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{a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f...

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  • {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}
36
{a, b, c, d, e, f, g, h, i, j} b c f d i j g e a h C1 = empty C2 = empty

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Page 1: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, i, j}

b

c

f

d

ij

g

ea

h

C1 = empty

C2 = empty

Page 2: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

i

b

c

f

d

j

g

ea

h

i

C1 = empty

C2 = empty

Page 3: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

i

0100

f

d

i

g

j

i

b

c

ea

h

C1 = 0100

C2 = empty

Page 4: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, f, g, j} {a, b, c, e, h}i

i

f

d

i

g

j

b

c

ea

h

C1 = 0100

C2 = empty

Page 5: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

f

d

g

j

b

c

ea

h

C1 = 0100

C2 = empty

{d, f, g, j} {a, b, c, e, h}i

Page 6: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}i

f

f

d

g

j

b

c

ea

h

C1 = 0100

C2 = empty

Page 7: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

010d

g

j

c

bf

f

ea

h

11

i

f f

C1 = 010011010

C2 = empty

Page 8: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{a, e, h}{b, c}{d, g, j}

f f

i

d

g

j

c

bf

f

ea

h

C1 = 010011010

C2 = empty

Page 9: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{b, c} {a, e, h}{d, g, j}

i

f f

d

g

j

c

b

ea

h

C1 = 010011010

C2 = empty

Page 10: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}d

{b, c} {a, e, h}{g, j}

i

f f

d

g

j

c

b

ea

h

C1 = 010011010

C2 = empty

Page 11: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}d

1100 01

{b, c} {a, e, h}{g, j}

i

f f

d d dd

g

j

c

b

ea

h

C1 = 010011010000111

C2 = empty

Page 12: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{c}

C1 = 010011010000111

C2 = empty

{g, j} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

d d d

i

f fd

d

g

j

c

b

ea

h

Page 13: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{g, j} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

d d d

i

f f

g

j

c

b

ea

h

C1 = 010011010000111

C2 = empty

Page 14: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

g

j

c

b

ea

h

C1 = 010011010000111

C2 = empty

j

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

d d d

i

f f

Page 15: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

011 0

C1 = 01001101000011101

C2 = 100

g

j

c

b

ea

h

j

{g} {c} {a, e, h}{b}

{d, g, j} {a, b, c, e, h}

{b, c} {a, e, h}{g, j}

d d d

i

f f

jj jj

0

Page 16: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

C1 = 01001101000011101

C2 = 100

{g} {c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

jj j

d d d

i

f fj

g

j

c

b

ea

h

j

Page 17: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{g} {c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

jj j

d d d

i

f f

jg

c

b

ea

h

C1 = 01001101000011101

C2 = 100

Page 18: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

g

c

b

ea

h

C1 = 01001101000011101

C2 = 100

g

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

jj j

d d d

i

f f

j

Page 19: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

011 0 1

g

c

b

ea

h

g

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

jj j

d d d

i

f f

j

g g g g

C1 = 0100110100001110101

C2 = 100101

Page 20: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

C1 = 0100110100001110101

C2 = 100101

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

{c}

g g g g

jj j

d d d

i

f fg

g

c

b

ea

h

j

Page 21: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

{c}

g g g g

jj j

d d d

i

f f

j

ea

hc

b

C1 = 0100110100001110101

C2 = 100101

Page 22: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

c

b

ea

h

C1 = 0100110100001110101

C2 = 100101

c

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

g g g g

jj j

d d d

i

f f

j

Page 23: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

01 00

c

b

ea

h

c

C1 = 0100110100001110101

C2 = 1001011000

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{d, g, j} {a, b, c, e, h}

{b, c} {a, e, h}{g, j}

g g g g

jj j

d d d

i

f f

j

c c c c

Page 24: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

C1 = 0100110100001110101

C2 = 1001011000

{h} {e} {a}{b}

c

b

ea

h

c

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

c c c c

g g g g

jj j

d d d

i

f f

j

Page 25: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}{g, j}

c c c c

g g g g

jj j

d d d

i

f f

j

ea

hb

{h} {e} {a}{b}

C1 = 0100110100001110101

C2 = 1001011000

Page 26: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

b

ea

h

C1 = 0100110100001110101

C2 = 1001011000

b

{g, j}

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

Page 27: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

0 00

b

ea

h

C1 = 0100110100001110101

C2 = 1001011000000

b

{g, j}

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{d, g, j} {a, b, c, e, h}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

b b b

Page 28: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

ea

h

C1 = 0100110100001110101

C2 = 1001011000000

{e} {a}{h}

{g, j}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

Page 29: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

ea

h

C1 = 0100110100001110101

C2 = 1001011000000

h

{e}

{g, j}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

{a}

Page 30: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

1 0

ea

h

h

C1 = 0100110100001110101

C2 = 100101100000010

{e} {a}

{g, j}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{d, g, j} {a, b, c, e, h}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

h h

Page 31: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a}{e}h h

{e}

{g, j}

{a}b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{d, g, j} {a, b, c, e, h}

{a, b, c, d, e, f, g, h, j}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

ea

h

h

j

C1 = 0100110100001110101

C2 = 100101100000010

Page 32: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

ea

h h

{e}

{g, j}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

{a}

C1 = 0100110100001110101{a}{e}

C2 = 100101100000010

Page 33: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

ea

C1 = 0100110100001110101

C2 = 100101100000010

e

{g, j}

{a}h h

{e}

{g, j}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

{a}

Page 34: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

1

C1 = 0100110100001110101

C2 = 1001011000000101

ea

e

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

{a}h h

{e} {a}

Page 35: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

{a, b, c, d, e, f, g, h, j}

{d, g, j} {a, b, c, e, h}

b b b

{h} {e} {a}

{h}{b} {e} {a}

{c} {h}{b} {a, e}

{g} {c} {a, e, h}{b}

{b, c} {a, e, h}

c c c c

g g g g

jj j

d d d

i

f f

j

a

{a}h h

{e} {a}

C1 = 0100110100001110101

C2 = 1001011000000101

Page 36: {a, b, c, d, e, f, g, h, i, j}{a, b, c, d, e, f, g, h, j} {d, g, j} {a, b, c, e, h} 010 d g j c b f f e a h 11 i f f C1 = 010011010 C2 = empty. {a, b, c, d, e, f, g, h, j} {d, g, j}

C1 = 0100110100001110101Arithmetic Encoder C1’, C2’

C2 = 1001011000000101

Output : (n, C1’, C2’)


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