How does Complexity affect any algorithm?

Time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of length of the input. While, the space complexity of an algorithm quantifies the amount of space or memory taken by an algorithm to run  as a function of the length of the input.

Complete Guide On Complexity Analysis – Data Structure and Algorithms Tutorial

Complexity analysis is defined as a technique to characterise the time taken by an algorithm with respect to input size (independent from the machine, language and compiler). It is used for evaluating the variations of execution time on different algorithms.

What is the need for Complexity Analysis?

  • Complexity Analysis determines the amount of time and space resources required to execute it.
  • It is used for comparing different algorithms on different input sizes.
  • Complexity helps to determine the difficulty of a problem.
  • often measured by how much time and space (memory) it takes to solve a particular problem

Complete Guide On Complexity Analysis

Things to learn about Complexity Analysis

  • What is Complexity Analysis?
  • What is the need for Complexity Analysis?
  • Asymptotic Notations
  • How to measure complexity?
    • 1. Time Complexity
    • 2. Space Complexity
    • 3. Auxiliary Space
  • How does Complexity affect any algorithm?
    • How to optimize the time and space complexity of an Algorithm?
  • Different types of Complexity exist in the program:
    • 1. Constant Complexity
    • 2. Logarithmic Complexity
    • 3. Linear Complexity
    • 4. Quadratic Complexity
    • 5. Factorial Complexity
    • 6. Exponential Complexity
  • Worst Case time complexity of different data structures for different operations
  • Complexity Analysis Of Popular Algorithms
  • Practice some questions on Complexity Analysis
  • practice with giving Quiz
  • Conclusion

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Asymptotic Notations in Complexity Analysis:

1. Big O Notation...

How to measure complexity?

The complexity of an algorithm can be measured in three ways:...

How does Complexity affect any algorithm?

Time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of length of the input. While, the space complexity of an algorithm quantifies the amount of space or memory taken by an algorithm to run  as a function of the length of the input....

How to optimize the time and space complexity of an Algorithm?

Optimization means modifying the brute-force approach to a problem. It is done to derive the best possible solution to solve the problem so that it will take less time and space complexity. We can optimize a program by either limiting the search space at each step or occupying less search space from the start....

Different types of Complexity exist in the program:

1. Constant Complexity...

Worst Case time complexity of different data structures for different operations

Data structure Access Search Insertion Deletion ArrayO(1) O(N) O(N) O(N) StackO(N) O(N) O(1) O(1) QueueO(N) O(N) O(1) O(1) Singly Linked listO(N) O(N) O(N) O(N) Doubly Linked ListO(N) O(N) O(1) O(1) Hash TableO(N) O(N) O(N) O(N) Binary Search TreeO(N) O(N) O(N) O(N) AVL TreeO(log N) O(log N) O(log N) O(log N) Binary TreeO(N) O(N) O(N) O(N) Red Black TreeO(log N) O(log N) O(log N) O(log N)...

Complexity Analysis Of Popular Algorithms:

Algorithm Complexity 1.  Linear Search Algorithm O(N) 2  Binary Search O(LogN) 3. Bubble Sort  O(N^2)  4. Insertion Sort O(N^2)  5. Selection Sort O(N^2)  6. QuickSort O(N^2) worst 7  Merge Sort O(N log(N)) 8. Counting Sort O(N) 9  Radix Sort O((n+b) * logb(k)). 10. Sieve of Eratosthenes O(n*log(log(n))) 11. KMP Algorithm O(N) 12.  Z algorithm O(M+N) 13.  Rabin-Karp Algorithm O(N*M). 14. Johnson’s algorithm O(V2log V + VE) 15.  Prim’s Algorithm O(V2) 16 Kruskal’s Algorithm O(ElogV) 17.  0/1 Knapsack  O(N * W) 18. Floyd Warshall Algorithm O(V3) 19. Breadth First Search O(V+E) 20. Depth first Search O(V + E)...

Practice some questions on Complexity Analysis:

Practice Questions on Time Complexity AnalysisMiscellaneous Problems of Time ComplexitySample Practice Problems on Complexity Analysis of Algorithm...

Practice with giving  Quiz :

Top MCQs on Complexity Analysis of Algorithms with AnswersTop MCQs on NP-Complete Complexity with AnswersTop MCQs on Complexity Analysis using Recurrence Relations with Answers...

Conclusion:

Complexity analysis is a very important technique to analyze any problem. The interviewer often checks your ideas and coding skills by asking you to write a code giving restrictions on its time or space complexities. By solving more and more problems anyone can improve their logical thinking day by day. Even in coding contests optimized solutions are accepted. The naive approach can give TLE(Time limit exceed)....