Why do we take value from the already constructed array in KMP algorithmn when moving back when there is a mismatch , instead of starting from first?

Question

Why do we take value from the already constructed array in KMP algorithm when moving back (when there is a mismatch), instead of starting from first? Also how does it guarantee from that point before, the values are fine?

eg :

id = 0 1 2 3 4 5 6 7 8
s =  a a b a a b a a a
arr  0 1 0 1 2 3 4 5 2  

Considering i = 0 and j = 1 , we start the algorithm.

Why do we have a condition of moving:

i > 0 and charAt(i) != charAt(j) then i = arr[i-1]

How exactly does this line in KMP work?

Answer 1

arr was built specifically to take advantage of what you have already previously matched to get a head start once a mismatch occurs.

For example: suppose you have matched aabaa , but the next character isn't the expected b , but an a . This means what we have processed so far ends with aa , which is why arr[i-1] is 2: the position where we've matched the aa at the start of string we're looking for.