Here is the pseudo code for longest increasing sub sequence given on Wikipedia
L = 0
for i = 1, 2, ... n:
binary search for the largest positive j ≤ L
such that X[M[j]] < X[i] (or set j = 0 if no such value exists)
P[i] = M[j]
if j == L or X[i] < X[M[j+1]]:
M[j+1] = i
L = max(L, j+1)
I have understood how the code works. The only thing i cannot understand is the necessity of this statement (if j == L or X[i] < X[M[j+1]]:) I have tried running the algorithm on many examples and what i could make out is that in all the cases either j == L or X[i] < X[M[j+1]] and so the if statement always evaluates to True. Could you give me an example where the if loop is false and thus required for the algorithm ??
