# Huffman Coding Python Heapq

Huffman coding for image compression I assume you want the code in Java P. Don't mind the print statements - they are just for me to test and see what. heapq solution in. Look for patterns (repeated words or phrases) in the text. How Computers Compress Text: Huffman Coding and Huffman Trees - Duration: 6:31. In computer science and information theory, Huffman coding is an entropy encoding algorithm used for lossless data compression. We'll be using the python heapq library to implement a priority queue, so if you're unfamiliar with that library, go back and read our previous guide. Python code coverage for Lib/sched. Introduction. The remaining steps, i. This is a binary heap implementation usually backed by a plain list and it supports insertion and extraction of the smallest element in O(log n) time. Some characters occur more often than others. Huffman Coding algorithm developed by David Huffman in 1952 when he was a graduate student at MIT. I am sorry, but in the Python 2. How do these adaptive Huffman encoders work?. Huffman coding is a compression method which generates variable-length codes for data – the more frequent the data item, the shorter the code generated. Huffman Coding Presented By: Ehtisham Ali Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The Python programming language has a speci c syntax (form) and semantics. If we have a code alphabet which is different than 0 and 1, then we may have non-binary Huffman codes. Compile and execute code online in C, C++, Java, Javascript, Python, C#, Go, Pascal, Ruby, Rust, Bash, Haskell, etc with our online compiler and powerful IDE. The code length is related with how frequently characters are used. Additional Huffman Requirement The two least likely symbols have codewords that differ only in the last bit These three requirements lead to a simple way of building a binary tree describing an optimum prefix code - THE Huffman Code • Build it from bottom up, starting w/ the two least likely symbols • The external nodes correspond to the. Code word: 011100101010. We are going to use Binary Tree and Minimum Priority Queue in this chapter. Base three Huffman coding works exactly like base two Huffman coding, but when we work with the priority queue, instead of taking out two elements and inserting one, we take out three. You can vote up the examples you like or vote down the ones you don't like. Bit vector and heap help the encoding tree generation algorithm. It is an algorithm which works with integer length codes. A text compression program based on Huffman algorithm. All computing systems follow definite rules, both in theory and in practice, in the realms of both computer science and everyday programming. Please report if you are facing any issue on this page. Used on command line in form: python huffman. Introduction. The purpose of the Algorithm is lossless data compression. CODE EXPLANATION: Run Length Encoding in a String. , the "agent" that carries out the decompression) must somehow ascertain the symbol-to-codeword mapping. Our next topic is greedy algorithms, and we ask the students to implement Huffman encoding in Python. There are mainly two major parts in Huffman Coding. java from §5. But it would seem an easy first test. I am a Computer Science Major and Psychology Minor trying to gain experience in software engineering, data analytics, and digital marketing. // #include "stdafx. This version of file encoder and decoder program is based on the Huffman coding method. The first variation is about non-binary huffman codes. py and binarytree. It makes use of a binary tree to develop codes of varying lengths for the letters used in the original message. Most frequent characters have smallest codes, and longer codes for least frequent characters. The Basics of Data Compression. interval scheduling (PDF) greedy approaches, weighted interval scheduling, DP and memoization ; segmented least squares (PDF) sum of subsets, knapsack (PDF) shortest paths in a graph with negative weights (B-F code in Python) Bellman-Ford, Floyd-Warshall ; STUDY BREAK Divide and Conquer. Huffman while going to MIT as a Ph. We consider the data to be a sequence of characters. Development Hi guys, I have an assignment for python in my class on Huffman Tree encode and decoding. Example: The message DCODEMESSAGE contains 3 times the letter E, 2 times the letters D and S, and 1 times the letters A, C, G, M and O. Huffman code bit-lengths are required to reconstruct each of the used canonical Huffman tables. The testing code in the template runs your code through several test cases. Unlike to ASCII or Unicode, Huffman code uses different number of bits to encode letters. Huffman coding. py, decompressor. Huffman coding in hindi:- Huffman कोड एक optimal prefix कोड होता है जिसका प्रयोग lossless डेटा कम्प्रेशन एल्गोरिथ्म में किया जाता है और वह प्रक्रिया जिसमें इस प्रकार के कोड का प्रयोग. There's no magic in this, we're just creating ranges on