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Time and Space Complexity:Understanding Algorithm Complexity
Understanding the efficiency of algorithms is crucial
Algorithms can vary greatly in their efficiency
We need to analyze the time and space complexity of algorithms
Quadratic Time Complexity Analysis
Quadratic time complexity refers to algorithms that scale with the square of the
input size
Examples: Bubble Sort, Selection Sort
Big O Notation and Time Complexity
Big O notation is used to describe the upper bound of an algorithm's time
complexity
It provides a high-level understanding of an algorithm's efficiency
Polynomial vs Exponential Run Times
Polynomial run times (O(n), O(n^2), etc.) are manageable
Exponential run times (2^n, O(3^n), etc.) can become unmanageable very quickly
Recursion and Divide and Conquer
Recursion is a powerful technique for solving complex problems
Divide and Conquer is a technique where a problem is divided into smaller
subproblems
Recursion and Divide-and-Conquer Technique
Recursion and Divide-and-Conquer are often used together
A problem is divided into smaller subproblems, solved recursively, and then
combined
Divide and Conquer Steps
Divide the problem into smaller subproblems
Conquer the subproblems recursively
Combine the solutions to the subproblems
Merging and Sorting Sublists
Merge Sort uses the Divide-and-Conquer technique to sort a list
The list is divided into two halves, each half is sorted recursively, and then
merged
Understanding Time Complexity
Understanding the time complexity of algorithms helps us make informed decisions
Different algorithms can have vastly different time complexities
Linear Search Algorithm Implementation
Linear Search is a simple algorithm for searching an element in a list
The time complexity is O(n) since the entire list is searched
Recursive Binary Search Implementation
Binary Search uses Divide and Conquer to search for an element in a sorted list
The list is divided into two halves, the search continues in one half recursively
The time complexity is O(log n)
Logarithmic Time Complexity Analysis
Logarithmic time complexity algorithms scale well with large input sizes
Examples: Binary Search, Merge Sort
Linked List Fundamentals and Construction
A Linked List is a data structure where elements are linked together
Elements are accessed through pointers
Common Complexities in Algorithms
Constant Time Complexity: O(1)
Linear Time Complexity: O(n)
Quadratic Time Complexity: O(n^2)
Logarithmic Time Complexity: O(log n)
Amortized Constant Time Complexity in Arrays
Amortized Constant Time Complexity refers to algorithms where most operations take
constant time, but some may take longer
For example: resizing a dynamic array
Analyzing Time and Space Complexity
Analyzing the time and space complexity of an algorithm provides insight into its
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