v4k-git-backup/tools/labs/fwk_diff.md

given a string A, we want it to be B.

A: hello world and thanks for the fish.
B: hello cruel o_o world and thanks for the fish!

however, the instructions to reconstruct B must be as small as possible, to minimize transmission costs.
this is why we dont transmit B entirely.

different algorithms as follow:

## ALGORITHM 1

- identify the first mismatching character (S).

         v-- S@6
A: hello world and thanks for the fish.
B: hello cruel o_o world and thanks for the fish!

- identify the last mismatch character (E).

                                                v-- E@-0
A:           hello world and thanks for the fish.
B: hello cruel o_o world and thanks for the fish!

- we construct the patch now with 3 numbers:
  - number of bytes to copy from A[0] till A[S] (not included)
  - number of bytes to copy from B[S] till B[E] (not included) + plus the substring that is get copied.
  - number of bytes to copy from A[E] till end of A string.

6 40 "cruel o_o world and thanks for the fish!" 0

- total patch size is 3 control bytes [6,40,0] + 40 (string) = 43 bytes

## ALGORITHM 2

- We delta every character in both strings, from head to tail, and from tail to head.

A: hello world and thanks for the fish.0000000000
B: hello cruel l_o world and thanks for the fish!
C: 000000XXXXX0XXX0XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX (-)

A: 0000000000hello world and thanks for the fish.
B: hello cruel l_o world and thanks for the fish!
C: XXXXXXXXXXXX0X0000000000000000000000000000000X (-)

- Pick the choice with most zeros (2nd choice) (aka, select the choice with less Xs).
- On C lane, promote gaps of one or two `0`s into `X`s.

A: 0000000000hello world and thanks for the fish.\0
B: hello cruel l_o world and thanks for the fish!\0
C: XXXXXXXXXXXXXX0000000000000000000000000000000X 0 (-)
                ^

- Do the number of leading Xs(C) - number of leading 0s(A) (14-10). If positive, write it [4].
  This number will be needed in the patch function.
- Do { Encode every XXXX island in C as a positive number indicating how many bytes to copy from.
       Otherwise, run-length the number of zeros into a negative number.
     } repeat till lane is exhausted.

 4
  XXXXXXXXXXXXXXX: +14 "hello cruel l_"
                 0000000000000000000000000000000: -31
                                                X: +1 "!"

 - Patch size is 4 control bytes [4,+14,-31,+1] + 14 (string) + 1 (string) = 19 bytes

## ALGORITHM 3

- start source (A) and target (B) strings. start with A:
- select how many bytes to copy (positive), how many to skip (negative), or switch A<-->B lanes (zero).
- repeat previous step over and over until both lanes do reach their respective string ends.

A: hello world and thanks for the fish.
B: hello cruel o_o world and thanks for the fish!

A: +6 0     >> hello
B: -6 +10 0 >> hello cruel o_o
A: +24 -1 0 >> hello cruel o_o world and thanks for the fish
B: -29 +1   >> hello cruel o_o world and thanks for the fish!
(10 bytes)

what if we always specify a dual +/- operation per lane?
lanes changed automatically after every tuple. in this case a 0 shall indicate a no op.

A: +6 0   >> hello
B: -6 +10 >> hello cruel o_o
A: +24 -1 >> hello cruel o_o world and thanks for the fish
B: -29 +1 >> hello cruel o_o world and thanks for the fish!
(8 bytes)

- we construct the patch now. a substring excerpt must come after any positive operations on lane B.

+6 0 -6 +10 "cruel o_o " +24 -1 -29 +1 "!"

- total patch size is 8 control bytes + 10 (string) + 1 (string) = 19 bytes