a. There are 26 small and 26 capital letters plus 10 numbers and 10 (or more) punc-. I first wanted to try implementing Huffman coding on my own, but later I found that probably does not worth of spending my time. Then the Huffman coding assigns to each symbol one bit, therefore each. Programming with Built-in Computational Intelligence. This algorithm is commonly used in JPEG Compression. Huffman coding can be used to compress all sorts of data. initialize it to text file path) UseHuffman. Check out my code on SoloLearn. pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35 to 49 without affecting their accuracy. Entropy coding • Entropy is a lower bound on the average number of bits needed to represent the symbols (the data compression limit). Huffman Coding - Python Implementation Huffman Coding is one of the lossless data compression techniques. For purposes of comparison, Welch cites results of Pechura and Rubin. Create your free Platform account to download our ready-to-use ActivePython or customize Python with any packages you require. it is used for Data Compression. Spring, Hibernate, JEE, Hadoop, Spark and BigData questions are covered with examples & tutorials to fast-track your Java career with highly paid skills. In Huffman coding, The algorithm goes through a message and depending on the frequency of the characters in that message, for each character, it assigns a variable length encoding. Animation Speed: w: h: Algorithm Visualizations. Learn more about doit4me, no attempt, huffman Image Processing Toolbox. py, decompressor. Programming. Python Slice Notation Explained. When I was doing an HPACK (HTTP/2 header compression, a large part of which is Huffman coding) implementation some time back I looked at the hpack crate (used by solicit, which was used by hyper) and it was using a couple of levels of. heappush(heap, item) - Push item onto the heap, maintaining heap invariant. After quantization, huffman / entropy coding is one of the more significant contributors to the file size savings in JPEG compression. We’re going to be using a heap as the preferred data structure to form our Huffman tree. But it is still fun. The process of finding or using such a code proceeds by means of Huffman coding, an algorithm developed by David A. Bit vector and heap help the encoding tree generation algorithm. To make things easy, let us say the input string is "abaabcd". Huffman coding mechanism is studied and a capacity model is constructed in term of information theory. This coding leads to ambiguity because code assigned to c is the prefix of codes assigned to a and b. Python 3; Linear Queue; Basic Python data structure concepts - lists, tuples What is a priority queue? Before you go ahead and read this tutorial, I highly recommend you to read the previous tutorial on Queues and Circular Queues as it will give you a better foundation and help you grasp the the content here. Download Source Code. So, what happens, is:. Huffman encoding Huffman encoding: Uses variable lengths for different characters to take advantage of their relative frequencies. The testing code in the template runs your code through several test cases. (Python is not unique in this. If sig is a cell array, it must be either a row or a column. Post navigation ← Linkdump Sort python dictionaries by values →. (There are better algorithms that can use more structure of the file than just letter frequencies. Watch my OTHER video on how HUFFMAN COMPRESSION work FIRST. txt (right click, save as) Save the code below, in the same directory as the above code, and Run this python code (edit the path variable below before running. xls files) but this project is more complicated so I shall need some advice from you. It can be created with WinRAR software. Huffman Coding Class Library for. Huffman coding & deciding algorithm is used in compressing data with variable-length codes. There are mainly two major parts in Huffman Coding. Follow @python_fiddle Browser Version Not Supported Due to Python Fiddle's reliance on advanced JavaScript techniques, older browsers might have problems running it correctly. The computer I am using now has over 1 million times the memory of my first PC that I bought in 1983, and the new 80 gigabyte disk holds 4000 times the amount of data. Python Slice Notation Explained. We'll show you how you can use the heapq module to implement heaps in Python in just a few lines of code. It’s short because I knew we’d use it frequently. