finding the longest common subsequence (lcs) of two strings:

ALGORITHM lcs(X,Y):
 INPUT: strings X and Y with n and m elements, respectively
 OUTPUT: for i = 0,..,n-1, j=0,..,m-1, the length L[i,j] of
   the longest common subsequence of X[0..i] and Y[0..j]

 FOR i <- -1 to n-1 DO
   L[i,-1] <- 0
 FOR j <- -1 to m-1 DO
   L[-1,j] <- 0

 FOR i <- 0 to n-1 DO
  FOR j <- 0 to m-1 DO
   IF X[i] = Y[j] THEN
     L[i,j] <- L[i-1,j-1] + 1
   ELSE 
     L[i,j] <- max{L[i-1,j],L[i,j-1]}


try:

A B C B D A B

B D C A B A