036
level 47 size = 403966
level 48 size = 526646
level 49 size = 686646
level 50 size = 894810
level 51 size = 1166642
level 52 size = 1520986
level 53 size = 1982710
level 54 size = 2584304
level 55 size = 3369156
level 56 size = 4391702
level 57 size = 5724486
level 58 size = 7462860
level 59 size = 9727930
level 60 size = 12680852
level 61 size = 16530884
level 62 size = 21549544
level 63 size = 28091184
level 64 size = 36619162
level 65 size = 47736936
level 66 size = 62226614
level 67 size = 81117366
level 68 size = 105745224
level 69 size = 137842560
level 70 size = 179691598
level 71 size = 234241786
level 72 size = 305351794
level 73 size = 398049970
level 74 size = 518891358
level 75 size = 676414798
level 76 size = 881752750
level 77 size = 1149440192
level 78 size = 1498380104
level 79 size = 1953245418
level 80 size = 2546222700
level 81 size = 3319186080
level 82 size = 4326816254
level 83 size = 5640348764
level 84 size = 7352630884
level 85 size = 9584715106
level 86 size = 12494412020
level 87 size = 16287462624
level 88 size = 21231903676
level 89 size = 27677468012
level 90 size = 36079732206
level 91 size = 47032657188
level 92 size = 61310766500
level 93 size = 79923316046
level 94 size = 104186199146
level 95 size = 135814773100
level 96 size = 177045063068
level 97 size = 230791944956
level 98 size = 300854953626
level 99 size = 392187941864
level 100 size = 511247092564
finished computation at Fri Dec 1 16:48:41 2017
elapsed time: 7205.75secs
modified 3-Dec-17 18:14pm.
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Congratulations! You're the first to post the correct answer.
Extra credit: how did you do it in 2 hours?
System.ItDidntWorkException: Something didn't work as expected.
C# - How to debug code[ ^].
Seriously, go read these articles.
Dave Kreskowiak
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Since we only need to compute the length, storing the entire string isn't necessary. Furthermore, the computation can be done recursively and requires very little code/storage for each level of recursion. The memory footprint while running was about 16k IIRC.
I removed some extraneous code and got the runtime at l=100 to about 1.5 hours. Probably could optimize it even more, but I don't see the point.
I'd post code here but it seems to be discouraged.
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