Chapter 18, Problem 54E

Explanation of Solution

Accessing the largest term in Big-O of a polynomial-time algorithm:

The polynomial-time algorithm is the algorithm in which the order of magnitude can be expressed as a polynomial in the size of the problem.

• In the algorithm, if the term with largest exponent increases, it rapidly states that the relative size of the problem is dominant when compare to others.
• The size of the problem and its complexity are represented with the help of a power.
  • The Big-O complexity has the highest power in the polynomial and it is considered more significant than other terms.

For example:

• Consider the expression “${\text{f(N)=N}}^{\text{3}}{\text{+ 50N}}^{\text{2}}\text{+ 10N + 25}$”.
• In the above expression, f(N) is of order N³ in Big-O notation, O(N³).
  • This expression states that for large values of “N”, it dominates the whole function