def generate_ch04():
"""Generate tables/figures for chapter 04."""
chapter = 4
with FigureNum(1) as figure_number:
description = 'Waiting in a queue at a nightclub'
label = caption(chapter, figure_number)
print('Redrawn by artist')
print('{}. {}'.format(label, description))
print()
with FigureNum(2) as figure_number:
description = 'modeling a nightclub queue with three nodes'
label = caption(chapter, figure_number)
print('Redrawn by artist')
print('{}. {}'.format(label, description))
print()
with FigureNum(3) as figure_number:
description = 'Patrons can advance quicker with a purchased pass'
label = caption(chapter, figure_number)
print('Redrawn by artist')
print('{}. {}'.format(label, description))
print()
# For full book output, remove "max_n=16384". Added to reduce time to generate all.
with TableNum(1) as table_number:
process(average_performance(max_n=16384),
chapter, table_number,
'Average operation performance (time in ns) on problem instances of size N',
yaxis='Time (in nanoseconds)')
with FigureNum(4) as figure_number:
description = 'O(log N) behavior of Heap outperforms O(N) behavior for other approaches'
label = caption(chapter, figure_number)
print('Generated by Excel')
print('{}. {}'.format(label, description))
print()
with FigureNum(5) as figure_number:
description = 'A sample max binary heap'
label = caption(chapter, figure_number)
heap = initial_heap()
output_heap(heap)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(6) as figure_number:
description = 'Determining levels needed for a binary heap with N entries'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(7) as figure_number:
description = 'Which of these are valid binary max heaps?'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(8) as figure_number:
description = 'The first step to inserting an entry is to place it in the next available position'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(9) as figure_number:
description = 'The second step is to swim the entry up one level as needed'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(10) as figure_number:
description = 'Third step swims the entry up one level as needed'
label = caption(chapter, figure_number)
heap2 = initial_heap()
heap2.enqueue(12, 12)
output_heap(heap2)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(11) as figure_number:
description = 'Adding an entry with priority 16 swims up to the top'
label = caption(chapter, figure_number)
heap3 = initial_heap()
heap3.enqueue(12, 12)
heap3.enqueue(16, 16)
output_heap(heap3)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(12) as figure_number:
description = 'The first step is to remove bottommost entry'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(13) as figure_number:
description = 'Broken heap resulting from swapping last entry with level 0'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(14) as figure_number:
description = 'Swap top entry with its left child which had a higher priority'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(15) as figure_number:
description = 'Sink down an additional level'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(16) as figure_number:
description = 'Resulting heap after sinking entry to its proper location'
label = caption(chapter, figure_number)
heap4 = initial_heap()
heap4.enqueue(12, 12)
heap4.enqueue(16, 16)
heap4.dequeue()
output_heap(heap4)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(17) as figure_number:
description = 'Storing a max binary heap in an array'
label = caption(chapter, figure_number)
heap4 = initial_heap()
heap4.enqueue(12, 12)
print(' -- |' + '|'.join([' {:>3} '.format(e.priority) for e in heap4.storage[1:heap4.N+1]]))
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(18) as figure_number:
description = 'Changes to storage after enqueue in Figure 4-8'
label = caption(chapter, figure_number)
heap_enqueue_animation()
print('{}. {}'.format(label, description))
print()
with FigureNum(19) as figure_number:
description = 'Changes to storage after dequeue in Figure 4-11'
label = caption(chapter, figure_number)
heap_dequeue_animation()
print('{}. {}'.format(label, description))
print()
with FigureNum(20) as figure_number:
description = 'Using an array as a circular queue'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
with FigureNum(21) as figure_number:
description = 'A novel factorial heap structure'
label = caption(chapter, figure_number)
print('Hand drawn')
print('{}. {}'.format(label, description))
print()
def generate_ch06():
"""Generate Tables and Figures for chapter 06."""
chapter = 6
with FigureNum(1) as figure_number:
description = 'Representing mathematical expressions using expression trees'
label = caption(chapter, figure_number)
mult7 = expression_tree()
print(mult7, '=', mult7.eval())
print('in postfix:', ' '.join(str(k) for k in mult7.postfix()))
print('{}. {}'.format(label, description))
print()
with FigureNum(2) as figure_number:
description = 'Visualizing recursive evaluation of ((1+5)*9)'
label = caption(chapter, figure_number)
mult2 = debug_expression()
print(mult2, '=', mult2.eval())
print('{}. {}'.format(label, description))
print()
with TableNum(1) as table_number:
process(
generate_list_table(),
chapter,
table_number,
'Comparing insert and remove performance of lists against binary search tree (time in ms)',
yaxis="Time (in ms)")
with FigureNum(3) as figure_number:
description = 'Binary Search Tree containing seven values'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with TableNum(2) as table_number:
description = 'Creating a binary search tree by inserting (in order) 19,14,15,53,58,3,26'
speaking_tree()
label = caption(chapter, table_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(4) as figure_number:
description = 'Insert 29 into the binary search tree example'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(5) as figure_number:
description = 'Different binary search trees when same values are inserted in different order'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(6) as figure_number:
description = 'Two possible binary search trees after removing 19 from Figure 6-4'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(7) as figure_number:
description = 'Removing minimum value in a subtree'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with TableNum(3) as table_number:
description = 'Demonstrating how node is removed from binary search tree'
label = caption(chapter, table_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(8) as figure_number:
description = 'Iterating over the values in a binary search tree in ascending order'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(9) as figure_number:
description = 'A complete binary tree stores the most values with the least height'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(10) as figure_number:
description = 'Unbalanced tree after two insertions.'
