Soviet String Distance

Given two strings, $A$ and $B$, your task is to find the Levenshtein distance between them. Mathematically, the Levenshtein distance between two strings, $A$ and $B$, having lengths, $|A|$ and $|B|$, is given by $lev_{a,b}(|A|, |B|)$ where - $lev_{a,b}(i, j) = \left\{\begin{array}{ll} max(i,j), & if\;min(i, j) = 0 \\\ min \left\{\begin{array}{II} lev_{a, b}(i-1,j)+1 \\\ lev_{a,b}(i, j-1)+1 \\\ l