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. cs 4 Computer Science Bootcamp Topics include coding basics, representing code and data using a computer, and applications of computing that are important to. I have created an implementation of the Huffman Compression Algorithm in python, but I am really not proud of how it looks or feels. right = right # masukkan node kanan 7 self. In earlier days, computers were small and conserving space in memory or on a disk drive was always a premium. implementation includes Huffman coding. Now traditionally to encode/decode a string, we can use ASCII values. How do I implement Huffman encoding and decoding using an array and not a tree? Based on how the question is formulated I'll assume you know how to do it with a tree. There's certainly not a lack of implementations for Huffman coding (a kind of data compression) in the web. Decoding binary data can be done massively faster if you hard-code the Huffman table and handle the data one byte at a time, generating enormous lookup tables. Efficient Huffman Decoding Oct. Be able to interpret /create Huffman trees. Golin, Claire Kenyon, Neal E. How do I create a Huffman coding tree in C++? I have an array of 26 integers called charCount. In this tutorial, you will understand the working of Huffman coding with working code in C, C++, Java, and Python. Download Source Code. Enkelt is the worlds first swedish programming language. Some are intended to illustrate python programming ideas. Create your free Platform account to download our ready-to-use ActivePython or customize Python with any packages you require. For my assignment, I am to do a encode and decode for huffman trees. Implement Simply Binary HuffMan Code program in C/C++. lossless predictive coding, huffman coding, prediction error,previous pixel coding Image Processing with Python Python is a high level programming language which. py is the template file for this problem. So, what happens, is:. Dijkstra Single Source Shortest Path - Directed Graph. py 1 class HuffmanNode(): # deklarasi class HuffmanNode 2 def __init__(self, symbol=None, probability= None, left=None, right=None): # inisialisasi 3 self. Or download a sample file from sample. The algorithm is based on a binary-tree frequency. This coding leads to ambiguity because code assigned to c is the prefix of codes assigned to a and b. Could somebody tell. The purpose of the Algorithm is lossless data compression. huffman free download. Its philosophy is that recoding data per character, the length of the cord and its frequency is inversely related, there is a number of shorter character encoding. The process of finding or using such a code proceeds by means of Huffman coding, an algorithm developed by David A. Project Option: Compression with LZW and Huffman Encoding As hard drives get bigger and cheaper, files sizes grow, and computer users get more lazy about cleaning their files up. CS106X teaches advanced programming and abstraction techniques, worrying first about C++ language mechanics and eventually focusing on topics such as recursion, C++ lists and maps, and the implementation techniques used to build complicated, dynamic data structures. HTML CSS JS. This page contains MatLab functions, m-files, which do Huffman coding and arithmetic coding of integer (symbol) sequences. • Entropy coding methods: • Aspire to achieve the entropy for a given alphabet, BPS Entropy • A code achieving the entropy limit is optimal BPS : bits per symbol original message encoded message BPS 8. The code length is related with how frequently characters are used. Huffman tree. Implement Simply Binary HuffMan Code program in C/C++. The term refers to the use of a variable-length code table for encoding a source symbol (such as a character in a file) where the variable-length code table has been. When I was doing an HPACK (HTTP/2 header compression, a large part of which is Huffman coding) implementation some time back I looked at the hpack crate (used by solicit, which was used by hyper) and it was using a couple of levels of. data = x and newrec. The Huffman Coding is a lossless data compression algorithm, developed by David Huffman in the early of 50s while he was a PhD student at MIT. // #include "stdafx. In normal Huffman coding, we encode our data using bits, that is, 0 and 1. Huffman coding is a well - known algorithm for generating minimum redundancy codes as compared to other algorithms. If you just want to jump into the code, the files compressor. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. Here's the basic idea: each ASCII character is usually represented with 8 bits, but if we had a text filed composed of only the lowercase a-z letters we could represent each character with only 5 bits (i. PCM and Huffman coding November 2013 – November 2013. The solution. Dynamic Programming. Read more ». Python's heapq module is another alternative. Huffman encoding is a way to assign binary codes to symbols that reduces the overall number of bits used to encode a typical string of those symbols. 