label = caption(chapter, figure_number)
show_unbalanced_result()
print('{}. {}'.format(label, description))
print()
with FigureNum(11) as figure_number:
description = 'Recursive invocation when inserting a value.'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(12) as figure_number:
description = 'Rebalancing this binary search tree by rotating the root node to the right'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(13) as figure_number:
description = 'Four different node rotations'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with TableNum(4) as table_number:
description = 'Implementation of rotate left-right'
label = caption(chapter, table_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(14) as figure_number:
description = 'Binary search tree as symbol table: keys are atomic numbers; values are element names'
label = caption(chapter, figure_number)
sample_binary_tree_as_symbol()
print('{}. {}'.format(label, description))
print()
with FigureNum(15) as figure_number:
description = 'Binary search tree as priority queue: priorities are atomic numbers; values are element names'
label = caption(chapter, figure_number)
sample_binary_tree_as_pq()
print('{}. {}'.format(label, description))
print()
with FigureNum(16) as figure_number:
description = 'A Fibonacci tree with twelve nodes'
label = caption(chapter, figure_number)
fibonacci_tree_sample()
print('{}. {}'.format(label, description))
print()
right = m + 1
else:
hi = m - 1
if right == len(A) or A[right] != target:
right -= 1
return (lo, right)
#######################################################################
if __name__ == '__main__':
chapter = 2
with ExerciseNum(1) as exercise_number:
fragment_counting()
print(caption(chapter, exercise_number), 'Fragment Evaluation')
with ExerciseNum(2) as exercise_number:
another_fragment_counting()
print(caption(chapter, exercise_number), 'Second Fragment Evaluation')
print()
with ExerciseNum(3) as exercise_number:
run_permutation_sort()
print(caption(chapter, exercise_number), 'Permutation Sort Exercise')
print()
with ExerciseNum(4) as exercise_number:
performance_bas()
print(caption(chapter, exercise_number),
'Binary Array Search Evidence')
def generate_ch05():
"""Generate Tables and Figures for chapter 05."""
chapter = 5
with FigureNum(1) as figure_number:
description = 'Sample array, A, to sort'
label = caption(chapter, figure_number)
A = [15, 21, 20, 2, 15, 24, 5, 19]
print('|'.join([' {:>2} '.format(k) for k in A]))
moves = [(0,3),(5,7),(1,6),None,(2,4),None,(4,5)]
for m in moves:
if m:
A[m[0]],A[m[1]] = A[m[1]],A[m[0]]
print('|'.join([' {:>2} '.format(k) for k in A]))
print('{}. {}'.format(label, description))
print()
with FigureNum(2) as figure_number:
description = 'Sorting sample array using Selection Sort'
label = caption(chapter, figure_number)
A = [15, 21, 20, 2, 15, 24, 5, 19]
print('|'.join([' {:>2} '.format(k) for k in A]))
moves = [(0,3),(1,6),(2,3),(3,4),(4,7),(5,7),(6,6)]
for m in moves:
if m:
A[m[0]],A[m[1]] = A[m[1]],A[m[0]]
print('|'.join([' {:>2} '.format(k) for k in A]))
print('{}. {}'.format(label, description))
print()
with FigureNum(3) as figure_number:
description = 'Visualizing the formula for triangle numbers: sum of 1 through 7 is 28'
label = caption(chapter, figure_number)
print('By hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(4) as figure_number:
description = 'Sorting sample array using Insertion Sort'
label = caption(chapter, figure_number)
A = [15, 21, 20, 2, 15, 24, 5, 19]
print('|'.join([' {:>2} '.format(k) for k in A]))
moves = [None,[(2,1)], [(3,2),(2,1),(1,0)], [(4,3),(3,2)],
None, [(6,5),(5,4),(4,3),(3,2),(2,1)],[(7,6),(6,5),(5,4)]]
for p in moves:
if p:
for m in p:
A[m[0]],A[m[1]] = A[m[1]],A[m[0]]
print('|'.join([' {:>2} '.format(k) for k in A]))
print('{}. {}'.format(label, description))
print()
with FigureNum(5) as figure_number:
