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Time Complexity - (BCA / B.Tech)

Time Complexity in Data Structures:

Time complexity is a way to measure the efficiency of an algorithm, indicating how long an algorithm will take to solve a problem. When we analyze an algorithm, time is a critical factor because it determines how efficiently the algorithm will work in the real world. Time complexity is based on the size of the algorithm's input and is usually expressed using Big-O Notation.

Definition of Time Complexity:

Time complexity is the time required to execute an algorithm, especially in relation to the size of the input data (n). It is a way to measure the different steps of an algorithm in terms of the input size.

Time is generally measured in three cases:

Best Case: The situation where the algorithm works the fastest.
Worst Case: The situation where the algorithm takes the most time.
Average Case: The average performance for all possible inputs.

Types of Time Complexity:

O(1) - Constant Time Complexity: The execution time does not depend on the input size.
O(n) - Linear Time Complexity: The execution time grows in direct proportion to the input size.
O(n^2) - Quadratic Time Complexity: The execution time grows in proportion to the square of the input size, often seen in nested loops.
O(log n) - Logarithmic Time Complexity: The execution time grows logarithmically, typically when the input size is halved at each step (e.g., binary search).
O(n log n) - Linearithmic Time Complexity: Often seen in sorting algorithms like Merge Sort and Quick Sort.
O(2^n) - Exponential Time Complexity: Very slow and not suitable for large inputs.
O(n!) - Factorial Time Complexity: Extremely slow, used only in special cases like permutation problems.

Advantages of Analyzing Time Complexity:

It helps measure the performance of an algorithm, makes it easy to compare different algorithms, and is important for analyzing and solving problems efficiently.

Time Complexity

Time Complexity in Data Structures:

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