1, first need to compress the. Your task is to print all the given alphabets Huffman Encoding. HUFFMAN CODE Huffman Code OBJECTIVE: 1. It is better for the length of a line of code to be within 80 characters, so when a line is too long, we need to separate it to two lines. data = x and newrec. He will convert this bit-string back into letters according to the `bits2letters` mapping defined below. I studied using this site and write. The purpose of the Algorithm is lossless data compression. Programming. That post was about a Lempel Ziv’s algorithm, which we wrote in Python. Huffman coding is lossless data compression algorithm. In basic Huffman coding, the encoder. Decoding binary data can be done massively faster if you hard-code the Huffman table and handle the data one byte at a time, generating enormous lookup tables. CEO Cryptonomica. Huffman Codes (i) Data can be encoded efficiently using Huffman Codes. There are some open-sourced Huffman coding codes on GitHub, and there are two Python libraries of huffman coding, huffman and dahuffman, available. • If temp->left and temp->right = NULL, then this is the leaf element of the tree. The three parts of the course - bits, signals, and packets - cover three corresponding layers of abstraction relevant to the system - free book at FreeComputerBooks. The below code takes a string as input, it encodes it and save in a variable encodedString. I first wanted to try implementing Huffman coding on my own, but later I found that probably does not worth of spending my time. Check out my code on SoloLearn. Huffman code in Java. In my KS3 programming lessons, I'm teaching students to "program" using BASIC (although I have also created Python versions of the resources). In python, 'heapq' is a library that lets us implement this easily. I believe Huffman is easier to explain and implement than arithmetic coding. How to Compress Data Using Huffman Encoding. Once I considered Huffman with the optimization of finding the most common character following each given character and then swapping the code for that character with the code for a space. Python lists have a built-in sort() method that modifies the list in-place and a sorted() built-in function that builds a new sorted list from an iterable. heappop(heap) - Pop and return the smallest item from the. If you are a beginner and want to start learning the C programming, then keep your close attention in this tutorial as I am going to share a program for C program for Huffman Coding With the output with the output. Huffman coding always generates an optimal symbol-by-symbol coding. code = None # kode awal adalah None 8 def. (There are better algorithms that can use more structure of the file than just letter frequencies. https://www. Post navigation ← Linkdump Sort python dictionaries by values →. Huffman coding is a well - known algorithm for generating minimum redundancy codes as compared to other algorithms. • The resulting code is unambiguous. Huffman coding implementation in Python. The Huffman. You will need to implement the functionality of the priority queue, the tree, and the Huffman encoder. It covers five key factors which determine performance of candidates: (1) the basics of programming languages, data structures and algorithms, (2) approaches to writing code with high quality, (3) tips to solve. Explain how data can be compressed using Huffman coding. Python's heapq module is another alternative. See this for applications of Huffman Coding. The Huffman coding has effectively used in text, image and video compression. Zigzag codification and Huffman coding in JPEG: Matlab code behindthesciences | July 5, 2016 In this post we are going to explain the science behind the JPEG codification. Huffman's algorithm is used to compress or encode data. combines a DCT transform and Huffman coding. sort() maintains the heap invariant! To create a heap, use a list initialized to [], or you can transform a populated list into a heap via function heapify(). Suppose that a file has been compressed using Huffman coding. This page offers a library of compression algorithms in python. An Algorithms is a step by step procedure for solving a problem or a finite set of sequence of specified actions for solving a problem or sequence of steps performed by computer to solve a problem. Huffman coding problem 138 One of difficulties has been when experimenting with in-built python data structures such as heapq or priority queue using the example. This book provides an extensive introduction to the theory underlying today's compression techniques with detailed instruction for their applications using several examples to explain the. For purposes of comparison, Welch cites results of Pechura and Rubin. Huffman tree based on the phrase „Implementation of Huffman Coding algorithm" (source: huffman. Teng has shown that the construction of a Huffman code is in class NC. For queries regarding questions and quizzes, use the comment area below respective pages. 4 ratio for English text when employing a complex technique for choosing the source messages to which Huffman coding is applied [Rubin 1976]. Huffman code is a data compression algorithm which uses the greedy technique for its implementation. I'm providing an implementation of the Huffman Coding algorithm in PHP and in JavaScript. 