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Data Structures & Algorithms in Python
 Data Structures & Algorithms in
Python

John Canning
Alan Broder
Robert Lafore

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ISBN-13: 978-0-13-485568-4
ISBN-10: 0-13-485568-X
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Pearson’s Commitment to
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 To my mother, who gave me a thirst for knowledge, to my father, who
taught me the joys of engineering, and to June, who made it possible to
pursue both.

John Canning

For my father Sol Broder, a computer science pioneer, who inspired me to

follow in his footsteps.

To my mother Marilyn Broder, for showing me the satisfaction of teaching

others.

To Fran, for making my life complete.

Alan Broder
 Contents
1. Overview

2. Arrays

3. Simple Sorting

4. Stacks and Queues

5. Linked Lists

6. Recursion

7. Advanced Sorting

8. Binary Trees

9. 2-3-4 Trees and External Storage

10. AVL and Red-Black Trees

11. Hash Tables

12. Spatial Data Structures

13. Heaps

14. Graphs

15. Weighted Graphs

16. What to Use and Why

Appendix A. Running the Visualizations

Appendix B. Further Reading

Appendix C. Answers to Questions

 Table of Contents
1. Overview
What Are Data Structures and Algorithms?
Overview of Data Structures
Overview of Algorithms
Some Definitions
Programming in Python
Object-Oriented Programming
Summary
Questions
Experiments

2. Arrays
The Array Visualization Tool
Using Python Lists to Implement the Array Class
The Ordered Array Visualization Tool
Python Code for an Ordered Array Class
Logarithms
Storing Objects
Big O Notation
Why Not Use Arrays for Everything?
Summary
Questions
Experiments
Programming Projects

3. Simple Sorting
How Would You Do It?
Bubble Sort
Selection Sort
nsertion Sort
Comparing the Simple Sorts
Summary
Questions
Experiments
Programming Projects

4. Stacks and Queues

Different Structures for Different Use Cases
Stacks
Queues
Priority Queues
Parsing Arithmetic Expressions
Summary
Questions
Experiments
Programming Projects

5. Linked Lists
Links
The Linked List Visualization Tool
A Simple Linked List
Linked List Efficiency
Abstract Data Types and Objects
Ordered Lists
Doubly Linked Lists
Circular Lists
terators
Summary
Questions
Experiments
Programming Projects
6. Recursion
Triangular Numbers
Factorials
Anagrams
A Recursive Binary Search
The Tower of Hanoi
Sorting with mergesort
Eliminating Recursion
Some Interesting Recursive Applications
Summary
Questions
Experiments
Programming Projects

7. Advanced Sorting
Shellsort
Partitioning
Quicksort
Degenerates to O(N2) Performance
Radix Sort
Timsort
Summary
Questions
Experiments
Programming Projects

8. Binary Trees
Why Use Binary Trees?
Tree Terminology
An Analogy
How Do Binary Search Trees Work?
Finding a Node
nserting a Node
Traversing the Tree
Finding Minimum and Maximum Key Values
Deleting a Node
The Efficiency of Binary Search Trees
Trees Represented as Arrays
Printing Trees
Duplicate Keys
The BinarySearchTreeTester.py Program
The Huffman Code
Summary
Questions
Experiments
Programming Projects

9. 2-3-4 Trees and External Storage

ntroduction to 2-3-4 Trees
The Tree234 Visualization Tool
Python Code for a 2-3-4 Tree
Efficiency of 2-3-4 Trees
-3 Trees
External Storage
Summary
Questions
Experiments
Programming Projects

10. AVL and Red-Black Trees

Our Approach to the Discussion
Balanced and Unbalanced Trees
AVL Trees
The Efficiency of AVL Trees
Red-Black Trees
Using the Red-Black Tree Visualization Tool
Experimenting with the Visualization Tool
Rotations in Red-Black Trees
 nserting a New Node
Deletion
The Efficiency of Red-Black Trees
-3-4 Trees and Red-Black Trees
Red-Black Tree Implementation
Summary
Questions
Experiments
Programming Projects

11. Hash Tables

ntroduction to Hashing
Open Addressing
Separate Chaining
Hash Functions
Hashing Efficiency
Hashing and External Storage
Summary
Questions
Experiments
Programming Projects

