We can use DP to solve this problem.

Let \(f(i,j)\) be the answer of the \(i\) first elements of \(A\) and \(j\) first elements of \(B\).

The we have:

• \(f(i,j)=\min(f(i-1,j)+1,f(i,j-1)+1,f(i-1,j-1)+[A_i\ne B_j])\ (i>0,j>0)\)
• \(f(i,j)=i+j\) \((i=0\) or \(j=0)\)

The answer is \(f(n,m)\). The time comlexity is \(O(nm)\).