5rc1 Documentation » ; The Python Standard Library » » |. Some have many features. This page provides a tutorial on how the huffman coding works in a JPEG image. 3 Outline of this Lecture Codes and Compression. Or download a sample file from sample. Save the above code, in a file huffman. CS2430 - DISCRETE STRUCTURE HUFFMAN CODE OBJECTIVE: 1. First, a disclaimer: this is a very superficial scientific vulgatisation post about a topic that I have no formal background about, and I try to keep it very simple. the print statem, ID #16203237. 1840 – Analytical Engine Code The Analytical Engine was a theoretical (i. This reduces the overall size of a file. Path to A is left, therefore its optimum code is 0, the length of this code is 1 bit. Since I've been learning Python and Java, as well as more php and MySQL related technicalities, I've decided to maintain an ongoing repository of files that I've coded; feel free to use these, on the one condition that attribution is made to myself, as maintained in the comments of each of the code. In python, 'heapq' is a library that lets us implement this easily. Huffman coding (asymptotically) gets within one bit of the entropy of the sequence. It’s a great intro to the Django Python framework. I ran diff on the original and decoded files and got 0 differences. With this knowledge the algorithm can change how the more frequent characters are represented in bits. Data compression is the art of reducing the number of bits needed to store or transmit data. Huffman while he was a Sc. Huffman Coding. The Huffman coding has effectively used in text, image and video compression. Library for working with streams. Decoding binary data can be done massively faster if you hard-code the Huffman table and handle the data one byte at a time, generating enormous lookup tables. Now you have the length of each code and you already computed the frequency of each symbol. Arithmetic Coding and Huffman Coding in MATLAB. Lecture 15: Huffman Coding CLRS- 16. To encode a text file using Huffman method 2. Huffman in the 1950s. London, United Kingdom. The property of this data structure in python is that each time the smallest of heap element is popped(min heap). Provided an iterable of 2-tuples in (symbol, weight) format, generate a Huffman codebook, returned as a dictionary in {symbol: code. Huffman Coding. More frequent characters are assigned shorter codewords and less frequent characters are assigned longer codewords. Huffman coding. Huffman while he was a Sc. 51 # Then disable the usb init in this test build. Now you have the length of each code and you already computed the frequency of each symbol. sort() maintains the heap invariant! To create a heap, use a list initialized to [], or you can transform a populated list into a heap via function heapify(). Golin, Claire Kenyon, Neal E. There may be times when you want to compress data on the server or in the browser. • Huffman encoder/decoder client connection via Bluetooth in Android. The algorithm was introduced by David Huffman in 1952 as part of a course assignment at MIT. Huffman coding is an efficient method of compressing data without losing information. The testing code in the template runs your code through several test cases. 1 / 16 Digital Communications III (ECE 154C) Introduction to Coding and Information Theory Tara Javidi These lecture notes were originally developed by late Prof. The encoding of a character according to this particular Huffman code is the path followed to reach the character from the root of the tree. For decades, different algorithms were proposed addressing the issue of constructing Huffman Codes. Indention is preferred after the first line. interval scheduling (PDF) greedy approaches, weighted interval scheduling, DP and memoization ; segmented least squares (PDF) sum of subsets, knapsack (PDF) shortest paths in a graph with negative weights (B-F code in Python) Bellman-Ford, Floyd-Warshall ; STUDY BREAK Divide and Conquer. Huffman Coding algorithm developed by David Huffman in 1952 when he was a graduate student at MIT. Huffman coding (asymptotically) gets within one bit of the entropy of the sequence. student at MIT, and published in the 1952 paper "A Method for the. Now traditionally to encode/decode a string, we can use ASCII values. Then the receiver could calculate which bit was wrong and correct it. If those characters use < 8 bits each, the file will be smaller. Generate Huffman codebooks! Huffman codes are the optimal way to compress individual symbols into a binary sequence that can be unambiguously decoded without inter-symbol separators (it is "prefix-free"). An Algorithms is a step by step procedure for solving a problem or a finite set of sequence of specified actions for solving a problem or sequence of steps performed by computer to solve a problem. Simply we can say that when a 'c' function calls itself. Others retrieve parts of the dict as a sequence, for use in a for statement. Level up your coding skills and quickly land a job. Huffman