12. Spatial Data Structures

Spatial Data
Computing Distances Between Points
Circles and Bounding Boxes
Searching Spatial Data
Lists of Points
Grids
Quadtrees
Theoretical Performance and Optimizations
Practical Considerations
Further Extensions
Summary
Discovering Diverse Content Through
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Koburg and Rudolstadt were also visited by a plague in 1626, while
towns in the vicinity of the latter, Königssee, Schwarza, Tanna, and
Schleiz, had 707, 129, 195, and 181 deaths respectively. The
neighbouring town of Pössnek in the year 1625 had already lost
1,000 inhabitants. Jena and Weimar both suffered, while there were
228 deaths in Gera and 1,100 deaths in Zeitz due to pestilence. Many
other places in Thuringia that suffered from plagues are not
mentioned here.
That part of Saxony which corresponds to the modern province of
Saxony fared in much the same way as Thuringia, while those parts
bordering directly on the kingdom of Saxony were relatively less
severely attacked. A plague broke out in Eilenburg in September
1625, and carried away many persons there and in the surrounding
country. At Delitsch (west of Eilenburg) a dangerous fever (febris
maligna—probably typhus fever) spread through the wandering
armies, and before the beginning of autumn carried away 150
persons. In the winter the disease subsided a little, but broke out
again in June 1626, and carried away 880 people—in September
alone there were 229 deaths, and numerous families were completely
wiped out. A plague also raged in the vicinity of Halle; not until the
following year, however, did it break out in the city itself, whither it
was borne by Imperialist soldiers, and where it caused, from June to
December, 3,400 deaths. In Eisleben (east of Halle) a plague began
in May 1626, and carried away 30 to 50 people daily, so that the total
number of deaths for the year was 3,068. Merseburg lost 341
inhabitants in the year 1626, and a plague raged in Naumburg in the
years 1625–6. The town of Querfurt (west of Merseburg) in 1625 was
for seven weeks the quarters of 3,000 of Wallenstein’s soldiers; they
brought dysentery with them, and the result was that 200 citizens
died. In the second half of the following year a plague broke out and
carried away 1,400 inhabitants of the city (including 200 soldiers)
and numerous inhabitants of the surrounding country. The town and
vicinity of Sangershausen were also severely attacked; the pestilence
began in the town in June 1626, and reached its climax in September
with 570 deaths—1,323 deaths, all told, are recorded in the church
register for that year, but the figure is said to be too small. Lammert
mentions sixteen surrounding villages in which a total of 2,960
deaths occurred in the year 1626. In Sondershausen 54 people died
up to the end of July of that year, 36 in August, 137 in September,
and 143 in October; the mortality then decreased, but not until 466
persons had died, 400 of them in consequence of the plague. In the
near-by towns of Frankenhausen and Langensalza the number of
deaths was 915 and 913 respectively, the latter town having been
visited by a plague the year before. Nordhausen, from January 1,
1626, to December 6, 1626, lost 3,283 inhabitants—2,504 natives
and 779 refugees from other places. In Stolberg (north-east of
Nordhausen) a plague broke out on June 27, 1626, and caused 623
deaths. Quedlinburg, Aschersleben, and Halberstadt were also
attacked; in Aschersleben a plague broke out on June 15, 1625, and
between then and the end of the year carried away 157 persons. The
total number of deaths in the year 1625 was 534, in the following
year 1,800 (1,066 in consequence of the plague), not including the
soldiers; the years 1627–9 had a remarkably low mortality. In 1626 a
plague carried away 549 persons in Gröningen (near Halberstadt).
The cities on the Elbe and the surrounding country were severely
attacked; a pestilence broke out in Dessau on September 3, 1625, and
between then and the end of the year 224 persons were buried—399
in the entire year. The disease reappeared in the summer of the
following year, having caused 662 deaths, while only 39 died in the
year following. In Aiken-on-the-Elbe (below Dessau) 1,000 persons,
including soldiers, succumbed to a plague in the year 1626. In the
cities on the Saale, above its confluence with the Elbe, a plague raged
furiously; in Bernburg it appeared in the second half of the year 1625,
carrying away 1,340 persons in that year (the number of deaths in
the following year being 425); Kalbe was also severely attacked. A
plague broke out in Magdeburg at the end of June 1625, and lasted
well into the next year; the wealthy citizens fled from the city, but
were compelled to return by the approach of the Imperialists, and
the result was that several thousand inhabitants died. The country to
the south-west of Magdeburg, as far as Bode, suffered severely—
Osterweddingen, Wanzleben, Gross-Salze, Förderstedt, Egeln,
Wolmirsleben, and other places. Several soldiers quartered in
