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13,700 | consider the following list of integers we shall partition this list using the partition function belowdef partition(unsorted_arrayfirst_indexlast_index)pivot unsorted_array[first_indexpivot_index first_index index_of_last_element last_index less_than_pivot_index index_of_last_element greater_than_pivot_index first_ind... |
13,701 | at the beginning of the execution of the main while loop the array looks like thisthe first inner while loop moves one index to the right until it lands on index because the value at that index is greater than at this pointthe first while loop breaks and does not continue at each test of the condition in the first whil... |
13,702 | since greater_than_pivot_index less_than_pivot_indexthe body of the if statement swaps the element at those indexes the else condition breaks the infinite loop any time greater_than_pivot_index becomes greater than less_than_pivot_index in such conditionit means that greater_than_pivot_index and less_than_pivot_index h... |
13,703 | to recapthe first time the quick sort function was calledit was partitioned about the element at index after the return of the partitioning functionwe obtain the array [ as you can seeall elements to the right of element are greaterwhile those to the left are smaller the partitioning is complete using the split point w... |
13,704 | heap sort in graphs and other algorithmswe implemented the (binaryheap data structure our implementation always made sure that after an element has been removed or added to heapthe heap order property is maintained by using the sink and float helper methods the heap data structure can be used to implement the sorting a... |
13,705 | summary in this we have explored number of sorting algorithms quick sort performs much better than the other sorting algorithms of all the algorithms discussedquick sort preserves the index of the list that it sorts we'll use this property in the next as we explore the selection algorithms |
13,706 | selection algorithms one interesting set of algorithms related to finding elements in an unordered list of items is selection algorithms in doing sowe shall be answering questions that have to do with selecting the median of set of numbers and selecting the ith-smallest or -largest element in listamong other things in ... |
13,707 | assume that perhaps the luxury of sorting before performing the search cannot be afforded is it possible to find the ith-smallest element without having to sort the list in the first placerandomized selection in the previous we examined the quick sort algorithm the quick sort algorithm allows us to sort an unordered li... |
13,708 | the quick_select function takes as parameters the index of the first element in the list as well as the last the ith element is specified by the third parameter values greater or equal to zero ( are allowed in such way that when is we know to search for the firstsmallest item in the list others like to treat the parame... |
13,709 | if the split index was less than kthen we would make call to quick_select like thispartition step the partition step is exactly like we had in the quick sort algorithm there are couple of things worthy of notedef partition(unsorted_arrayfirst_indexlast_index)if first_index =last_indexreturn first_index pivot unsorted_a... |
13,710 | unsorted_array[pivot_indexunsorted_array[less_than_pivot_indexunsorted_array[less_than_pivot_indexpivot return less_than_pivot_index an if statement has been inserted at the beginning of the function definition to cater for situations where first_index is equal to last_index in such casesit means there is only one elem... |
13,711 | pivot selection previouslyin the random selection algorithmwe selected the first element as the pivot we shall replace that step with sequence of steps that enables us to obtain the true or approximate median this will improve the partitioning of the list about the pivotdef partition(unsorted_arrayfirst_indexlast_index... |
13,712 | median of medians the median_of_medians function is responsible for finding the approximate median of any given list of items the function uses recursion to return the true mediandef median_of_medians(elems)sublists [elems[ : + for in range( len(elems) )medians [for sublist in sublistsmedians append(sorted(sublist)[len... |
13,713 | thereafterif the list now contains five or fewer elementswe shall sort the medians list and return the element located in its middle indexif len(medians< return sorted(medians)[len(medians)/ ifon the other handthe size of the list is greater than fivewe recursively call the median_of_medians function againsupplying it ... |
13,714 | once againwe only return the first index if there is only one element in the list the arraylist[first:secondreturns an array with index up to the size of the list - when we find the index of the medianwe lose the portion in the list where it occurs because of the new range indexing the [first:secondcode returns therefo... |
13,715 | as you will have already observedthe main function of the deterministic selection algorithm looks exactly the same as its random selection counterpart after the initial array_list has been partitioned about the approximate mediana comparison with the kth element is made if split is less than kthen recursive call to det... |
