This is a Data Structures and Algorithms problem..Please proof my work and if needed make the necessary corrections ;)

3. Multiplying rectangular matres Assume that every possible way of evaluating a sequence of n such matrees reverz posable way of plannya Parentheses) is equally likely. Desgn and algorithm that defermines the average amount of work in terms of scalar multiplications) for a given sequence of in matrices. Precisely define what is haverage work "! Determine its time and space complexity. Average work is defined by the handbook as: multiplying n matrees would be equal to the total som of the scalar multprications of the t-Vales a n d divided by the total number of K-values used in the operations. From the textbook, we calculate the K-value as: S[j] = s[ik] + S[k4 1,;, thiththith Algorithm : int K-counter = 0; for (i= 1 to n-1) where n is the number of columns, we used n-1 because 1st column iso for (j=- i ton) for CR=2 to ;) S[i, j] S[c,F] + [kt 1;;] 71, Mexzthy H& Il calculate the K- Values K-counterati Average = { sci; ]] /K_counter; The fine complexity would he Oln 3) because of the 3 nested for loops while the space complenty is O(n)