Förderstedt had succumbed to a plague in June and July 1626, and
had infected the citizens with the disease, which carried away 155 of
them. A plague broke out in Egeln in October 1625, and reached its
climax in February 1626; from January until August 16 of that year
296 persons died there. In Unseberg, which had been infected in
August 1625, some 400 citizens and soldiers were buried in the year
1626, in addition to many who were secretly buried in gardens,
thickets, and fields. The plague raged with particular fury in August
1626; in Volmirstadt 246 persons died between July 6 and October
1626—144 in September alone.
In Lower Saxony, in the region between the Elbe and the Weser,
most of which to-day belongs to Hanover, a plague raged virulently
in the years 1625–7. In Osterode, whither numerous country people
had fled from the approaching war, a very severe pestilence broke
out; in the Saint Aegidius community alone 1,500 persons died,
among them many outsiders. In Klausthal 1,350, in Andreasberg
700, in Einbeck 3,000, and in Hameln 1,143 people succumbed to
bubonic plague and ‘head disease’. In Goslar, where the pestilence
had appeared in 1625, conditions were rendered particularly bad by
the fact that many wounded Imperialists were brought there after the
battle of Barenberg (near Lutter—August 27, 1626); most of these
soldiers died there, 3,000 deaths due to pestilence having occurred
in Goslar in the years 1625–6. Wallenstein’s soldiers also brought
pestilence with them to Helmstedt (in the region of Brunswick); here
one-third of the citizens died, and 295 houses were rendered
tenantless. The university faculty fled several times to Brunswick, the
students either going home or enlisting in the army. This plague did
not come to an end for two years. The surrounding villages,
furthermore, were severely attacked by it; during the siege of
Göttingen by Tilly (June to August 12, 1626) it became very
widespread, since the city was overcrowded with fugitives. From 50
to 60 persons were buried every day. In near-by Dransfeld 700
people died, in Wolfenbüttel 1,705. In Hanover, where a plague had
already broken out in the year 1625, a reappearance of it in March
1626 drove out the garrison. The severity of this plague, which
carried away 3,000 people, was increased by the numerous fugitives
in the city; about one-third of the population survived. In the city of
Nienburg, which was besieged by the Imperialists after the battle of
Barenberg, a pestilence likewise broke out among the inhabitants
and in the garrison. In Lüneburg it lasted from 1625 to 1628, and in
Osnabrück from August 1625 to the end of the year.
In the years 1625–6 Wallenstein’s soldiers carried pestilence into
the region north of Magdeburg; in Neuhaldensleben 76 persons were
carried away between the end of August and the first of the year, not
including those who were buried secretly. The following year it
demanded a considerably larger number of victims—583; the
maximum was in June—147. In the Altmark (north-eastern part of
the province of Saxony) dysentery, bubonic plague, and typhus fever
broke out almost everywhere during the years 1625–8. Dysentery
appeared in the Danish garrison at Tangermünde and carried away
1,600 people, and on June 29, 1626, the Danes withdrew from the
place. Stendal was also visited by a plague after the departure of the
Danes; it broke out in July, and in a few months caused 2,511 deaths,
the normal mortality being 280–290. Numerous bodies were
secretly buried, while many peasants who had fled to the city were
among the dead; thus the total number of deaths was estimated at
5,000. In Osterburg 624 people died in the years 1626–8, and in
Bismark 163 persons died in the year 1626. In the city of Havelberg
668 persons succumbed to dysentery, ‘head-disease’, and bubonic
plague, the latter alone carrying away about 400. A pestilence was
conveyed to Gardenlegen by the soldiers of Count George of
Brunswick, who had his head-quarters there; the number of deaths
there in the year 1626 amounted to no less than 1,514. In Salzwedel
335 persons died in the year 1625, and 451 in the following year, the
plague being responsible for 400 of the latter. In Seehausen
dysentery first appeared, and soon gave way to ‘war-plague’ (typhus
fever), which lasted until 1628; some 200 of the soldiers quartered
there died, and as many as 1,100 inhabitants.
Brandenburg also suffered, particularly in the south-eastern part,
when Wallenstein’s army, in pursuit of Count Mansfeld, turned into
Silesia; there were 386 deaths in Luckau, 900 in Kottbus, 500 in
Forst, 112 in Spremberg, and 902 in Jüterbog.
Further north, plagues were considerably less widespread in the
years 1625–6. In 1625 typhus fever broke out severely in Lübeck and
the surrounding country, carrying away 6,952 people, while in
Bremen, which had had cases of plague in 1625, a widespread
outbreak in 1627 carried away some 10,000 people, natives and
refugees. Mecklenburg, being further away from the scene of the war,
suffered somewhat less. In the year 1625 bubonic plague, ‘head-