13,716 | design techniques and strategies in this we will take step back and look into the broader topics in computer algorithm design as your experience with programming growscertain patterns begin to become apparent to you and just like with any other skilled tradeyou cannot do without some techniques and principles to achiev... |
13,717 | classification by implementation when translating series of steps or processes into working algorithmthere are number of forms that it may take the heart of the algorithm may employ some assetsdescribed further in this section recursion recursive algorithms are the ones that make calls to themselves until certain condi... |
13,718 | to be able to process several instructions at oncea different model or computing technique is required parallel algorithms perform more than one operation at time in the pram modelthere are serial processors that share global memory the processors can also perform various arithmetic and logical operations in parallel t... |
13,719 | let' now examine practical scenario by which means do we arrive at the conclusion that the bubble sort algorithm is slower than the quick sort algorithmor in generalhow do we measure the efficiency of one algorithm against the otherwellwe can compare the big of any number of algorithms to determine their efficiency it ... |
13,720 | divide and conquer this approach to problem-solving is just as its name suggests to solve (conquercertain problemsthis algorithm divides the problem into subproblems identical to the original problem that can easily be solved solutions to the subproblems are combined in such way that the final solution is the solution ... |
13,721 | technical implementation let' dig into the implementation of some of the theoretical programming techniques that we discussed previously in this we will start with dynamic programming dynamic programming as we have already describedin this approachwe divide problem into smaller subproblems in finding the solutions to t... |
13,722 | the fibonacci series we will use the fibonacci series to illustrate both memoization and tabulation techniques of generating the series the memoization technique let' generate the fibonacci series to the fifth term recursive style of program to generate the sequence is as followsdef fib( )if < return elsereturn fib( - ... |
13,723 | careful observation of the preceding tree shows some interesting patterns the call to ( happens twice the call to ( happens thrice alsothe call to ( happens twice the return values of the function calls to all the times that fib( was called never changes the same goes for fib( and fib( the computational time is wasted ... |
13,724 | to create list of , elementswe do the following and pass it to the lookup parameter of the dyna_fib functionmap_set [none]*( this list will store the value of the computation of the various calls to the dyna_fib(functionif < lookup[ any call to the dyna_fib(with being less than or equal to will return when dyna_fib( is... |
13,725 | the results variable is at index and the values and this represents the return values of fib( and fib( to calculate the values of the fib(function for higher than we simply call the for loop appends the sum of the results[ - results[ - to the list of results divide and conquer this programming approach to problem-solvi... |
13,726 | merge sort the merge sort algorithm is based on the divide and conquer rule given list of unsorted elementswe split the list into approximately two halves we continue to divide the two halves recursively after whilethe sublists created as result of the recursive call will contain only one element at that pointwe begin ... |
13,727 | while len(first_sublistand len(second_sublist)if first_sublist[isecond_sublist[ ]merged_list append(first_sublist[ ] + elsemerged_list append(second_sublist[ ] + while len(first_sublist)merged_list append(first_sublist[ ] + while len(second_sublist)merged_list append(second_sublist[ ] + return merged_list the merge fun... |
13,728 | let' give the algorithm dry run by playing the last step of merging the two sublists [ and [ ]step first_sublist second_sublist merged_list step [ [ [step [ [ step [ step [ step [ step [ note that the text in bold represents the current item referenced in the loops first_sublist (which uses the index iand second_sublis... |
13,729 | the remainder ghccannot be divided by so we try the ghc denomination and realize that we can multiply it by to obtain ghc at the end of the daythe least possible number of denominations to create ghc is to get one ghc and four ghc notes so farour greedy algorithm seems to be doing pretty well function that returns the ... |
13,730 | better greedy algorithm is presented here this timethe function returns list of tuples that allow us to investigate the better resultsdef optimal_small_change(denomtotal_amount)sorted_denominations sorted(denomreverse=trueseries [for in range(len(sorted_denominations))term sorted_denominations[ :number_of_denoms [local... |
13,731 | consider the following graphby inspectionthe first answer to the question of finding the shortest path between node and node that comes to mind is the edge with value or distance from the diagramit would seem that the straight path from node to would also yield the shortest route between the two nodes but the assumptio... |
13,732 | node shortest distance from source previous node none none none none none none the adjacency list for the diagram and table is as followsgraph dict(graph[' '{' ' ' ' ' ' graph[' '{' ' ' ' graph[' '{' ' ' ' graph[' '{' ' ' ' ' ' graph[' '{' ' ' ' graph[' '{' ' ' ' the nested dictionary holds the distance and adjacent no... |
