5
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Last time you were required to write program that output a file, such that no byte is same as original file. The request meant to let everyone carry part of information, but it ends up that everyone carry same info to reduce their storage... This challenge is similar.

Write at most 1024 programs that output at least 8524 bytes each. Say the \$j\$th byte of program \$i\$'s output is \$a_{i,j}\$, and \$x_j\$ is the \$j\$th byte of the file given below, then it's a requirement that:

$$ \left\{a_{i,j}\middle|1\le i\le 1024\right\}=\left\{0,1,2,...,255\right\}-\left\{x_j\right\} $$

i.e., for each index \$ j \$, the \$ j \$th byte of the output of each program collectively includes every byte value 0 to 255, except the \$ j \$th byte of the file given below.

Your score is the longest of your programs. Lowest score in each language wins.

xxd of the file:

00000000: fd37 7a58 5a00 0004 e6d6 b446 0200 2101  .7zXZ......F..!.
00000010: 1600 0000 742f e5a3 e06b 6f21 0a5d 0026  ....t/...ko!.].&
00000020: 9509 6f34 76f2 ffad 4150 0e26 f227 9480  ..o4v...AP.&.'..
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00000040: a0c3 cc6a 167c ca6b 36e7 ba6a ac7b fdc3  ...j.|.k6..j.{..
00000050: 4388 c9ed 6ae5 4f42 3b2f be2c cd16 5588  C...j.OB;/.,..U.
00000060: 1f3a ba35 dfde 7adf 7f73 db53 9474 93dc  .:.5..z..s.S.t..
00000070: b9f3 0cd6 4143 0731 f96e 6b93 4b13 4dcd  ....AC.1.nk.K.M.
00000080: 07bd 4b4c b31c 82a2 3276 3cfb b11f b04f  ..KL....2v<....O
00000090: a764 5640 6c43 e7e2 bb2b 8024 9a9e 9e1b  .dV@lC...+.$....
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000000c0: c3f9 4452 9fd7 96a7 1160 eae6 33e6 6b0c  ..DR.....`..3.k.
000000d0: de0e 39bc f867 fc8e bee8 7dd1 8d84 59b9  ..9..g....}...Y.
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\$\endgroup\$
4
  • 1
    \$\begingroup\$ I fail to see what is unclear about this question. It would be ideal if a comment could be left so that the OP, or even other potential close voters could understand what clarity issues there might be. \$\endgroup\$
    – Wheat Wizard
    Dec 30, 2022 at 22:44
  • \$\begingroup\$ To make it easy for us (both to implement and check), could you also post a comma- or space- separated list of the byte values in decimal? Thanks. \$\endgroup\$ Dec 31, 2022 at 9:17
  • 1
    \$\begingroup\$ @DominicvanEssen gist.github.com/pxeger/f53f939f530f536648acba5c2daf5ce1 \$\endgroup\$
    – pxeger
    Dec 31, 2022 at 9:45
  • 1
    \$\begingroup\$ This is a great challenge which is currently underrated, IMO. I think it would have been even better with a smaller data set, though. (I had to truncate the list of programs in my answer so that it fits in the maximum size allowed for a post.) \$\endgroup\$
    – Arnauld
    Jan 4, 2023 at 15:46

2 Answers 2

3
\$\begingroup\$

Gzip, 140 bytes

The following 256 programs were written by for i in $(seq 0 255); do self=$(printf \\%o $i); comp=$(printf \\%o $[i^1]); temp=$(printf \\%o $[i^2]); cat file.midi.xz|tr -c $self $temp|tr $self $comp|tr $temp $self|gzip --best>file.midi.xz.$i.gz;done and the zeroes' first is the longest:

