Math Problem Statement

Exercise: How many instructions do you have to execute to find out if the element is in the list in the worst case, if n represents the length of the list? boolean find( String[] theList, String toFind ) { for ( int i = 0; i < theList.length; i++ ) { if ( theList[i].equals( toFind )) return true; } return false; }

Solution

To analyze the worst-case time complexity of the given code snippet, we need to count the number of instructions executed in the worst-case scenario, where the element is either not in the list or is the last element.

Explanation:

  1. Initialization of the loop variable: int i = 0 (1 instruction).
  2. Comparison in the loop condition: i < theList.length (1 instruction per iteration).
  3. Increment of the loop variable: i++ (1 instruction per iteration).
  4. Accessing an element in the list: theList[i] (1 instruction per iteration).
  5. Equality check: theList[i].equals(toFind) (1 instruction per iteration).

Each iteration of the loop executes 4 instructions (steps 2–5).


Worst-Case:

The worst-case occurs when either:

  • The element is not in the list, or
  • The element is at the last position in the list.

For a list of length n, the loop runs n times.

  • Loop instructions: 4n4n (for nn iterations).
  • Initial setup (outside the loop): 11.

Total instructions in the worst case:
4n+14n + 1

Thus, the number of instructions is proportional to nn, and the time complexity is O(n)O(n).


Final Answer:

In the worst case, the number of instructions is 4n + 1, where nn is the length of the list.


Would you like more details or examples?


Related Questions:

  1. What is the best-case number of instructions for this algorithm?
  2. How does the number of instructions change if we add a break statement after finding the element?
  3. What is the impact of having duplicates in the list on the average-case performance?
  4. How would this algorithm's performance change if the list were sorted?
  5. Can this algorithm be optimized using a different search technique, such as binary search?

Tip: Understanding the big-O notation helps you analyze the scalability of algorithms with respect to input size.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algorithm Analysis
Time Complexity
Worst-Case Analysis

Formulas

Total instructions = 4n + 1

Theorems

Big-O Notation

Suitable Grade Level

Grades 10-12 (High School) or Undergraduate Computer Science