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:
- Initialization of the loop variable:
int i = 0
(1 instruction). - Comparison in the loop condition:
i < theList.length
(1 instruction per iteration). - Increment of the loop variable:
i++
(1 instruction per iteration). - Accessing an element in the list:
theList[i]
(1 instruction per iteration). - 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: (for iterations).
- Initial setup (outside the loop): .
Total instructions in the worst case:
Thus, the number of instructions is proportional to , and the time complexity is .
Final Answer:
In the worst case, the number of instructions is 4n + 1, where is the length of the list.
Would you like more details or examples?
Related Questions:
- What is the best-case number of instructions for this algorithm?
- How does the number of instructions change if we add a
break
statement after finding the element? - What is the impact of having duplicates in the list on the average-case performance?
- How would this algorithm's performance change if the list were sorted?
- 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.
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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
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