disease’, and dysentery appeared in Rostock, Wismar, Schwerin,
Plau, and New Brandenburg. In the following year a plague broke out
in Parchim, reached its climax in May, and lasted until November,
carrying away 1,600 persons. In Flensburg a plague broke out during
the occupation of the Imperialists (1627) and lasted until their
departure (1630).
The pestilences of the year 1627 were not very widespread, and
this applies also to the territory in Saxony and Thuringia which had
suffered so severely in the years 1625–6. On the other hand, the
countries in the northern part of Germany, particularly Pomerania
and Schleswig-Holstein, were severely attacked in those years, owing
to the fact that Wallenstein had transferred thither the scene of the
war. In the year 1628 Hamburg had taken in a great many foreign
fugitives, and the result was that typhus fever soon broke out in the
city and carried away many thousands of people. The war brought
great misery into North Friesland and the Frisian Islands; the
Imperialists and Danes oppressed the people by enforced quartering
and extortions of all kinds, and the result was famine and plague,
lasting until 1630. In Stade, which Tilly in 1629 had made his head-
quarters, both the inhabitants and the garrison suffered terribly from
a severe epidemic of dysentery. In the city of Schleswig a plague
broke out in September, and again in November, in consequence of
the quartering of Imperialist troops; it devastated the entire city, so
that 211 houses stood absolutely empty on Christmas Day, 1628.
Mecklenburg was revisited in 1629, and on August 13 of that year a
plague broke out in Rostock and Teterow. Imperialist soldiers
conveyed pestilence to the city of Plau, where they passed the night
of November 29; but in 1630 it appeared in a much more severe form
there and carried away 600 people. In the year 1630 a plague broke
out in Mecklenburg, and in Gustrow one raged from May 7 to the
beginning of September.
In the years 1628–9 Pomerania was ravaged by the Imperialists,
with resulting pestilence and famine. Greifswald suffered for four
years from a pestilence which reached its climax in the year 1631.
Grimmen, Stargard (3,500 deaths in the years 1627–30),
Freienwalde, and other places were also attacked. In Greifenberg,
where soldiers had been quartered in large numbers, it raged with
unusual fury; three-fourths of the city were devastated, and when the
Swedes arrived only 42 houses were uninfected. Kolberg (on the
Persante) in six months lost 3,000 inhabitants in consequence of a
pestilence. On account of the oppression caused by the war, many
citizens fled from Koslin, which, despite the decrease in population,
lost 919 inhabitants in the year 1630. In Stolp 800 people died in
consequence of a plague.
A plague was borne into Silesia in July 1623, and in Bunzlau an
average of thirty persons per week died; of 760 deaths in the year,
640 were due to the pestilence. Many adults fled to near-by villages
and died there. In the following year a plague broke out again in
Bunzlau, but as only 130 people died there in 1625, it seemed as
though the pestilence was over. In September and October, 1626,
however, it broke out again, and of 228 deaths that occurred that
year, 149 were directly attributable to the plague. In July 1624 it
appeared in Friedeberg and carried away 51 persons. In Löwenberg it
began in September 1624; the citizens fled from the city and set up
tents in the fields, but in spite of this, from forty to fifty people died
every day, and the total number of deaths for the year was some
3,000. In the year 1625 the pestilence was very widespread in Silesia
—Hirschberg, Löwenberg, Herzogswaldau, Liegnitz, Neumarkt,
Waldenburg, Neisse, and other places were attacked. In Breslau
‘head-disease’ raged from June to the end of that year, carrying away
3,000 people; 1626 was also a year of pestilence for Breslau. In
Neustadt (Governmental District of Oppeln) a pestilence raged with
particular fury from May till September 1625; for the years 1624 to
1627 the deaths were respectively 198, 420, 175, and 472. On August
21, 1626, an army of 6,000 Imperialists under Count von Merode
encamped at Goldberg; most of them were infected with disease; and
after their departure a plague broke out with such severity that a
large part of the population died.
During this time, from 1625 to 1630, when epidemics were raging
almost everywhere in North Germany, South Germany also suffered,
since diseases were often brought there by Imperialist troops and
wandering rabble. In the year 1626 Württemberg alone lost 28,000
people in consequence of plagues.[31] A pestilence in Augsburg (1628)
became very widespread and caused 9,000 deaths. In the year 1629
‘head-disease’ broke out in Württemberg and Alsace. During the
isolation of the city of Hanau (from December 6, 1629, to March 12,
1630) by the Imperialist commander Witzleben, a pestilential
disease, which the soldiers had brought with them, broke out and
caused many deaths throughout the entire vicinity.
 III. The War Years 1630–40

