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Learning Functional Data Structures and Algorithms

You're reading from   Learning Functional Data Structures and Algorithms Learn functional data structures and algorithms for your applications and bring their benefits to your work now

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Product type Paperback
Published in Feb 2017
Publisher Packt
ISBN-13 9781785888731
Length 318 pages
Edition 1st Edition
Languages
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Authors (2):
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Raju Kumar Mishra Raju Kumar Mishra
Author Profile Icon Raju Kumar Mishra
Raju Kumar Mishra
Atul S. Khot Atul S. Khot
Author Profile Icon Atul S. Khot
Atul S. Khot
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Table of Contents (14) Chapters Close

Preface 1. Why Functional Programming? 2. Building Blocks FREE CHAPTER 3. Lists 4. Binary Trees 5. More List Algorithms 6. Graph Algorithms 7. Random Access Lists 8. Queues 9. Streams, Laziness, and Algorithms 10. Being Lazy - Queues and Deques 11. Red-Black Trees 12. Binomial Heaps 13. Sorting

Space/time trade-off


A trade-off is a balancing act: when we take something, we give away another thing!

Algorithm designs too, at times, trade-off some amount of memory to save on the overall time. Let's look at two problems to better appreciate this important concept.

A word frequency counter

Let's say we have a list of words. The task is to find how many times a word occurs in the list in order to compute every word's frequency.

Here is a brute force approach:

    w <- each word in the list, count <- 1  
      w1 <- all other words in the list 
        If (w == w1)  
           Increment count  
                  println(w, " = ", count) 

The following diagram shows the comparisons for the first two elements:

The preceding diagram shows how the algorithm works for the first two words. Each word ends up being compared with other words. Note that even if we know the answer for the word "is," we end up recomputing it again.

The algorithm performs O(n2) comparison. Thus, the runtime complexity...

You have been reading a chapter from
Learning Functional Data Structures and Algorithms
Published in: Feb 2017
Publisher: Packt
ISBN-13: 9781785888731
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