Three algorithms A, B, and C, are under consideration for the Insert operation of a particular data set. Through an analysis of these algorithms, their speed functions have been determined to be: Algorithm A: 23n + 36n ² ; Algorithm B: 6 + nlog ₂ (n) + n; Algorithm C: log ₂ n + 36n ² .

(a)  Calculate the value of these three functions when n , the number of nodes in the data structure, is equal to 1,000,000.

(b)  Using Big-O analysis, calculate the value of each function.

(c)  Determine the percent difference between the values calculated in parts (a) and (b) for each algorithm.