13,733 | any time the shortest distance of node is replaced by lesser valuewe need to update the previous node column too at the end of the first stepour table looks as followsnode shortest distance from source previous node none none none at this pointnode is considered visited as suchwe add node to the list of visited nodes i... |
13,734 | node shortest distance from source previous node none none at this pointwe initiate another step the smallest value in the shortest distance column is we choose instead of purely on an alphabetical basis the adjacent nodes of are and cbut node has already been visited using the rule we established earlierthe shortest d... |
13,735 | the node with the shortest distance yet unvisited is node the adjacent nodes of are nodes and but node has already been visited as suchwe focus on finding the shortest distance from the starting node to node we calculate this distance by adding the distance from node to to the distance from node to this sums up to whic... |
13,736 | let' verify this table with our graph from the graphwe know that the shortest distance from to is we will need to go through to get to node according to the tablethe shortest distance from the source column for node is the value this is true it is also tells us that to get to node fwe need to visit node eand from enode... |
13,737 | the heavy lifting of the whole process is accomplished by the use of while loopwhile trueadjacent_nodes graph[current_nodeif set(adjacent_nodesissubset(set(visited_nodes))nothing here to do all adjacent nodes have been visited pass elseunvisited_nodes set(adjacent_nodesdifference(set(visited_nodes)for vertex in unvisit... |
13,738 | the statement set(adjacent_nodesdifference(set(visited_nodes)returns the nodes that have not been visited the loop iterates over this list of unvisited nodesdistance_from_starting_node get_shortest_distance(tablevertexthe helper method get_shortest_distance(tablevertexwill return the value stored in the shortest distan... |
13,739 | the whole method ends by returning the updated table to print the tablewe use the following statementsshortest_distance_table find_shortest_path(graphtable' 'for in sorted(shortest_distance_table)print("{{}format( ,shortest_distance_table[ ])output for the preceding statementa [ noneb [ ' ' [ ' ' [ ' ' [ ' ' [ ' 'for t... |
13,740 | the last helper method is the get_next_node functiondef get_next_node(tablevisited_nodes)unvisited_nodes list(set(table keys()difference(set(visited_nodes))assumed_min table[unvisited_nodes[ ]][distancemin_vertex unvisited_nodes[ for node in unvisited_nodesif table[node][distanceassumed_minassumed_min table[node][dista... |
13,741 | in computer sciencethe class of problems that computers can solve within polynomial time using step-wise process of logical steps is called -type problemswhere stands for polynomial these are relatively easy to solve then there is another class of problems that is considered very hard to solve the word "hard problemis ... |
13,742 | all -type problems are subsets of np problems this means that any problem that can be solved in polynomial time can also be verified in polynomial time but the questionis npinvestigates whether problems that can be verified in polynomial time can also be solved in polynomial time in particularif they are equalit would ... |
13,743 | np-hard problem is np-hard if all other problems in np can be polynomial time reducible or mapped to it np-complete problem is considered an np-complete problem if it is first of all an np hard and is also found in the np class summary in this last we looked at the theories that support the computer science field witho... |
13,744 | implementationsapplicationsand tools learning about algorithms without any real-life application remains purely academic pursuit in this we will explore data structures and algorithms that are shaping our world one of the golden nuggets of this age is the abundance of data -mailsphone numberstextand image documents con... |
13,745 | tools of the trade in order to proceed with this you will need to install the following packages these packages will be used to preprocess and visually represent the data being processed some of the packages also contain well-written and perfected algorithms that will operate on our data preferablythese modules should ... |
13,746 | the data collected may also be inconsistent with other records collected over time the existence of duplicate entries and incomplete records warrant that we treat the data in such way as to bring out hidden and buried treasure the raw data may also be shrouded in sea of irrelevant data to clean the data upwe can totall... |
13,747 | to apply the mean values insteadwe do the followingprint(data fillna(data mean())the mean value for each column is calculated and inserted in those data areas with the np nan value for the first columncolumn the mean value was obtained by ( )/ the resulting is then stored at data[ ][ similar operation is carried out fo... |
13,748 | min-max scalar the min-max scalar form of normalization uses the mean and standard deviation to box all the data into range lying between certain min and max value for most purposesthe range is set between and at other timesother ranges may be applied but the to range remains the defaultscaled_values preprocessing minm... |