1. North Germany until the Peace of Prague

In the year 1630 began in Saxony—in the wake of marching troops

—that deadly pestilence which soon spread over all Germany and
was chiefly responsible for the enormous loss of human life there in
the course of the Thirty Years’ War. We may safely assume that
bubonic plague was the most common disease, although both typhus
fever and dysentery were of frequent occurrence. In the years 1630–1
the pestilence was confined for the most part to North Germany; the
Electorate of Saxony suffered the worst, 934,000 people, according
to the reports, having died there in consequence of the war and of
diseases.[32]
The pestilence broke out in Leipzig in October 1630, and carried
away 301 persons; it was borne there presumably by two foreign
orange-pedlars. In October of the following year it broke out again,
when the Imperialists, after besieging the city for several weeks, on
September 13 had finally captured it. The number of deaths in the
entire year was 1,754. In the year 1632 Leipzig was once more the
scene of grave warlike events, and was compelled to live through a
second siege by Wallenstein; the plague began in June, became very
widespread in August, and from then till October caused a great
many deaths, the total number for the year amounting to 1,390. In
August 1633, Leipzig was again besieged, and this likewise caused
the outbreak of a plague which lasted until December and carried
away 761 persons; in 1634 it was apparently over, for of 306 deaths
that are recorded for that year, only 24 were attributable to the
plague. In the years 1636–7, however, it reappeared with great
severity throughout the entire city. The country surrounding Leipzig
suffered a great deal in the year 1633, which was the worst plague-
year that Saxony passed through. In the year 1632 Altenburg was
occupied by the Swedes, who were infected with some pestilential
disease, the germ of which they left behind them when they withdrew
on January 13, 1633. The disease spread rapidly, acquired a virulent
character, and carried away 2,104 persons, among them many
foreign refugees. Grimma and Borna were severely attacked in 1633,
while Wurzen suffered less severely.
The country north-east of Leipzig suffered severely from plagues in
1631. After the battle of Breitenfeld (September 15, 1631) most of the
wounded were brought to Eilenburg, where in a few weeks a plague
broke out and spread so rapidly that 300 people died in the month of
October alone. After an abatement during the winter, it
recommenced in 1632; the number of deaths for that year was 670,
although only 492 of them were due to the plague, while the disease
did not entirely disappear until 1636. The city of Belgern, after it was
plundered by Holk’s troops on October 1, 1632, was visited by a
plague; also Dommitsch, Oschatz (where 563 deaths occurred in
1631, and many more in 1633–4), and Ortrand (where there were
800 deaths in the years 1631–3). Plagues raged very frequently in
Leisnig, Colditz, and Mittweida, and in the villages and towns
surrounding them. In February 1631, Palatinate, Imperialist, and
League troops quartered in Leisnig, and the result was that ‘head-
disease’ and bubonic plague became very widespread; in the
following year they reappeared, causing 443 deaths, while many
thousands are said to have died in the country districts. The same
was true of the year 1633. A pestilence broke out in Colditz in the
year 1631, and in the following year ‘soldier’s disease’ (typhus fever)
was brought there by Swedish troops, while in 1633 bubonic plague
caused 567 deaths. Mittweida suffered from plague in the years
1631–4, 243 persons dying there in the year 1634. In the year 1630 a
very severe plague broke out in Freiberg; 1,147 people died in the
course of the year, 1,000 of them in consequence of the disease. In
the following year there were 124 more deaths. In the autumn of
1632 pestilence raged so furiously that several thousand people died
in a short time—about one-third of the population. Most of the
