Python - how to find all intersections of two strings?

Question

How to find all intersections (also called the longest common substrings) of two strings and their positions in both strings?

For example, if S1=\"never\"

Answer 1

This can be done in O(n+m) where n and m are lengths of input strings.

The pseudocode is:

function LCSubstr(S[1..m], T[1..n])
    L := array(1..m, 1..n)
    z := 0
    ret := {}
    for i := 1..m
        for j := 1..n
            if S[i] = T[j]
                if i = 1 or j = 1
                    L[i,j] := 1
                else
                    L[i,j] := L[i-1,j-1] + 1
                if L[i,j] > z
                    z := L[i,j]
                    ret := {}
                if L[i,j] = z
                    ret := ret ∪ {S[i-z+1..z]}
    return ret

See the Longest_common_substring_problem wikipedia article for more details.