Question

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 + n log2 (n ) + n ; Algorithm C: log2 n + 36n 2 .

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

Answer 1

Using Big-O analysis, the value of each function are:

• Algorithm A: O(n^2)
• Algorithm B: O(n*log(n))
• Algorithm C: O(n^2).

Algorithm A:

Speed function: 23n + 36n^2

Using Big-O notation, we focus on the dominant term, which is 36n^2.

So, the Big-O notation for Algorithm A is O(n^2).

Algorithm B:

Speed function: 6 + n*log2(n) + n

Using Big-O notation, we focus on the dominant term, which is n*log2(n).

So, the Big-O notation for Algorithm B is O(n*log(n)).

Algorithm C:

Speed function: log2(n) + 36n^2

Using Big-O notation, we focus on the dominant term, which is 36n^2.

So, the Big-O notation for Algorithm C is O(n^2).