87 lines
3.0 KiB
Markdown
87 lines
3.0 KiB
Markdown
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given a string A, we want it to be B.
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A: hello world and thanks for the fish.
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B: hello cruel o_o world and thanks for the fish!
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however, the instructions to reconstruct B must be as small as possible, to minimize transmission costs. this is why we dont send B entirely.
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different algorithms as follow:
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## ALGORITHM 1
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- identify the first mismatching character (S).
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v-- 6(S)
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A: hello world and thanks for the fish.
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B: hello cruel o_o world and thanks for the fish!
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- identify the last mismatch character (E).
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v-- 0(E)
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A: hello world and thanks for the fish.
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B: hello cruel o_o world and thanks for the fish!
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- we construct the patch now with 3 numbers:
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- number of bytes to copy from beginning(A) till S(A)
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- number of bytes to copy from S(B) till E(B). plus the substring that is get copied.
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- number of bytes to copy from E(A) till end of string.
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6 40 "cruel o_o world and thanks for the fish!" 0
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- total patch size is 3 control bytes + 40 (string) = 43 bytes
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## ALGORITHM 2
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- We delta every character in both strings, from beginning to end, and from end to beginning.
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A: hello world and thanks for the fish.0000000000
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B: hello cruel o_o world and thanks for the fish!
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C: 000000XXXXX0XXX0XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX (-)
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A: 0000000000hello world and thanks for the fish.
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B: hello cruel o_o world and thanks for the fish!
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C: XXXXXXXXXXXXXX0000000000000000000000000000000X (-)
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- Pick the option with most zeros (2nd). Aka, select the option with less Xs.
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do { Encode every XXXX island in C as a positive operation indicating how many bytes to copy from.
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Run-length the number of zeros into a negative operation.
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} repeat till lane is exhausted.
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XXXXXXXXXXXXXXX: +14 "hello cruel o_"
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0000000000000000000000000000000: -29
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X: +1 "!"
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- Patch size is 3 control bytes + 14 (string) + 1 (string) = 18 bytes
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## ALGORITHM 3
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- start source (A) and target (B) strings. start with A:
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- select how many bytes to copy (positive), how many to skip (negative), or switch A<-->B lanes (zero).
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- repeat previous step over and over until both lanes do reach their respective string ends.
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A: hello world and thanks for the fish.
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B: hello cruel o_o world and thanks for the fish!
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A: +6 0 >> hello
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B: -6 +10 0 >> hello cruel o_o
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A: +24 -1 0 >> hello cruel o_o world and thanks for the fish
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B: -29 +1 >> hello cruel o_o world and thanks for the fish!
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(10 bytes)
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what if we always specify a dual +/- operation per lane?
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lanes changed automatically after every tuple. in this case a 0 shall indicate a no op.
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A: +6 0 >> hello
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B: -6 +10 >> hello cruel o_o
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A: +24 -1 >> hello cruel o_o world and thanks for the fish
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B: -29 +1 >> hello cruel o_o world and thanks for the fish!
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(8 bytes)
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- we construct the patch now. a substring excerpt must come after any positive operations on lane B.
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+6 0 -6 +10 "cruel o_o " +24 -1 -29 +1 "!"
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- total patch size is 8 control bytes + 10 (string) + 1 (string) = 19 bytes
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