May 1, 2024
Updated July 10, 2025
12 minute read
Space complexity examines the amount of memory a computer program needs to run. In programming, space and time complexities are the two sides of the performance equation. For a given task, you try to design an algorithm that minimizes the amount of resources it consumes and produces the correct results. Space complexity deals with memory and time complexity deals with time.
Understanding Space Complexity
Space complexity refers to how much memory a computer program needs to run. It measures the amount of memory that a program occupies while it is running. Space complexity is typically measured in terms of the number of bytes of memory that the program uses.
Space complexity is important because it can affect the performance of a program. A program with high space complexity may require more memory than is available, which can cause the program to crash. In some cases, a program with high space complexity may even cause the computer to run out of memory.
Factors Affecting Space Complexity
There are several factors that can affect the space complexity of a program. These factors include:
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The size of the input data. The larger the input data, the more memory the program will need to store it.
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The number of variables used. The more variables a program uses, the more memory the program will need to store them.
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The number of loops and recursion. Loops and recursion can cause a program to use more memory because they can create multiple copies of the same data.
Reducing Space Complexity
There are several techniques that can be used to reduce the space complexity of a program. These techniques include:
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Reading list
We've selected 16 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Space Complexity.
Comprehensive graduate-level textbook on computational complexity theory. It delves deeply into space complexity classes, hierarchy theorems, and advanced topics. It is an essential reference for graduate students and researchers in the field.
This widely recognized textbook in the field of algorithms and data structures. It provides a solid foundation in analyzing algorithm efficiency, including space complexity. It is commonly used as a textbook in undergraduate and graduate programs.
Fundamental text in theoretical computer science, covering automata theory, computability, and complexity theory. It includes dedicated sections on space complexity, providing a rigorous theoretical grounding. It is suitable for advanced undergraduate and graduate students.
Offers a broad overview of algorithms and data structures with clear explanations and practical examples. It covers the analysis of algorithms, including their space requirements. It's a strong resource for both students and professionals looking to solidify their understanding.
This textbook focuses on the design of algorithms and includes the analysis of their efficiency, including space complexity. It presents a wide range of algorithmic techniques and is suitable for undergraduate and graduate courses.
Explores the boundaries of computation and the complexity of problems from a broad perspective. It covers space complexity within the context of computational limits and the Church-Turing thesis. It's a good resource for gaining a wider theoretical context.
Offers a problem-solving approach to data structures and algorithms, frequently encountered in coding interviews. It covers the analysis of space complexity for various algorithms and data structures through practical examples. It valuable resource for interview preparation and solidifying understanding through practice.
The second part of the 'Algorithms Illuminated' series continues with more advanced graph algorithms and data structures, including their space complexity analysis. It builds upon the first volume and is suitable for those who have a basic understanding of algorithms.
The final part of the series focuses on NP-hard problems and approaches to solving them. While primarily about complexity classes related to time, it provides context on the landscape of hard problems, which is relevant to understanding the limits of efficient computation in terms of both time and space.
Provides a very accessible and illustrated introduction to common algorithms and data structures. While not focusing exclusively on space complexity theory, it introduces the concept of analyzing algorithm performance in a highly intuitive way, making it great for beginners or those seeking a less formal introduction.
Covers fundamental concepts in data science, including algorithms and their analysis. It discusses space complexity in the context of processing and analyzing large datasets, providing a practical perspective on the topic.
Offers a more gentle introduction to the theoretical foundations of computer science, including computability and complexity. It covers space complexity at an introductory level, making it suitable for those new to the theoretical aspects.
While focused on machine learning, this book delves into the algorithmic foundations and theoretical guarantees, which often involve analyzing the space complexity of learning algorithms. It's relevant for those interested in the intersection of complexity theory and machine learning.
Similar to Hopcroft, Motwani, and Ullman, this book focuses on formal languages and automata but also includes an introduction to computability and complexity, touching upon space complexity. It serves as a good foundational text for the theoretical concepts.
A strong foundation in discrete mathematics is crucial for understanding algorithms and complexity. This comprehensive textbook covers relevant mathematical concepts, including proof techniques and graph theory, which are essential prerequisites for studying space complexity.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/kp7bcv/space
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