13,749 | binarizing data to binarize given feature setwe make use of threshold if any value within given dataset is greater than the thresholdthe value is replaced by if the value is less than the threshold we will replace itresults preprocessing binarizer( fit(datatransform(dataprint(resultsan instance of binarizer is created ... |
13,750 | types of machine learning there are three broad categories of machine learningas followssupervised learningherean algorithm is fed set of inputs and their corresponding outputs the algorithm then has to figure out what the output will be for an unfamiliar input examples of such algorithms include naive bayeslinear regr... |
13,751 | ('that is my best sword ''pos')('this is an awesome post''pos')(' do not like this cafe''neg')(' am tired of this bed ''neg')(" can' deal with this"'neg')('she is my sworn enemy!''neg')(' never had caring mom ''neg'firstwe will import the naivebayesclassifier class from the textblob package this classifier is very easy... |
13,752 | the specialized class naivebayesclassifier also did some heavy lifting for us in the background so we could not appreciate the innards by which the algorithm arrived at the various predictions our next example will use the scikit module to predict the category that phrase may belong to supervised learning example assum... |
13,753 | now that the training data has been obtainedwe must feed the data to machine learning algorithm the bag of words model will break down the training data in order to make it ready for the learning algorithm or model bag of words the bag of words is model that is used for representing text data in such way that it does n... |
13,754 | to generate the values that go into the columns of our matrixwe have to tokenize our training datafrom sklearn feature_extraction text import countvectorizer from sklearn feature_extraction text import tfidftransformer from sklearn naive_bayes import multinomialnb count_vect countvectorizer(training_matrix count_vect f... |
13,755 | the list test_data is passed to the count_vect transform function to obtain the vectorized form of the test data to obtain the term frequency--inverse document frequency representation of the test datasetwe call the transform method of the matrix_transformer object to predict which category the docs may belong towe do ... |
13,756 | note that in this kind of algorithmonly the raw uncategorized data is fed to the algorithm it is up to the algorithm to find out if the data has inherent groups within it to understand how this algorithm workswe will examine data points consisting of and values we will feed these values to the learning algorithm and ex... |
13,757 | the mean points when printed appear as follows[ [- - ]each data point in original_set will belong to cluster after our -means algorithm has finished its training the -mean algorithm represents the two clusters it discovers as and if we had asked the algorithm to cluster the data into fourthe internal representation of ... |
13,758 | the algorithm discovers two distinct clusters in our sample data the two mean points of the two clusters are denoted with the red star symbol prediction with the two clusters that we have obtainedwe can predict the group that new set of data might belong to let' predict which group the points [[- - ]and [[ ]will belong... |
13,759 | at the barest minimumwe can expect the two test datasets to belong to different clusters our expectation is proved right when the print statement prints and thus confirming that our test data does indeed fall under two different clusters data visualization numerical analysis does not sometimes lend itself to easy under... |
13,760 | the width of each bar can be changed by modifying the following lineplt bar(x_valuesdatawidth= this should produce the following graph |
13,761 | howeverthis is not visually appealing because there is no space anymore between the barswhich makes it look clumsy each bar now occupies one unit on the -axis multiple bar charts in trying to visualize datastacking number of bars enables one to further understand how one piece of data or variable varies with anotherdat... |
13,762 | box plot the box plot is used to visualize the median value and low and high ranges of distribution it is also referred to as box and whisker plot let' chart simple box plot we begin by generating numbers from normal distribution these are then passed to plt boxplot(datato be chartedimport numpy as np import matplotlib... |
13,763 | the following figure is what is produceda few comments on the preceding figurethe features of the box plot include box spanning the interquartile rangewhich measures the dispersionthe outer fringes of the data are denoted by the whiskers attached to the central boxthe red line represents the median the box plot is usef... |
13,764 | the sectors in the graph are labeled with the strings in the labels arraybubble chart another variant of the scatter plot is the bubble chart in scatter plotwe only plot the xy points of the data bubble charts add another dimension by illustrating the size of the points this third dimension may represent sizes of marke... |
13,765 | the following figure shows this bubble chartsummary in this we have explored how data and algorithms come together to aid machine learning making sense of huge amounts of data is made possible by first pruning our data through normalization processes feeding this data to specialized algorithmswe are able to predict the... |