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231 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3W0QkAMQgE0f4bddu4j1QQCIfKmwIC646SqkNqPOkRIq3ey5yg6LhTAC10KxQGFZP1ymSl5RYVBMW86kI7K4vWZWWFKuE63bWOB3owx1/jv4nkZkDZ2Ww4BAdrIR8FrCDNTCEAAA==
232 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3UARHAIAwDQP9GUxuIoAej+xewG0mgqkmqUevHjsn1Q7yZ27fOGG3YmUwxPhi/t7gefyg+L0wzE3qN1Xkx9sPIvZ+IdpiZurLBawF2h9GhXQGxbwHAf0fyTCEAAA==
233 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+2VQQEAMQjD/DslLk7B/tc2MbBBA9yVwu3AWsETdhloUzdM014kdhwNkokQiHyEsMTQirBfMb8ZXJEijnL9aPOn0giUQrzb+iKdmWuvPI2gWyacDheYyJsPeP5C6EwhAAA=
234 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3UyQ0AIAgEwP47XbqwAxM/CmamAq6lCkaKEfSapYUgDQD+oR4ZeAj5+sgiFwP3l5sFZvSBc7qLmIGyX7YaF6Zaawda5i7Sj6BobWcB4u4kF0whAAA=
235 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3YwQ0AIQhE0f5blSaswGAMF+H9q174M5jNrtWFeDgZBQ2ABQax106ooSGdPs5X9Uf/IG5moBiqXT10cKosti0f0ybAw1hqhMNPQxQcbW3CionJ9Brav/YWH0Ibl+zn6kwhAAA=
236 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3WCREAMAgDQf9Wg4nKKM+eAgKXTqtOk7pOzAQX7pEn7gePw2ZxNQcrakhk+JdcWU9G7D8MU7P5iThGnSmBuArFAxOksboO0egDxfww8gMtUWu8TCEAAA==
237 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VAQ0AIAhFwf5d+R3swNQxdpdA30CrgIZIADYIw2orJNhRVvvrZTN8DWItPXUA+Hzc13mXVIrK4CkaXUJdno1EdPziAFZs+thMIQAA
238 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VCRHAMAwDQf5cZQ4l0U6VeA9AYusZz7xOBothP2S94/Gc2tT02iLozf9kubyi/7MiIdD5c2uRWH40W3TZ2tQBVMDedICghLL0utxSnvXYkjtSlfLIY9VpfwCfZDjDTCEAAA==
239 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3XSREAMAgEQf9mWQvxkE8C9CiAPaii6oIUbqEdxL7lYKrr9o3XODvMjDR/tE46rRLOOfy0xo9O5eUIaR7VPBspqq/lgMyBw5Bsfdh2HGKSSd8gKLtq/wP44tP2TCEAAA==
240 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3YgQ0AIAgDwf2XrSu4hAbB+wVobQOJa2EYYdurd1UcQiAw3gUhfa3oYCgSGeLRIgFcmOrZEcWhofmz+KnX45YC/Taqb2TASgHeKlZKHaW/ndsTNzf29XBMIQAA
241 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VURUAIAgDwP5tWQNK+CFwV8DHhloFPJFzB2OFGRBdRLtjori23gkJGU+yS/vVkZDg422Pq2ofTqemAQD8CkZH5w1U9GNdTCEAAA==
242 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3UwQ0AIAgEwf67PTqwAn1pAnH2TyTrcVU4knsjYRMAOtT0g0bW8CRRwSZPbAIANCTrP5lIh90ihZJIw/Z9XwFXpuUgv113dkijWIM87oNMIQAA
243 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VsRXAMAxCwf3XNQukdpfGEc+537hFCOG1XpDt6aBKTJcFuc0puwb+W2jARK5yJJhSrjuYc+90kgigpzFSrk/h+mNtHhDwIa8Y/Yk5bJYOio+pjBMFhs7vAdiZ7bdMIQAA