bodies were buried secretly, only about 3,000 regular funerals taking
place. In the year 1633 there were 1,632 interments, not including
those buried in secret. The plague affected the entire vicinity of
Freiberg and spared scarcely a single village; many places were left
empty and deserted.
In Chemnitz 1,234 interments for the year 1632 are recorded in the
church register, and in the following year the plague raged even more
furiously: almost every house was attacked, and the number of
deaths amounted to 2,500. In Glauchau and vicinity, as in all
Saxony, 1633 was the worst year; 964 people died there in that year.
The plague raged most furiously from August to November, and
lasted until 1634; many bodies were found in the open fields. In the
neighbouring Waldenburg 392 people died in a few weeks in 1633, in
Lichtenstein 370, in Thurm 400. In Marienberg, a village lying at the
foot of the mountains, 1,000 people succumbed in the year 1633 to
typhus fever; the plague spread into the Erzgebirge and caused 2,300
deaths in Schneeberg and 157 deaths in the adjacent Neustädtle. A
plague had already broken out in Zwickau in 1632, and in the first
part of 1633 it became so severe that 1,500 people died in two
months in the summer of that year. The city was full of sick people
and dead bodies, and the number of reported deaths for the year
1633 was 1,897; but the total number of deaths, excluding the
soldiers, is said to have been no less than 6,000. Entire streets were
devastated. Many of the inhabitants fled to near-by villages, and thus
spread the infection. Crimmitschau was visited by a plague in 1630
(601 deaths), and again in 1633 (409 deaths); 92 families in the last-
named year were completely wiped out. Many neighbouring places
were also attacked; there were 700 deaths in Werdau, 300 in
Steinpleiss, 150 in Königswalde, &c.
The invasion of Holk caused Vogtland to suffer terribly in August
of the year 1632, while his second invasion in the summer of 1633
resulted in an even worse outbreak of disease. In Reichenbach and
vicinity, typhus fever, bubonic plague, and dysentery prevailed in the
year 1633; at first it was called ‘soldier’s disease’, and later ‘bright
plague’ (helle Pest). Of 904 deaths that occurred that year, 785 were
due to the plague. In Plauen the number of deaths in 1633 was 1,748,
in Oelsnitz 325 (217 due to the plague). Holk himself succumbed to
the plague in Adorf on August 30, 1633, while 1,000 of his troops
also died.
The eastern part of Saxony was also attacked. In Dresden a plague
broke out in 1632 and carried away numerous people; it continued to
rage in the following year, since the war prevented the adoption of
the usual measures of precaution. In the year 1632 the number of
Protestants buried by the church was 3,129, and in the following year
it was 4,585. Numerous families were wiped out, and many houses
were rendered tenantless. In the year 1634 one half of the
inhabitants fell victims to the pestilence, while a large part of the city
was devastated in 1635. Since the reports of E. J. J. Meyer and of the
town council continually speak of ‘swellings’, the disease was no
doubt bubonic plague.[33] In Dippoldiswalde (south-west of Dresden)
it raged so furiously in the years 1631–3 that entire families were
wiped out; in those years there were 189, 510, and 250 deaths
respectively. Pirna is said to have lost 4,000 inhabitants in
consequence of the plague in the years 1632–4, while Dittersdorf
(south of Pirna) lost 405 inhabitants in the year 1632. The pestilence
was borne by Saxon troops to Sebnitz (south-east of Dresden). In
Stolpen it raged from 1632 to 1634. In October 1631 the Croats
brought pestilence to Bischofswerda, and more than 200 persons
died in consequence of it. In March 1632 another pestilence broke
out there, carrying away 660 persons, so that more than one-third of
the houses stood empty. In the year 1631 there were 1,000 deaths in
Camenz. In Bautzen there was a garrison of 500 men, almost all of
whom died in the year 1631; including the residents that were carried
away by the pestilence, the number of deaths there for that year was
