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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

How to Calculate Algorithm Efficiency?

Janvi Kumari
Janvi Kumari Last Updated : 16 Jul, 2024
4 min read

Introduction

Have you ever wondered what makes some algorithms faster and more efficient than others? It all boils down to two crucial factors: time and space complexity. Think of time complexity as the clock ticking away, measuring how long an algorithm takes to complete based on the size of its input. On the other hand, space complexity is like a storage unit, keeping track of how much memory the algorithm needs as the input size grows. To make sense of this, we use Big O notation—a handy way to describe the upper limits of an algorithm’s growth rate. Let’s dive into the fascinating world of calculating algorithm efficiency!

Overview

  • Algorithms are measured by their efficiency, defined by time and space complexity.
  • Time complexity measures the execution time of an algorithm relative to input size.
  • Space complexity tracks the memory usage of an algorithm as the input size grows.
  • Big O notation helps describe the upper limits of an algorithm’s growth rate.
  • Understanding algorithm efficiency involves analyzing and optimizing both time and space complexity.
Algorithm Efficiency

Table of contents

What is Time Complexity?

Time complexity and space complexity are two fundamental concepts used to evaluate the efficiency of algorithms.

Time complexity refers to the amount of time an algorithm takes to complete as a function of the input size. It’s essentially a measure of the speed of an algorithm. Time complexity is usually expressed using Big O notation, which provides an upper bound on the algorithm’s growth rate. Some common time complexities are:

  • O(1): Constant time – The algorithm takes the same time regardless of the input size.
  • O(log n): Logarithmic time – The time grows logarithmically as the input size increases.
  • O(n): Linear time – The time grows linearly with the input size.
  • O(n log n): Linearithmic time – The time grows in linear and logarithmic rates.
  • O(n^2): Quadratic time – The time grows quadratically with the input size.
  • O(2^n): Exponential time – The time doubles with each additional element in the input.
  • O(n!): Factorial time – The time grows factorially with the input size.

What is Space Complexity?

Space complexity refers to the amount of memory an algorithm uses as a function of the input size. It measures the efficiency of an algorithm in terms of the amount of memory it requires to run. Similar to time complexity, space complexity is also expressed using Big O notation. Some common space complexities are:

  • O(1): Constant space – the algorithm uses a fixed amount of memory regardless of the input size.
  • O(n): Linear space – the memory usage grows linearly with the input size.
  • O(n^2): Quadratic space – the memory usage grows quadratically with the input size.

By analyzing both time and space complexity, you can understand an algorithm’s efficiency comprehensively and make informed decisions about which algorithm to use for a specific problem.

Step-by-Step Guide To Calculate Algorithm Efficiency

Step 1: Understand the Algorithm

  • Define the Problem
    • Clearly understand what the algorithm is supposed to do.
    • Identify the input size (n), typically the number of elements in the input data.
  • Identify Basic Operations
    • Determine the key operations in the algorithm, such as comparisons, arithmetic operations, and assignments.

Step 2: Analyze Time Complexity

  • Identify Basic Operations
    • Focus on the algorithm’s most time-consuming operations, such as comparisons, arithmetic operations, and data structure manipulations.
  • Count Basic Operations
    • Determine how often each basic operation is performed relative to the input size (n).

Example

def example_algorithm(arr):
    n = len(arr)
    sum = 0
    for i in range(n):
        sum += arr[i]
    return sum

Explanation of Code

  • Initialization: sum = 0 (O(1))
  • Loop: for i in range(n) (O(n))
  • Inside Loop: sum += arr[i] (O(1) per iteration, O(n) total)

Express Time Complexity

  • Combine the operations to express the overall time complexity in Big O notation.
  • Example: The above algorithm has an O(n) time complexity.

Consider Best, Average, and Worst Cases

  • Best Case: The scenario where the algorithm performs the fewest steps.
  • Average Case: The expected time complexity over all possible inputs.
  • Worst Case: The scenario where the algorithm performs the most steps.

Step 3: Analyze Space Complexity

  • Identify Memory Usage
    • Determine the memory required for variables, data structures, and function call stack.
  • Count Memory Usage
    • Analyze the algorithm to count the memory used relative to the input size (n).

Example

def example_algorithm(arr):
    n = len(arr)
    sum = 0
    for i in range(n):
        sum += arr[i]
    return sum

Space Complexity of Each Variable

  • Variables: sum (O(1)), n (O(1)), arr (O(n))

Express Space Complexity

  • Combine the memory usage to express the overall space complexity in Big O notation.
  • Example: The above algorithm has an O(n) space complexity.

Step 4: Simplify the Complexity Expression

  • Ignore Lower-Order Terms
    • Focus on the term with the highest growth rate in Big O notation.
  • Ignore Constant Coefficients
    • Big O notation is concerned with growth rates, not specific values.

Conclusion

Calculating the efficiency of an algorithm entails reading each time and space complexity using Big O notation. Following the above mentioned steps, you can systematically compare and optimize your algorithms to ensure they carry out correctly for various input sizes. Practice and familiarity with distinctive varieties of algorithms will assist you in grasping this vital thing of computer science.

Frequently Asked Questions

Q1. How can I improve the efficiency of an algorithm?

Ans. To improve the efficiency of an algorithm:
A. Optimize the logic to reduce the number of operations.
B. Use efficient data structures.
C. Avoid unnecessary computations and redundant code.
D. Implement memoization or caching where applicable.
E. Break down the problem and solve subproblems more efficiently.

Q2. What is the difference between best, average, and worst-case time complexities?

Ans. Here is the difference between best, average, and worst-case time complexities:
A. Best Case: The scenario where the algorithm performs the fewest steps.
B. Average Case: The expected time complexity over all possible inputs.
C. Worst Case: The scenario where the algorithm performs the most steps.

Q3. What is algorithm efficiency?

Ans. Algorithm efficiency refers to how effectively an algorithm performs in terms of time (how fast it runs) and space (how much memory it uses). Efficient algorithms solve problems in less time and use fewer resources.

Q4. What is Big O notation?

Ans. Big O notation is a mathematical representation used to describe the upper bound of an algorithm’s running time or space requirements in the worst-case scenario. It provides an asymptotic analysis of the algorithm’s efficiency.

Janvi Kumari
Janvi Kumari

Hi, I am Janvi, a passionate data science enthusiast currently working at Analytics Vidhya. My journey into the world of data began with a deep curiosity about how we can extract meaningful insights from complex datasets.

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