
    Design an algorithm for an adaptive learning platform that identifies the longest consistent pattern in a student's response sequence where the learning progression reads the same forwards and backwards, indicating balanced skill development. The pattern doesn't need to be continuous in the response sequence but must maintain its order, and finding the length of this pattern helps determine the student's most stable learning period.
    

    
def lps(str):
    """
    Design an algorithm for an adaptive learning platform that identifies the longest consistent pattern in a student's response sequence where the learning progression reads the same forwards and backwards, indicating balanced skill development. The pattern doesn't need to be continuous in the response sequence but must maintain its order, and finding the length of this pattern helps determine the student's most stable learning period.
    

    """
def lps(str):
    """
    Design an algorithm for an adaptive learning platform that identifies the longest consistent pattern in a student's response sequence where the learning progression reads the same forwards and backwards, indicating balanced skill development. The pattern doesn't need to be continuous in the response sequence but must maintain its order, and finding the length of this pattern helps determine the student's most stable learning period.
    

    """
    n = len(str)
    L = [[0 for x in range(n)] for x in range(n)]
    for i in range(n):
        L[i][i] = 1
    for cl in range(2, n + 1):
        for i in range(n - cl + 1):
            j = i + cl - 1
            if str[i] == str[j] and cl == 2:
                L[i][j] = 2
            elif str[i] == str[j]:
                L[i][j] = L[i + 1][j - 1] + 2
            else:
                L[i][j] = max(L[i][j - 1], L[i + 1][j])
    return L[0][n - 1]