about 1,000. Nor did the pestilence disappear from Bautzen the
following year.
Lusatia was also the scene of pestilence; only a few places were
spared, and in Upper Lusatia 40,000 persons are said to have been
carried away by pestilences in the years 1631–3. In the last part of
September 1631, dysentery and bubonic plague broke out in Görlitz,
which had a Saxon garrison, and carried away some 400 persons
(excluding the soldiers) between then and the end of the year. In
June 1632 there was a second outbreak of plague; it reached its
climax in October, and carried away 6,105 people (including 106
soldiers) in the course of the entire year. In the following year 726
inhabitants and 435 soldiers succumbed to the disease. Zittau
suffered severely; as early as 1633 several hundred soldiers and
inhabitants succumbed to typhus fever, while in the year 1632
‘burning fever’, dysentery, and bubonic plague appeared and carried
away 1,246 persons (according to other reports, 1,642 persons).
Petechial fever and bubonic plague, after a period of inactivity in the
winter, recommenced in the first part of 1633; the latter disease
reached its climax in September, carrying away 1,860 inhabitants in
that year, in addition to many Imperialist soldiers. From October to
December, 1634, Saxon and Brandenburg soldiers, after their return
from Bohemia, encamped near Zittau, where various diseases soon
broke out; the result was that hundreds died, and the entire region
became infected.
The Province of Brandenburg was severely attacked by a plague in
the year 1631, but in the next year suffered considerably less owing to
the fact that the scene of the war was transferred to other parts of
Germany. In Berlin 777 people succumbed to a plague in the year
1630, while in the following year it reappeared in a much severer
form and carried away 2,066 persons. In Spandau, after the capture
of the city by the Swedes on May 6, 1631, famine and pestilence
broke out and caused 1,500 deaths. A plague in Potsdam caused 457
deaths between June and December, 1631. Neuruppin, in February of
that year, after the occupation of the District of Ruppin by Tilly,
suffered from a severe pestilence. Dysentery and ‘head-disease’ broke
out in Rathenow in 1631, reached a climax in July, and carried away
662 people (not including those buried in secret). In Prenzlau 1,500
persons, about one-fourth of the population, died in the year 1631,
while Havelberg had 227 deaths, Lindow 400, and Kyritz (after the
soldiers had quartered there) 231. Frankfurt-on-the-Oder, which had
been occupied by the Imperialists, on April 13, 1631, was captured by
Gustavus Adolphus, whereupon a severe epidemic broke out and
carried away entire families in the course of a few days; the alleged
number of deaths was 6,000. Müncheberg (north-west of Frankfurt),
Quilitz, Drossen, and Guben were also attacked; there were 365
deaths in Quilitz and 2,000 in Drossen. In the year 1634, when the
Imperialists once more devastated the Electorate of Saxony, a severe
plague broke out in Luckau, whither many country people had fled;
the spread of the disease is said to have been favoured by the fact
that the soldiers broke into and robbed the closed houses of the dead.
In Seftenberg (near Kalau) a plague broke out in 1630 and carried
away 305 persons that year; it remained there until 1633, and spread
to many near-by villages.
Silesia, after the devastation caused by the pestilences of the years
1624–7, had a few years of rest. In the year 1632, however, infection
was brought there from Saxony, though only to a limited extent. On
August 1, 1632, Lauban was obliged to surrender to the Saxon
garrison, so that for ten days the city and the surrounding country
were crowded with troops; the result was that after their departure a
severe epidemic broke out and between July and December carried
away 1,400 persons. In the very next year severe plagues broke out
all over Silesia, when Wallenstein appeared there for the purpose of
driving out the Saxons and Swedes. The plague raged so furiously in
