Longest Increasing Sub sequence

Question

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 ??

Answer 1

When there are duplicates the if condition will fail

Consider X={2, 2, 2}

if Condition fails when j=0 and L=1