244 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3WyQ0AMQhD0f7bdRqYAnKLJht5/44EtkG0NkgW193Pu5OzYW6HkgW4Unv7coW8D+g9i4hN6sZKYOsjnRdEEQygQMBC9luliXUA6oYvZae2+1TjgUnAh3+VO03ND9CiyhZMIQAA
245 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3V0Q3AIAwD0f33jf87AVJbJBDh3QAQmXOoOocU8MKF7PaJqUIRjof5emSIgWb7I82HUFD/4v9Z2QNNAw1ujC2U4ZwekAULlWCQVgp69r7c5hfFtQrSHPIA1fSuZ0whAAA=
246 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3WMRLAIAgF0fvf99unSpUqUZk4vK2dQWFBxsBNth7/5Rta3GT79SNl3bRRKnDUY6QEKDY030LpF5PsGTfHqpEWNfIx4l3Js1oSPuHIsZW5ULxH/S5mHYDpD1B9oiuiESlWWs8LDS6pIUwhAAA=
247 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3XwREAIAgDwf4bNl+bENBxrwGVHDCuhT7iKtKSAswk1OeZAYHohCtHDjF/dkL6qJWAYXYO1FvlwQdA5zx2fNQcPuiDT8vB03SS5YJGNk5rQCZMIQAA
248 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3V0Q0AIAgD0f0XLr/uYDQRfLcA4Wi1CsAZQsEk4aELwIwCa/+GKtJU696YDNlKMtgBZAZyKPVArw6krUjPCnxThFDx0vJxxd9YXyvaSUwhAAA=
249 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VuQ0AIAwEsP035joWoEIKT2TXIFByhDH6ifuh89AhhPHeAD7/LLK1J6pPQbVScESE48lYRE++eLjqdzeZWS/XFgkBMB3fn5xGuZyqAZw0AR99RdJMIQAA
250 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3UwQ0AIAgEwf47Pn4+LUATIc4WQLw9pOoNaTcIlMJifeQrHV+XMatknUfaUBt8P9AODd/PGLokOZ7usJKjFqVzpRcw30lWNAB3Qh7CJd0sfiGLVkwhAAA=
251 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VsQ0AIAwDwf1Xxg0T0CEB5r6mSPJOGAMr8nj5oXCH1JwrMNeFUabqhh5x6U0BAQDgWgL3L4QdBPDpHXX+8P7vmV8bx35jMYnlkzQKV1alxDAhz8UTnQ/nH5NMIQAA
252 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3TtxHAMBADwf5bxifKFDMQZ0Bxr4A3MDM1pGlVppfm284/d5cKZPiFjSQgD9DbjGydFM5BfeWQ7fd9m25Vs7hEky4NPuMJgpK8ReEcg9eGiLOkH/d+GLX0QqQWaMt2PhzxAApy8LpMIQAA
253 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3WywkAIAxEwf57zoJFiBjNvHsO+4NU/UhqBCEGzYzM7kkmF8QIuIMmQUf18Ej3wxsCAT2VDZoZJ5Kuhv31beWROzOy0atJR8kMc1LgIQ4AjrEAUh212EwhAAA=
254 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3WgQ0AIAgDwf13rok7GE0E7ieAp6BZN8lqQqpUkMFDQovdksc7G8qjN4cibZEx21ckRCAAOdUVAEfBCL4fYYQXU82Hpz7tuxhV7JiUf0fVEOSs8DzzsQG1CPYFTCEAAA==
255 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+3VsREAIAxC0f2XFkfQIqeeeb+2CATiGACAXVL6jHnAvexF2VDuNed14cg8giZXZALr+KaZXmO9KSdCRo7vFtIDS/zNQIuD8vU7mxOKPT6QTCEAAA==
256 (base64 -d|gzip -d)<<<H4sIAAAAAAACA+2VsRHAMAjE9l9aZIWkiO8fS6Ubg3jsmTcwiVByUaa9FfD9QMyxmmVnKDDdQTXTIweTYM8i0rniKFuU3tE+SjikAhN+18vB5nkT4d31uOlnddrFVh2e/J8P1CcHlWZqfwBAoQFhTCEAAA==
\$\endgroup\$
1
\$\begingroup\$