# for actual results from book, use max_k=18 as an argument, but it will take hours.
timing_selection_insertion()
description = 'Timing results of Insertion Sort and Selection Sort'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(6) as figure_number:
description = 'Visualizing the recursive invocation of fact(3)'
label = caption(chapter, figure_number)
print('Fact(3) = ', fact(3))
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(7) as figure_number:
description = 'Recursive invocation when calling rmax(0,3) on A=[15,21,20,2]'
label = caption(chapter, figure_number)
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(8) as figure_number:
description = 'Complete recursive invocation of rmax(0,7)'
label = caption(chapter, figure_number)
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(9) as figure_number:
description = 'Merging two stacks into one'
label = caption(chapter, figure_number)
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(10) as figure_number:
description = 'Step by step merge sort of two sorted sub-arrays of size 4'
label = caption(chapter, figure_number)
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(11) as figure_number:
show_partition()
description = 'Results of partition(A,0,7,0) using A[0] as pivot'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(12) as figure_number:
description = 'Full recursive invocation of Quicksort'
label = caption(chapter, figure_number)
print('Done by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(13) as figure_number:
heapsort_intuition()
description = 'Intuition behind how a max binary heap can be used for sorting'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(14) as figure_number:
show_heapify()
description = 'Converting array into a max binary heap'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with TableNum(1) as table_number:
timing_nlogn_sorting()
description = 'Runtime performance (in seconds) for different sorting algorithms'
label = caption(chapter, table_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(15) as figure_number:
tim_sort_figure()
description = 'Changes to array when applying Tim Sort with initial size of 4'
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
DG.add_edge('b', 'd', weight=-3)
DG.add_edge('d', 'c', weight=5)
DG.add_edge('c', 'b', weight=-4)
try:
bellman_ford_returns_negative_cycle(DG, 'a')
except NegativeCycleError as nce:
print('detected negative cycle:', nce)
#######################################################################
if __name__ == '__main__':
chapter = 7
with ExerciseNum(1) as exercise_number:
print('dfs_search_recursive in ch07.challenge')
print(caption(chapter, exercise_number), 'Recursive depth first search')
print()
with ExerciseNum(2) as exercise_number:
print('path_to_recursive implementation')
print(caption(chapter, exercise_number), 'Recursive Path_to')
print()
with ExerciseNum(3) as exercise_number:
print('recover_cycle in ch07.digraph_search')
print(caption(chapter, exercise_number), 'Recover cycle')
print()
with ExerciseNum(4) as exercise_number:
print('recover_negative_cycle in ch07.digraph_search')
recover_negative_cycle_example()
"""Failed attempt to implement two largest."""
m1 = max(A[:len(A) // 2])
m2 = max(A[len(A) // 2:])
if m1 < m2:
return (m2, m1)
return (m1, m2)
#######################################################################
if __name__ == '__main__':
chapter = 1
with ExerciseNum(1) as exercise_number:
sample = 'A man, a plan, a canal. Panama!'
print(sample, 'is a palindrome:', is_palindrome_letters_only(sample))
print(caption(chapter, exercise_number), 'Palindrome Detector')
with ExerciseNum(2) as exercise_number:
run_median_less_than_trial()
print()
run_median_trial()
print(caption(chapter, exercise_number), 'Median Counting')
with ExerciseNum(3) as exercise_number:
run_counting_sort_trials()
print(caption(chapter, exercise_number), 'Counting Sort Trials')
with ExerciseNum(4) as exercise_number:
print('see tournament_allows_odd in ch01.challenge')
print(caption(chapter, exercise_number), 'Odd tournament')
i = (i * 2) + 1
print(rights)
print([i.value for i in pq.storage[1:]])
pq = PQ(num)
for i in range(num, 0, -1):
pq.enqueue(i, i)
#######################################################################
if __name__ == '__main__':
chapter = 4
with ExerciseNum(1) as exercise_number:
print('implementation in ch04.circular_queue')
print(caption(chapter, exercise_number), 'Circular Queue')
print()
with ExerciseNum(2) as exercise_number:
inspect_heap_array()
print(
'When inserting N=2^k-1 values in ascending order, right most values'
)
print(
'in each of the k levels contains largest. When inserting in reverse'
)
print(
'order, each value remains where it was inserted, so all are descending.'
)
print(caption(chapter, exercise_number), 'Values in heap')
print()
def generate_ch01():
"""Generate Tables and Figures for chapter 01."""
chapter = 1
with FigureNum(1) as figure_number:
pi1 = [13, 2, 18, 7, 50]
pi2 = [-19, -236, -17, -204, -97, -20, -928, -454, -92, -19]
pi3 = list(range(1, 1000001))
print(pi1, '->', max(pi1))
print(pi2, '->', max(pi2))
print(pi3[:5] + ['...'] + pi3[-3:], '->', max(pi3))
print(caption(chapter, figure_number),
'Three different problem instances processed by an algorithm')
print()
with TableNum(1) as table_number:
process(
run_init_trial(),
chapter,
table_number,
'Executing max() on two kinds of problem instances of size N (time in ms)',
yaxis='Time (in ms)')
with FigureNum(2) as figure_number:
visualize_flawed([1, 5, 2, 9, 3, 4])
print(caption(chapter, figure_number),
'Visualizing the execution of flawed()')
with FigureNum(3) as figure_number:
visualize_alternate([1, 5, 2, 9, 3, 4])
print(caption(chapter, figure_number),
'Visualizing the execution of alternate()')
with FigureNum(4) as figure_number:
visualize_alternate([9, 5, 2, 1, 3, 4])
visualize_alternate([1, 2, 3, 4, 5, 9])
print(
caption(chapter, figure_number),
'Visualizing the execution of alternate() on best and worst cases')
# TODO: Option for secondary axis specification
with TableNum(2) as table_number:
process(
run_largest_alternate(), chapter, table_number,
'Comparing largest() with alternate() on worst case problem instances'
)
# Take results and plot #LessA on left-axis as line, and TimesA on right axis as column
with FigureNum(5) as figure_number:
print(caption(chapter, figure_number),
'Relationship between #Less-Than and runtime performance')
with TableNum(3) as table_number:
process(run_best_worst(), chapter, table_number,
'Performance of largest() and max() on best and worst cases')
with TableNum(4) as table_number:
process(
performance_different_approaches(),
chapter,
table_number,
'Performance of different approached on 524,288 values in different orders',
create_image=False)
with FigureNum(6) as figure_number:
print('by hand')
print(caption(chapter, figure_number),
'A tournament with eight initial values')
with FigureNum(7) as figure_number:
print('by hand')
print(caption(chapter, figure_number), 'A tournament with 32 values')
with FigureNum(8) as figure_number:
visualize_tournament_two([3, 1, 4, 1, 5, 9, 2, 6])
print(caption(chapter, figure_number),
'Step-by-step execution of tournament algorithm')
with TableNum(5) as table_number:
process(run_largest_two_trials(Order.SHUFFLED),
chapter,
table_number,
'Comparing runtime performance (in ms) of all four algorithms',
yaxis='Time (in ms)')
# Taken from table
with FigureNum(9) as figure_number:
print(caption(chapter, figure_number),
'Runtime performance comparison')
with TableNum(6) as table_number:
process(count_operations(),
chapter,
table_number,
'Counting operations in four different functions',
yaxis='Number of times ct is incremented')
tbl = DataTable([20, 8, 8], ['Hashtable Type', 'Build', 'Remove All'],
output=output)
tbl.format('Hashtable Type', 's')
tbl.row(['Open Addressing:', build_time_oa, delete_time_oa])
tbl.row(['Separate Chaining:', build_time_sc, delete_time_sc])
return tbl
#######################################################################
if __name__ == '__main__':
chapter = 3
with ExerciseNum(1) as exercise_number:
exercise_triangle_number_probing()
print(caption(chapter, exercise_number), 'Fragment evaluation')
with ExerciseNum(2) as exercise_number:
evaluate_hashtable_sorted_chains()
print(caption(chapter, exercise_number),
'Hashtable with sorted linked list chains')
# To provide a full exercise, remove the "[:5000]" from below, otherwise takes too long for book.
with ExerciseNum(3) as exercise_number:
bad_timing(english_words()[:5000])
print(caption(chapter, exercise_number), 'ValueBadHash exercise')
with ExerciseNum(4) as exercise_number:
prime_number_difference(english_words())
print(caption(chapter, exercise_number), 'Prime Number exercise')
def generate_ch03():
"""Generate Tables and Figures for chapter 03."""
chapter = 3
# Starts without a formal figure number
from ch03.months import print_month
print_month('February', 2024)
with FigureNum(1) as figure_number:
description = 'Array containing month lengths interspersed with unneeded -1 values'
label = caption(chapter, figure_number)
(_, day_array) = search_for_base()
print('day_array =', day_array)
print('{}. {}'.format(label, description))
print()
with TableNum(1) as table_number:
process(generate_hash(),
chapter, table_number,
'Example hash() and hash code expressions for a table of size 15 (because of salting will be different from book)',
create_image=False)
with FigureNum(2) as figure_number:
description = 'Structure of Hashtable storage after adding five (key, value) entries'
label = caption(chapter, figure_number)
sample_hashtable()
print('{}. {}'.format(label, description))
print()
with TableNum(2) as table_number:
process(time_results_open_addressing(),
chapter, table_number,
'Average performance to insert N keys into a Hashtable of size M (in milliseconds)',
yaxis='Time (in microseconds)')
with FigureNum(3) as figure_number:
description = 'Structure of Hashtable linked list storage after adding five (key, value) pairs'
label = caption(chapter, figure_number)
sample_separate_chaining_hashtable()
print('{}. {}'.format(label, description))
print()
with FigureNum(4) as figure_number:
description = 'Removing the first node in a linked list'
label = caption(chapter, figure_number)
print('hand-drawn image')
print('{}. {}'.format(label, description))
print()
with FigureNum(5) as figure_number:
description = 'Removing any other node in a linked list'
label = caption(chapter, figure_number)
print('hand-drawn image')
print('{}. {}'.format(label, description))
print()
with TableNum(3) as table_number:
process(count_collisions(),
chapter, table_number,
'Average performance when inserting N=321,129 keys into a Hashtable of size M as M decreases in size')
with FigureNum(6) as figure_number:
description = 'For a fixed number of elements, N, the average and maximum chain length follow predictable paths'
label = caption(chapter, figure_number)
print('The result of plotting Table 3-3')
print('{}. {}'.format(label, description))
print()
with FigureNum(7) as figure_number:
description = 'Some entries can get "lost" if they are simply copied when M increases'
label = caption(chapter, figure_number)
sample_hashtable()
sample_separate_chaining_hashtable()
print('The above are original before resize.')
print('{}. {}'.format(label, description))
print()
with FigureNum(8) as figure_number:
description = 'Resulting Hashtable storage after successful resizing'
label = caption(chapter, figure_number)
sample_hashtable_resize()
sample_separate_chaining_hashtable_resize()
print('The above are original before resize.')
print('{}. {}'.format(label, description))
print()
print('The following table takes hours to generate. Remove arguments for full table shown in book.')
with TableNum(4) as table_number:
process(compare_dynamic_build_and_access_time(repeat=1, num=5),
chapter, table_number,
'Comparing growing tables against fixed-size construction',
yaxis = 'Time (in ms)')
with TableNum(5) as table_number:
process(count_hash(),
chapter, table_number,
'Words whose addition causes a resize event, with total # of insertions and average number of times a word was inserted')
print('Additional computations for perfect hashing for shakespeare example')
perfect_shakespeare_trial('a')
perfect_shakespeare_trial('by')
print('Additional computations for perfect hashing')
perfect_trial('by')
perfect_trial('watered')
perfect_trial('not-a-word')
with TableNum(6) as table_number:
process(iteration_order(),
chapter, table_number,
'Order of words returned by hashtable iterators',
create_image = False)
def generate_ch07():
"""Generate Tables and Figures for chapter 07."""
chapter = 7
with FigureNum(23) as figure_number:
description = 'Initialize dist_to[][] and node_from[][] based on G'
label = caption(chapter, figure_number)
DG_TABLE = nx.DiGraph()
DG_TABLE.add_edge('a', 'b', weight=4)
DG_TABLE.add_edge('b', 'a', weight=2)
DG_TABLE.add_edge('a', 'c', weight=3)
DG_TABLE.add_edge('b', 'd', weight=5)
DG_TABLE.add_edge('c', 'b', weight=6)
DG_TABLE.add_edge('d', 'b', weight=1)
DG_TABLE.add_edge('d', 'c', weight=7)
visualize_results_floyd_warshall_just_initialize(DG_TABLE)
print('{}. {}'.format(label, description))
print()
with FigureNum(24) as figure_number:
description = 'Changes to node_from[][] and dist_to[][] after k processes a and b'
label = caption(chapter, figure_number)
DG_TABLE = nx.DiGraph()
DG_TABLE.add_edge('a', 'b', weight=4)
DG_TABLE.add_edge('b', 'a', weight=2)
DG_TABLE.add_edge('a', 'c', weight=3)
DG_TABLE.add_edge('b', 'd', weight=5)
DG_TABLE.add_edge('c', 'b', weight=6)
DG_TABLE.add_edge('d', 'b', weight=1)
DG_TABLE.add_edge('d', 'c', weight=7)
visualize_results_floyd_warshall_two_steps(DG_TABLE)
print('{}. {}'.format(label, description))
print()
with FigureNum(1) as figure_number:
description = 'Modeling different problems using graphs'
print('by hand')
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(2) as figure_number:
description = 'An undirected graph of 12 vertices and 12 edges'
make_sample_graph()
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(3) as figure_number:
description = 'A graph modeling a rectangular maze'
label = caption(chapter, figure_number)
from ch07.viewer import Viewer
random.seed(15)
m = Maze(3, 5)
g = to_networkx(m)
postscript_output = '{}-graph.ps'.format(label)
if tkinter_error:
print('unable to generate {}'.format(postscript_output))
else:
root = tkinter.Tk()
canvas = Viewer(m, 50).view(root)
tkinter_register_snapshot(root, canvas, postscript_output)
root.mainloop()
# For obscure reasons, this must come AFTER root.mainloop()
if plt_error:
pass
else:
import matplotlib.pyplot as plt
pos = nx.get_node_attributes(g, 'pos')
nx.draw(g, pos, with_labels=True, node_color='w', font_size=8)
output_file = image_file('{}-graph.svg'.format(label))
plt.savefig(output_file, format="svg")
print('created {}'.format(output_file))
print('{}. {}'.format(label, description))
print()
with FigureNum(4) as figure_number:
description = 'Hitting a dead end while exploring a maze'
print('Hand drawn overlay to Figure 7-2.')
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(5) as figure_number:
from ch07.search import dfs_search, draw_solution
description = 'Depth First Search locates target if reachable from source'
label = caption(chapter, figure_number)
random.seed(15)
m = Maze(3, 5)
graph = to_networkx(m)
if plt_error:
print('unable to draw graph')
else:
draw_solution(graph, dfs_search(graph, m.start()), m.start(),
m.end())
output_file = image_file('{}-graph.svg'.format(label))
plt.savefig(output_file, format="svg")
print('created {}'.format(output_file))
print('{}. {}'.format(label, description))
print()
with FigureNum(6) as figure_number:
description = 'Breadth First Search will locate shortest path to target, if reachable from source'
print('Hand drawn overlay to Figure 7-2.')
label = caption(chapter, figure_number)
print('{}. {}'.format(label, description))
print()
with FigureNum(7) as figure_number:
description = 'Breadth First Search finds shortest path to each node'
label = caption(chapter, figure_number)
random.seed(15)
m = Maze(3, 5)
graph = to_networkx(m)
if plt_error:
print('unable to draw graph')
else:
draw_solution(graph, bfs_search(graph, m.start()), m.start(),
m.end())
output_file = image_file('{}-graph.svg'.format(label))
plt.savefig(output_file, format="svg")
print('created {}'.format(output_file))
print('{}. {}'.format(label, description))
print()
with FigureNum(8) as figure_number:
description = 'Comparing Depth First Search, Breadth First Search, and Guided Search'
label = caption(chapter, figure_number)
from ch07.solver_bfs import BreadthFirstSearchSolver
from ch07.solver_dfs import DepthFirstSearchSolver
from ch07.solver_guided import GuidedSearchSolver
random.seed(15)
m = Maze(13, 13)
if tkinter_error:
print('unable to generate {}'.format(postscript_output))
else:
root = tkinter.Tk()
bfs = BreadthFirstSearchSolver(root,
m,
15,
refresh_rate=0,
stop_end=True)
tkinter_register_snapshot(root, bfs.canvas,
'{}-BFS.ps'.format(label))
root.mainloop()
root = tkinter.Tk()
dfs = DepthFirstSearchSolver(root,
m,
15,
refresh_rate=0,
stop_end=True)
tkinter_register_snapshot(root, dfs.canvas,
'{}-DFS.ps'.format(label))
root.mainloop()
root = tkinter.Tk()
sfs = GuidedSearchSolver(root,
m,
15,
refresh_rate=0,
stop_end=True)
tkinter_register_snapshot(root, sfs.canvas,
'{}-Guided.ps'.format(label))
root.mainloop()
print(
'Generated BFS, DFS and Guided Postscript files for {}'.format(
label))
print('{}. {}'.format(label, description))
print()
with FigureNum(9) as figure_number:
description = 'Adjacency Matrix vs. Adjacency List representation'
label = caption(chapter, figure_number)
output_adjacency_matrix()
output_adjacency_list()
print('{}. {}'.format(label, description))
print()
with FigureNum(10) as figure_number:
description = 'Sample directed graph with 12 nodes and 14 edges.'
label = caption(chapter, figure_number)
make_sample_directed_graph()
print('{}. {}'.format(label, description))
print()
with FigureNum(11) as figure_number:
description = 'Sample spreadsheet with underlying directed graph.'
label = caption(chapter, figure_number)
print('Screen shots from Excel, together with graph from Figure 7-9')
print('{}. {}'.format(label, description))
print()
with FigureNum(12) as figure_number:
description = 'Visualizing execution of Depth First Search for Cycle Detection.'
label = caption(chapter, figure_number)
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
# In-text linear ordering
print_sample_linear_ordering()
print('Linear ordering of spreadsheet cells after Figure 12.')
print()
with FigureNum(13) as figure_number:
description = 'Visualizing execution of Depth First Search for Topological Sort.'
label = caption(chapter, figure_number)
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
with FigureNum(14) as figure_number:
description = 'Modeling highway infrastructure in Massachusetts.'
label = caption(chapter, figure_number)
(_, mapPositions, _) = tmg_load(highway_map())
(_, EAST, _, WEST) = bounding_ids(mapPositions)
output_file = generate_bfs_and_dijkstra_figure(WEST, EAST)
print('Generated {}'.format(output_file))
print('Augmented by hand in SVG')
print('{}. {}'.format(label, description))
print()
with FigureNum(15) as figure_number:
description = 'Modeling highway infrastructure in Massachusetts.'
label = caption(chapter, figure_number)
(_, mapPositions, _) = tmg_load(highway_map())
(_, EAST, _, WEST) = bounding_ids(mapPositions)
output_file = generate_dfs_figure(WEST, EAST)
print('Generated {}'.format(output_file))
print('Augmented by hand in SVG')
print('{}. {}'.format(label, description))
print()
with FigureNum(16) as figure_number:
description = 'The shortest path from a to c has accumulated total of 8'
label = caption(chapter, figure_number)
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
with FigureNum(17) as figure_number:
description = "Executing Dijkstra's algorithm on small graph"
label = caption(chapter, figure_number)
DG_GOOD = nx.DiGraph()
DG_GOOD.add_edge('a', 'b', weight=3)
DG_GOOD.add_edge('a', 'c', weight=9)
DG_GOOD.add_edge('b', 'c', weight=4)
DG_GOOD.add_edge('b', 'd', weight=2)
DG_GOOD.add_edge('d', 'c', weight=1)
visualize_dijkstra_small_graph(DG_GOOD)
print('{}. {}'.format(label, description))
print()
with FigureNum(18) as figure_number:
description = "A negative edge weight in the wrong place breaks Dijkstra's algorithm"
label = caption(chapter, figure_number)
DG_GOOD = nx.DiGraph()
DG_GOOD.add_edge('a', 'b', weight=3)
DG_GOOD.add_edge('a', 'c', weight=1)
DG_GOOD.add_edge('b', 'd', weight=-2) # THIS BREAKS IT
DG_GOOD.add_edge('c', 'd', weight=1)
try:
visualize_dijkstra_small_graph(DG_GOOD)
print('WARNING: ValueError should have occurred! WARNING WARNING!')
except ValueError:
print('Unable to relax from final "b" node')
print('{}. {}'.format(label, description))
print()
with FigureNum(19) as figure_number:
description = 'Two graphs with negative edge weights, but only one has a negative cycle'
label = caption(chapter, figure_number)
DG_GOOD = nx.DiGraph()
DG_GOOD.add_edge('a', 'b', weight=1)
DG_GOOD.add_edge('b', 'd', weight=-3)
DG_GOOD.add_edge('d', 'c', weight=5)
DG_GOOD.add_edge('c', 'b', weight=-1)
(dist_to, _) = bellman_ford(DG_GOOD, 'a')
print('Good Graph: shortest distance from a to b is {}'.format(
dist_to['b']))
DG_BAD = nx.DiGraph()
DG_BAD.add_edge('a', 'b', weight=1)
DG_BAD.add_edge('b', 'd', weight=-3)
DG_BAD.add_edge('d', 'c', weight=5)
DG_BAD.add_edge('c', 'b', weight=-4)
try:
(dist_to, _) = bellman_ford(DG_BAD, 'a')
print(
'WARNING: RuntimeError should have occurred! WARNING WARNING!')
except RuntimeError:
print('Bad Graph: Negative cycle exists in the graph.')
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
with FigureNum(20) as figure_number:
description = 'Example for all-pairs shortest path problem'
label = caption(chapter, figure_number)
DG_AP = nx.DiGraph()
DG_AP.add_edge('a', 'b', weight=4)
DG_AP.add_edge('b', 'a', weight=2)
DG_AP.add_edge('a', 'c', weight=3)
DG_AP.add_edge('b', 'd', weight=5)
DG_AP.add_edge('c', 'b', weight=6)
DG_AP.add_edge('d', 'b', weight=1)
DG_AP.add_edge('d', 'c', weight=7)
print(DG_AP.nodes())
print(DG_AP.edges(data=True))
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
with FigureNum(21) as figure_number:
description = 'Intuition behind the all-pairs shortest path problem'
label = caption(chapter, figure_number)
print('by hand')
print('{}. {}'.format(label, description))
print()
with FigureNum(22) as figure_number:
description = 'dist_to, node_from, and actual shortest paths for graph in Figure 7-20'
label = caption(chapter, figure_number)
DG_TABLE = nx.DiGraph()
DG_TABLE.add_edge('a', 'b', weight=4)
DG_TABLE.add_edge('b', 'a', weight=2)
DG_TABLE.add_edge('a', 'c', weight=3)
DG_TABLE.add_edge('b', 'd', weight=5)
DG_TABLE.add_edge('c', 'b', weight=6)
DG_TABLE.add_edge('d', 'b', weight=1)
DG_TABLE.add_edge('d', 'c', weight=7)
visualize_results_floyd_warshall(DG_TABLE)
print('{}. {}'.format(label, description))
print()
with FigureNum(23) as figure_number:
description = 'Initialize dist_to[][] and node_from[][] based on G'
label = caption(chapter, figure_number)
DG_TABLE = nx.DiGraph()
DG_TABLE.add_edge('a', 'b', weight=4)
DG_TABLE.add_edge('b', 'a', weight=2)
DG_TABLE.add_edge('a', 'c', weight=3)
DG_TABLE.add_edge('b', 'd', weight=5)
DG_TABLE.add_edge('c', 'b', weight=6)
DG_TABLE.add_edge('d', 'b', weight=1)
DG_TABLE.add_edge('d', 'c', weight=7)
visualize_results_floyd_warshall_just_initialize(DG_TABLE)
print('{}. {}'.format(label, description))
print()
with FigureNum(24) as figure_number:
description = 'Changes to node_from[][] and dist_to[][] after k processes a and b'
label = caption(chapter, figure_number)
DG_TABLE = nx.DiGraph()
DG_TABLE.add_edge('a', 'b', weight=4)
DG_TABLE.add_edge('b', 'a', weight=2)
DG_TABLE.add_edge('a', 'c', weight=3)
DG_TABLE.add_edge('b', 'd', weight=5)
DG_TABLE.add_edge('c', 'b', weight=6)
DG_TABLE.add_edge('d', 'b', weight=1)
DG_TABLE.add_edge('d', 'c', weight=7)
visualize_results_floyd_warshall_two_steps(DG_TABLE)
print('{}. {}'.format(label, description))
print()
with FigureNum(25) as figure_number:
description = 'Sample Maze to defeat Guided Search'
label = caption(chapter, figure_number)
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
with FigureNum(26) as figure_number:
description = 'Sample directed, acyclic graph for single-source, shortest path optimization'
label = caption(chapter, figure_number)
print('Done by hand.')