13,766 | abstract data types (adts adjacency adjacency list adjacency matrix algorithm analysisapproaches average case analysis benchmarking algorithm design divide and conquer paradigm dynamic programming approach algorithmsclassifying by complexity about complexity curves algorithmsclassifying by design about divide and conqu... |
13,767 | implementing built-in data types about none type numeric types sequences canopy reference chaining chainmaps about advantage child circular buffer circular list about elementsappending elementsdeleting iterating through class methods classes co-routines coin counting problem collections module about data type compariso... |
13,768 | |
13,769 | preface xiii abstract data types introduction abstractions abstract data types data structures general definitions the date abstract data type defining the adt using the adt preconditions and postconditions implementing the adt bags the bag abstract data type selecting data structure list-based implementation iterators... |
13,770 | contents creating python list appending items extending list inserting items list slice two-dimensional arrays the array abstract data type implementing the - array the matrix abstract data type matrix operations implementing the matrix applicationthe game of life rules of the game designing solution implementation exe... |
13,771 | applicationthe sparse matrix list-based implementation efficiency analysis exercises programming projects searching and sorting searching the linear search the binary search sorting bubble sort selection sort insertion sort working with sorted lists maintaining sorted list merging sorted lists the set adt revisited sor... |
13,772 | contents the polynomial adt implementation exercises programming projects stacks the stack adt implementing the stack using python list using linked list stack applications balanced delimiters evaluating postfix expressions applicationsolving maze backtracking designing solution the maze adt implementation exercises pr... |
13,773 | organization list operations multi-linked lists multiple chains the sparse matrix complex iterators applicationtext editor typical editor operations the edit buffer adt implementation exercises programming projects recursion recursive functions properties of recursion factorials recursive call trees the fibonacci seque... |
13,774 | contents hash functions the hashmap abstract data type applicationhistograms the histogram abstract data type the color histogram exercises programming projects advanced sorting merge sort algorithm description basic implementation improved implementation efficiency analysis quick sort algorithm description implementat... |
13,775 | implementation the priority queue revisited heapsort simple implementation sorting in place applicationmorse code decision trees the adt definition exercises programming projects search trees the binary search tree searching min and max values insertions deletions efficiency of binary search trees search tree iterators... |
13,776 | contents standard output control structures selection constructs repetition constructs collections strings lists tuples dictionaries text files file access writing to files reading from files user-defined functions the function definition variable scope main routine appendix buser-defined modules structured programs na... |
13,777 | the standard second course in computer science has traditionally covered the fundamental data structures and algorithmsbut more recently these topics have been included in the broader topic of abstract data types this book is no exceptionwith the main focus on the designuseand implementation of abstract data types the ... |
13,778 | preface basicsapproach to learning data structures and algorithms without overwhelming the reader with all of the oop terminology and conceptswhich is especially important when the instructor has no plans to cover such topics seconddifferent instructors take different approaches with python in their first course our ai... |
13,779 | reordering of some topics for examplethe on recursion and hashing can be presented at any time after the discussion of algorithm analysis in abstract data types introduces the concept of abstract data types (adtsfor both simple typesthose containing individual data fieldsand the more complex typesthose containing data ... |
13,780 | preface searching and sorting introduces the concepts of searching and sorting and illustrates how the efficiency of some adts can be improved when working with sorted sequences search operations for an unsorted sequence are discussed and the binary search algorithm is introduced as way of improving this operation thre... |
13,781 | hash tables introduces the concept of hashing and the use of hash tables for performing fast searches different addressing techniques are presentedincluding those for both closed and open addressing collision resolution techniques and hash function design are also discussed the magic behind python' dictionary structure... |
13,782 | preface acknowledgments there are number of individuals would like to thank for helping to make this book possible firsti must acknowledge two individuals who served as mentors in the early part of my career mary dayne gregg (university of southern mississippi)who was the best computer science teacher have ever knownsh... |
13,783 | abstract data types the foundation of computer science is based on the study of algorithms an algorithm is sequence of clear and precise step-by-step instructions for solving problem in finite amount of time algorithms are implemented by translating the step-by-step instructions into computer program that can be execut... |