Coding • The Huffman code is completely reversible, i. Decompressing a Huffman-compressed File. Applying a Huffman encoding/decoding technique manually. View Notes - Class 21 - Huffman Codes from CS 260 at University of Alabama. This is an implementation of Huffman code. 01 and that is 'h'. (But I am new to python, so I am sure there are better ways to do everything!) Some are intended to illustrate literate programming and testing. Efficient Huffman Decoding Oct. So, what happens, is:. Huffman coding takes advantage of how some letters occur more often than others do. This book provides an extensive introduction to the theory underlying today's compression techniques with detailed instruction for their applications using several examples to explain the. py and binarytree. Path to A is left, therefore its optimum code is 0, the length of this code is 1 bit. Huffman encoding is a way to assign binary codes to symbols that reduces the overall number of bits used to encode a typical string of those symbols. The entered message. huffman coding is a data compression technology, using a binary tree and two priority queue data structure. Below you’ll find a chronological order of some popular and/or important programming languages. CEO Cryptonomica. You can check the article out here! This time we are going to look at Huffman coding, an algorithm developed by David A. Huffman Coding For huffman coding one creates a binary tree of the source symbols, using the probabilities in P(x). It makes use of a binary tree to develop codes of varying lengths for the letters used in the original message. It is better for the length of a line of code to be within 80 characters, so when a line is too long, we need to separate it to two lines. Notes on gzip and DEFLATE format. JPEG Huffman Coding Tutorial. 4 Mon, 13 Mar 2017 12:43. Huffman tables • DC tables • AC tables Quantization tables Encoding steps: Image separated into Y, C b and C r components 8 x 8 blocks on each component are transformed using DCT transform Image data is entropy encoded Run-length coding Huffman coding Split JPEG decoding into several kernels. txt (right click, save as) Save the code below, in the same directory as the above code, and Run this python code (edit the path variable below before running. We are going to use Binary Tree and Minimum Priority Queue in this chapter. Please either accept the cookies, or find out how to remove them Accept Accept cookies. Or download a sample file from sample. It’s a great intro to the Django Python framework. English, on the other hand, is very context-sensitive. Python supports slice notation for any sequential data types like lists, tuples, strings, bytes, bytearrays, and ranges. The tree that actually results from a programmed implementation of Huffman's algorithm will be the same each time the program is run for the same weights (assuming no randomness is used in creating the tree). Some characters occur more often than others. There are some open-sourced Huffman coding codes on GitHub, and there are two Python libraries of huffman coding, huffman and dahuffman, available. The Python module heapq implements a priority queue data structure that is particularly efficient at letting you select the minimum element of the list. Animation Speed: w: h: Algorithm Visualizations. Save the above code, in a file huffman. The code length is related with how frequently characters are used. Used on command line in form: python huffman. Level up your coding skills and quickly land a job. that was used by the compressor. More often than not, the optimal number of bits is fractional. Huffman code is also part of the JPEG image compression scheme. I have created an implementation of the Huffman Compression Algorithm in python, but I am really not proud of how it looks or feels. Law 2: The rate of change in the software is directly proportional to the payment received from client and takes place at the quick rate as when. Huffman Coding Matlab Code Huffman code is an optimal prefix code found using the algorithm developed by David A. The following are code examples for showing how to use heapq. Sometimes it refers to the Huffman code. If you continue browsing the site, you agree to the use of cookies on this website. Here is a demonstration project for the class. This is an implementation of Huffman code. CS106X teaches advanced programming and abstraction techniques, worrying first about C++ language mechanics and eventually focusing on topics such as recursion, C++ lists and maps, and the implementation techniques used to build complicated, dynamic data structures. Note: If two elements have same frequency, then the element which if at first will be taken on left of Binary Tree and other one to. Note: Please use this button to report only Software related issues. The argument sig can have the form of a numeric vector, numeric cell array, or alphanumeric cell array. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: