Knuth-Morris-PrattPattern Matching Algorithm

Instructor : Prof. Jyh-Shing Roger Jang

Designer ： Shao-Huan WangThe ideas are reference to the textbook “Fundamentals of Data Structures in C “ and “名題精選百則 - 使用 C 語言 ( 技巧篇 )”.

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j)

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1

First, initial f(0) = -1

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

-1

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

0 1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1 0 1 -1Not equal!

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1 If i == -1 compare p[0] and p[j]

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1 0 1 -1 0 1 2 3

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1 If i == -1 compare p[0] and p[j]

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1 0 1 -1 0 1 2 3Not equal!

If p[i+1] == p[j], put i+1

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1

Equal!2

If i == -1 compare p[0] and p[j]

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1 0 1 -1 0 1 2 3 2

If p[i+1] == p[j], put i+1

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1

Not equal!

If i == -1 compare p[0] and p[j]

If i == -1 and p[0] == p[j], put i+1

0

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function

j 0 1 2 3 4 5 6 7 8 9 10

p[] a b a b b a b a b a a

f(j) -1 -1 0 1 -1 0 1 2 3 2 0

If p[i+1] == p[j], put i+1

First, initial f(0) = -1

j++, i = f(j-1), then compare p[i+1] and p[j]

If p[i+1] != p[j] and f(i-1) == -1, put -1

Else if p[i+1] == p[j], put i+1

Else if p[i+1] != p[j] and i != -1, let i = f(i),until p[i+1] == p[j] or i == -1 If i == -1 compare p[0] and p[j]

If i == -1 and p[0] == p[j], put i+1

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++

Knuth-Morris-PrattPattern Matching Algorithm

Use failure function Compare with a string s[] :

a b a a b a b a b b a b a b a a

p[]

a b a b b a b a b a a

f(j)

-1 -1 0 1 -1 0 1 2 3 2 0

j 0 1 2 3 4 5 6 7 8 9 10

If s[i] != p[j] and j != 0, j = f(j-1)+1Compare with s[i] and p[j], start with i = j = 0

Else if s[i] != p[j] and j == 0, i++Following the rules and you can finish this comparison