the k factor of a string is defined as the number of times abba appears as a substring given two numbers length and kfactor find the number of strings of length length with k factor kfactor the algorithms is as follows dplengthkfactor will be a 4 element array wherein each element can be the number of strings of length length and k factor kfactor which belong to the criteria represented by that index dplengthkfactor0 can be the number of strings of length length and kfactor kfactor which end with substring a dplengthkfactor1 can be the number of strings of length length and kfactor kfactor which end with substring ab dplengthkfactor2 can be the number of strings of length length and kfactor kfactor which end with substring abb dplengthkfactor3 can be the number of strings of length and kfactor kfactor which end with anything other than the above substrings anything other than a ab abb example inputs length4 kfactor1 no of strings 1 length7 kfactor1 no of strings 70302 length10 kfactor2 no of strings 74357 find the number of strings of length length with k factor kfactor keyword arguments length integer kfactor integer base cases adding a at the end adding b at the end adding any other lowercase character adding a at the end adding b at the end adding any other lowercase character find the number of strings of length length with k factor k_factor keyword arguments length integer k_factor integer base cases adding a at the end adding b at the end adding any other lowercase character adding a at the end adding b at the end adding any other lowercase character
def find_k_factor(length, k_factor):
    
    mat=[[[0 for i in range(4)]for j in range((length-1)//3+2)]for k in range(length+1)]
    if 3*k_factor+1>length:
        return 0
    
    mat[1][0][0]=1
    mat[1][0][1]=0
    mat[1][0][2]=0
    mat[1][0][3]=25

    for i in range(2,length+1):
        for j in range((length-1)//3+2):
            if j==0:
                
                mat[i][j][0]=mat[i-1][j][0]+mat[i-1][j][1]+mat[i-1][j][3]

                
                mat[i][j][1]=mat[i-1][j][0]
                mat[i][j][2]=mat[i-1][j][1]

                
                mat[i][j][3]=mat[i-1][j][0]*24+mat[i-1][j][1]*24+mat[i-1][j][2]*25+mat[i-1][j][3]*25

            elif 3*j+1<i:
                
                mat[i][j][0]=mat[i-1][j][0]+mat[i-1][j][1]+mat[i-1][j][3]+mat[i-1][j-1][2]

                
                mat[i][j][1]=mat[i-1][j][0]
                mat[i][j][2]=mat[i-1][j][1]

                
                mat[i][j][3]=mat[i-1][j][0]*24+mat[i-1][j][1]*24+mat[i-1][j][2]*25+mat[i-1][j][3]*25

            elif 3*j+1==i:
                mat[i][j][0]=1
                mat[i][j][1]=0
                mat[i][j][2]=0
                mat[i][j][3]=0

            else:
                mat[i][j][0]=0
                mat[i][j][1]=0
                mat[i][j][2]=0
                mat[i][j][3]=0

    return sum(mat[length][k_factor])