Time complexity.
Towhidul Islam
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Imagine a classroom of 100 students in which you gave your pen to one person. You have to find that pen without knowing to whom you gave it.
Let's break down the explanation of time complexity using the given scenario:
1. O(n^2):
- This scenario involves checking each student in the classroom one by one to see if they have the pen.
- You start by asking the first student if they have the pen. Then you ask the second student, then the third, and so on until you have asked all 100 students.
- Each student is checked against all other students in the class, resulting in a total of 100 * 100 = 10,000 checks.
- This is represented as O(n^2) because the number of checks grows quadratically with the number of students (n), where n is 100 in this case.
2. O(n):
- In this scenario, you still ask each student individually, but you don't repeat the process for every student once you find the pen.
- You start by asking the first student if they have the pen. If not, you move on to the second student, then the third, and so on until you find the pen.
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- The maximum number of checks required would be 100, which is directly proportional to the number of students (n).
- This is represented as O(n) because the number of checks grows linearly with the number of students.
3. O(log n):
- Here, you employ a binary search strategy to find the pen.
- You divide the class into two equal halves and ask if the pen is in the left or right half.
- Then, you continue dividing the remaining group into halves and asking until you narrow down to a single student who has the pen.
- This approach significantly reduces the number of checks required, as each division eliminates half of the remaining students.
- With 100 students, you would require a maximum of 7 divisions to find the pen (log2(100) ≈ 6.64).
- This is represented as O(log n) because the number of checks grows logarithmically with the number of students.
In summary, time complexity helps us understand how the time required to perform a task grows as the input size increases. It allows us to analyze and compare different algorithms based on their efficiency in handling larger datasets.