JavaScript (Node.js),  126 120 bytes

Method

Each value is encoded with 3 to 5 Bloom filters, for a total of 1023 programs with a maximum size of 120 bytes.

Each filter is using a single hash function.

The least frequent value \$171\$ is used for padding and therefore not explicitly encoded by a specific set of filters.

Generator

The logic of the generator I used is as follows:

  • for each value \$v\neq 171\$, create a random hash function of the form: $$h:x\mapsto (p\times x)\bmod m$$ or: $$h:x\mapsto ((p\times x)\bmod m)\bmod m'$$

  • build the corresponding Bloom filter taking an index \$i\$ and returning:

$$B_h(i)=\cases{171&\text{if positive}\\v&\text{if negative}}$$

  • if the length of the filter code is greater than an arbitrary threshold, reject the filter

  • if any false positive would put \$171\$ at a position where this value actually appears in the file, reject the filter

  • otherwise add it to a pool \$P_v\$ of valid filters

  • find the shortest subset of \$P_v\$ that successfully puts \$v\$ at all locations where \$v\$ does not appear in the file

  • keep trying until all values are processed with 1024 filters or less

Code and test link

Only the first few programs are listed below. Please refer to the TIO link for the full list.

for(i=8524n;i--;)console.log(0x4140C81000910300021904291208610E5180A1101E4C5584A0n>>i*38n%201n&1n?171:0)
for(i=8524n;i--;)console.log(0x640411351C44008082600030200102404302102041000B8307004014002n>>i*673n%789n%237n&1n?171:0)
for(i=8524n;i--;)console.log(0x821080220001000C1180B8010148300A0A0805980183110340B000C03802n>>i*12n%947n%240n&1n?171:0)
for(i=8524n;i--;)console.log(0x400408900A828400286988E00CA42800304084E44201081E2006A0130n>>i*491n%913n%241n&1n?171:0)
for(i=8524n;i--;)console.log(0x488001268000001240C0D6C004A1880500402004002212602588035128n>>i*88n%523n%232n&1n?171:0)
for(i=8524n;i--;)console.log(0x8C802500010201010200010222000102432001100n>>i*355n%398n%223n&1n?171:1)
for(i=8524n;i--;)console.log(0x852104001000455700120000000001008000040800A00042n>>i*197n%198n&1n?171:1)
for(i=8524n;i--;)console.log(0x82800220010000011500000880090682440430121n>>i*738n%827n%183n&1n?171:1)
for(i=8524n;i--;)console.log(0x48020002940A00240008848200080001212An>>i*186n%977n%149n&1n?171:1)
for(i=8524n;i--;)console.log(0x1000025004004000A058400200020212020740041200002C041n>>i*75n%208n&1n?171:2)
for(i=8524n;i--;)console.log(0x8073028020124020000C001010804034080020802004504n>>i*618n%653n%199n&1n?171:2)
for(i=8524n;i--;)console.log(0x504000250040402049200284000010048682802220020020A100800n>>i*50n%219n&1n?171:2)
for(i=8524n;i--;)console.log(0x1443120E00040A1005280801210401850204000n>>i*221n%710n%156n&1n?171:2)
for(i=8524n;i--;)console.log(0x5000800088020800A0040482810002491024000082102004200912404040n>>i*39n%565n%240n&1n?171:3)
for(i=8524n;i--;)console.log(0x68004001C8004000040941002080600008002444415200000A1811090000n>>i*189n%524n%241n&1n?171:3)
for(i=8524n;i--;)console.log(0x40D010000080010AC444C20200F502220004104A00024E00n>>i*127n%202n&1n?171:3)
for(i=8524n;i--;)console.log(0x8200040000982000064248028020012040020D1010100840011C202009n>>i*367n%463n%235n&1n?171:3)
for(i=8524n;i--;)console.log(0x19810003008108405D02024001500808030002n>>i*23n%656n%150n&1n?171:4)
for(i=8524n;i--;)console.log(0x404200082183400268A8220418882000100808021n>>i*613n%877n%167n&1n?171:4)
for(i=8524n;i--;)console.log(0x128010088800280004008104001100024B8000C500000000100610002n>>i*204n%233n&1n?171:4)
for(i=8524n;i--;)console.log(0x20B001100002405020002002040040219100008402005B4050n>>i*88n%205n&1n?171:4)
for(i=8524n;i--;)console.log(0x403C41900880200421800802001C811000800190000D000000004215080004040n>>i*213n%260n&1n?171:5)
for(i=8524n;i--;)console.log(0x140048090080040472000444910008600060400002014108006000000144n>>i*858n%961n%253n&1n?171:5)
for(i=8524n;i--;)console.log(0x800000408000C8000000810008C721000A010510000000060854010C380n>>i*629n%852n%236n&1n?171:5)
for(i=8524n;i--;)console.log(0x200008A212000428600000005A8C08120103002B4040112100016040000n>>i*191n%235n&1n?171:5)
for(i=8524n;i--;)console.log(0x300A0180113004082218120104400A0087084080002450n>>i*494n%999n%199n&1n?171:6)
for(i=8524n;i--;)console.log(0xA02060040A0C0040001100831040C34000C89000840040002240284n>>i*191n%220n&1n?171:6)
for(i=8524n;i--;)console.log(0x16200020A00090902002002020006B0D40014001020C08088014000n>>i*397n%750n%217n&1n?171:6)
for(i=8524n;i--;)console.log(0x18A00802008004493000800CB00000440008910402400010025241030880n>>i*11n%238n&1n?171:6)
for(i=8524n;i--;)console.log(0x20210002000100C0683100000310284282043C0A806n>>i*430n%641n%177n&1n?171:7)
for(i=8524n;i--;)console.log(0x141000000400408EA5020800C0842210804200810A2040022000n>>i*189n%206n&1n?171:7)
for(i=8524n;i--;)console.log(0x68100000920120000008208002002000202088104030606040Cn>>i*109n%978n%212n&1n?171:7)
for(i=8524n;i--;)console.log(0xD002204020008428000800088120908008020E4000048049n>>i*307n%392n%198n&1n?171:7)
for(i=8524n;i--;)console.log(0x400208040088000000242100611008400C30084004014A20n>>i*206n%249n&1n?171:8)
for(i=8524n;i--;)console.log(0x40060000000A8C0200840800328400403800204n>>i*109n%395n%162n&1n?171:8)
for(i=8524n;i--;)console.log(0x3028000400400A820009000100001412200006691n>>i*580n%784n%165n&1n?171:8)
for(i=8524n;i--;)console.log(0x2000628088810108800410004001B440034D000n>>i*67n%156n&1n?171:8)
for(i=8524n;i--;)console.log(0x140009600860240200C0100005000420100084804C200000000830200n>>i*60n%233n&1n?171:9)
for(i=8524n;i--;)console.log(0x112062801184002004885608000024800048040210400Cn>>i*135n%196n&1n?171:9)
for(i=8524n;i--;)console.log(0x10261003012200840800240AC080000060100200C401840000040040n>>i*205n%228n&1n?171:9)
for(i=8524n;i--;)console.log(0x420040202414000440001800000081041084200240025100001004010200000n>>i*235n%253n&1n?171:9)

Try it online!

\$\endgroup\$

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