print('{}. {}'.format(label, description))
print()
def generate_ch02():
"""Generate tables/figures for chapter 02."""
chapter = 2
with TableNum(1) as table_number:
process(actual_table(), chapter, table_number,
'Prototype runtime performance')
with TableNum(2) as table_number:
process(
prototype_table(), chapter, table_number,
'Comparing different mathematical models against actual performance'
)
with TableNum(3) as table_number:
process(large_multiplication(), chapter, table_number,
'Multiplying two n-digit integers')
with FigureNum(1) as figure_number:
print('Excel plot')
print(caption(chapter, figure_number),
'Compare models against performance')
with FigureNum(2) as figure_number:
algorithms_x_y()
print(caption(chapter, figure_number),
'Performance of algorithms X and Y on different computers')
with FigureNum(3) as figure_number:
print('Excel plots')
print(caption(chapter, figure_number),
'Visualizing the numbers from Figure 2-2')
with TableNum(4) as table_number:
process(growth_table(), chapter, table_number,
'Growth of different computations')
with FigureNum(4) as figure_number:
print('by hand')
print(caption(chapter, figure_number), 'Doors of destiny!')
with FigureNum(5) as figure_number:
print('by hand')
print(caption(chapter, figure_number),
'Searching for 53 in a sorted array that contains the value.')
with FigureNum(6) as figure_number:
print('by hand')
print(
caption(chapter, figure_number),
'Searching for 17 in a sorted array that does not contain the value.'
)
with FigureNum(7) as figure_number:
print('by hand')
print(caption(chapter, figure_number),
'All complexity classes are arranged in dominance hierarchy')
with FigureNum(8) as figure_number:
print(
caption(chapter, figure_number),
'Runtime performance plotted against problem instance size for complexity classes'
)
A=list(range({}))
random.shuffle(A)'''.format(n),
repeat=10,
number=10))
tbl.row([n, m_merge, m_slice])
return tbl
#######################################################################
if __name__ == '__main__':
chapter = 5
with ExerciseNum(1) as exercise_number:
print('find count() in ch05.recursion')
print(caption(chapter, exercise_number), 'Recursive count method')
print()
with ExerciseNum(2) as exercise_number:
print('find num_swaps() in ch05.challenge')
print(caption(chapter, exercise_number),
'Compute number of swaps in array with 0 .. N-1')
print()
with ExerciseNum(3) as exercise_number:
from ch05.recursion import find_max_with_count
print('how many comparisons to find max in array of size N=15:',
find_max_with_count(list(range(15)))[0], 'or N-1')
print()
with ExerciseNum(4) as exercise_number:
return 1
binomial = scipy.special.comb(2**k - 2, 2**(k - 1) - 1)
return binomial * (counting(k - 1)**2)
for n in range(1, 8):
print(n, counting(n))
#######################################################################
if __name__ == '__main__':
chapter = 6
with ExerciseNum(1) as exercise_number:
print('find count() in ch05.challenge')
print(caption(chapter, exercise_number), 'Recursive count method')
print()
with ExerciseNum(2) as exercise_number:
print('A binary tree that only has right children.')
print(caption(chapter, exercise_number),
'What binary tree has O(N) to find two largest?')
print()
with ExerciseNum(3) as exercise_number:
print('RankBinaryTree in ch06.challenge')
print(caption(chapter, exercise_number), 'select() and rank() methods')
print()
with ExerciseNum(4) as exercise_number:
num_perfect_balanced_sequences()