13,784 | abstract data types contain multiple valuesare all examples of complex types the primitive types provided by language may not be sufficient for solving large complex problems thusmost languages allow for the construction of additional data typesknown as user-defined types since they are defined by the programmer and no... |
13,785 | add sub storetomemr 'xto avoid this level of complexityhigh-level programming languages add another layer of abstraction above the assembly language level this abstraction is provided through primitive data type for storing integer values and set of well-defined operations that can be performed on those values by provi... |
13,786 | abstract data types implementationallowing us to focus on the use of the new data type instead of how it' implemented this separation is typically enforced by requiring interaction with the abstract data type through an interface or defined set of operations this is known as information hiding by hiding the implementat... |
13,787 | where it was not intended this type of logical error can be difficult to track down by using adts and requiring access via the interfacewe have fewer access points to debug the implementation of the abstract data type can be changed without having to modify the program code that uses the adt there are many times when w... |
13,788 | abstract data types there are many common data structuresincluding arrayslinked listsstacksqueuesand treesto name few all data structures store collection of valuesbut differ in how they organize the individual data items and by what operations can be applied to manage the collection the choice of particular data struc... |
13,789 | list or vector abstract data type to avoid confusionwe will use the term list to refer to the data type provided by python and use the terms general list or list structure when referring to the more general list structure as defined earlier the date abstract data type an abstract data type is defined by specifying the ... |
13,790 | abstract data types advancebydays )advances the date by the given number of days the date is incremented if days is positive and decremented if days is negative the date is capped to november bcif necessary comparable otherdate )compares this date to the otherdate to determine their logical ordering this comparison can... |
13,791 | listing the checkdates py program extracts collection of birth dates from the user and determines if each individual is at least years of age from date import date def main()date before which person must have been born to be or older bornbefore date( extract birth dates from the user and determine if or older date prom... |
13,792 | abstract data types via the constructor before any operation can be used other than the initialization requirementan operation may not have any other preconditions it all depends on the type of adt and the respective operation likewisesome operations may not have postconditionas is the case for simple access methodswhi... |
13,793 | which occurs first or how many days separate the two dates we are going to use the latter approach as it is very common for storing dates in computer applications and provides for an easy implementation listing partial implementation of the date py module implements proleptic gregorian calendar date as julian day numbe... |
13,794 | abstract data types listing continued def __lt__selfotherdate )return self _julianday otherdate _julianday def __le__selfotherdate )return self _julianday <otherdate _julianday the remaining methods are to be included at this point returns the gregorian date as tuple(monthdayyeardef _togregorianself ) self _julianday /... |
13,795 | the date abstract data type comments class definitions and methods should be properly commented to aide the user in knowing what the class and/or methods do to conserve spacehoweverclasses and methods presented in this book do not routinely include these comments since the surrounding text provides full explanation cau... |
13,796 | abstract data types firstday date printfirstday comparing date objects we can logically compare two date instances to determine their calendar order when using julian day to represent the datesthe date comparison is as simple as comparing the two integer values and returning the appropriate boolean value based on the r... |
13,797 | the bag abstract data type there are several variations of the bag adt with the one described here being simple bag grab bag is similar to the simple bag but the items are removed from the bag at random another common variation is the counting bagwhich includes an operation that returns the number of occurrences in the... |
13,798 | abstract data types mybag bag(mybag add mybag add mybag add mybag add mybag add value intinput("guess value contained in the bag "if value in mybagprint"the bag contains the value"value else print"the bag does not contain the value"value nextconsider the checkdates py sample program from the previous section where we e... |
13,799 | implementation of the containerbreduce the chance of introducing errors from misuse of the list since it provides additional operations that are not appropriate for bagcprovide better coordination between different modules and designersand deasily swap out our current implementation of the bag adt for differentpossibly... |
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