Consider the function: f(1)=1 (if(fi)), for n > 1 -1 to n-1 a. Give a recursive algorithm which, given n, calculates f(n). b. Give and solve a recurrence, as a function of n, for the number of scalar multiplications required by your algorithm from part (a). c. Give a dynamic programming algorithm which, given n, calculates f(n). d. Find, as a function of n, the number of scalar multiplication operations required by your algorithm from part (c). e. Give an algorithm which, given n, calculates f(n) using only a linear number of scalar multiplications (this includes multiplications and divisions). Hint: First find a closed form for the value of f(n) Consider the function: f(1)=1 (if(fi)), for n > 1 -1 to n-1 a. Give a recursive algorithm which, given n, calculates f(n). b. Give and solve a recurrence, as a function of n, for the number of scalar multiplications required by your algorithm from part (a). c. Give a dynamic programming algorithm which, given n, calculates f(n). d. Find, as a function of n, the number of scalar multiplication operations required by your algorithm from part (c). e. Give an algorithm which, given n, calculates f(n) using only a linear number of scalar multiplications (this includes multiplications and divisions). Hint: First find a closed form for the value of f(n)