Silesia that the armies were almost entirely exterminated, and whole
communities were wiped out. Golgau, Bunzlau (and vicinity),
Greiffenberg, and Friedeberg were attacked. An epidemic of typhus
fever carried away 500 people in Hirschberg in the year 1632, and in
the following year it became much more widespread and carried
away 2,600 persons. ‘The infected persons are said to have looked
very red, like drunkards, and to have died suddenly.’ Almost the
entire population of Landshut died in the year 1633. Goldberg
(south-west of Liegnitz) had been plundered by Wallenstein’s
soldiers on October 4 and 5, 1633, and on October 10 Colonel Sparre
quartered 200 ‘badly infected’ soldiers there; the result was that a
severe pestilence broke out in the city. In August of the year 1633
such a severe pestilence broke out in Liegnitz that it was impossible
to bury the victims in the regular way; deep, broad ditches were dug,
and from 100 to 200 bodies laid in them. From August 14 to
December 22 the number of deaths is said to have been 5,794.
Breslau, which at that time had upwards of 40,000 inhabitants, was
visited by a plague in September 1633; in the Protestant parishes
13,231 people died in that year, in the Catholic 4,800. Neumarkt
(north-west of Breslau) had 1,400 deaths in the same year, while in
Brieg, which had a Swedish garrison, there were 3,439 deaths. The
city of Schweidnitz suffered terribly; 30,000 soldiers under
Wallenstein and 25,000 Swedish soldiers were encamped there, and
the plague was so severe that 8,000 of the former and 12,000 of the
latter are said to have died. In the city itself, which was harbouring
innumerable fugitives from the surrounding country, sick people and
dead bodies soon filled all the streets; on August 25 alone, 300
people died. The number of the dead, including from 2,000 to 3,000
that were buried secretly, and also the outsiders, was 16,000 to
17,000; more than two-thirds of the population are said to have
succumbed. The pestilence was borne from Schweidnitz to
Peterswaldau and Nimptsch, where from 2,000 to 2,400 persons
died. On May 31, 1633, Wallenstein came with his army to Glatz,
bringing pestilence with him; in Glatz itself 4,284 people were
carried away, while many hundreds died in the surrounding country.
Petschkau was almost completely wiped out. In Neisse the number of
victims is estimated at 6,000; 5,272 are recorded in the church
registers.
Generally speaking, Thuringia was but slightly affected by plagues
in the years 1631–3, but suffered terribly in the years 1634–5; for in
those years there, as in all Germany, a great famine prevailed. In
Koburg a plague broke out in the year 1630; in 1632 there was an
epidemic of ‘head-disease’, which carried away 300 persons in
October alone, and in 1634 an epidemic of bubonic plague, rendered
even more destructive by famine, carried away 1,143 victims. Several
pestilences (dysentery and ‘burning fever’) also broke out in the
Koburg region, caused by the quartering and ravaging of Swedish
troops; the inhabitants died by hundreds. Hildburghausen suffered
from a plague from June on; whereas only 106 people had died there
from January to May, the number of deaths in June alone was 215.
In the following year 534 people died there from starvation and
pestilence, while 169 died in near-by Streufdorf. Eisfeld (west of
Hildburghausen) in 1632 had been plundered by Swedish troops,
and from that time on suffered from pestilence. In Meiningen, in the
latter part of 1635 and the first part of 1636, 500 people succumbed
to a plague (106 in November alone). Suhl, which on October 16 had
been burned by Isolani’s soldiers, and Themar—both near Meiningen
—had 1,634 deaths. In the following year 519 people died in
Schmalkalden and vicinity—250 in Tambach, 300 in Vachdorf, and
1,600 in Salzungen. In the year 1634 the number of deaths in
Eisenach was 1,800, and in the following year 1,600; in the year 1636
there were only 405 deaths there. Erfurt suffered very little in 1635,
while Ohrdruf had 1,065 deaths, Wechmar 503, and Arnstadt 464. In
Weimar 1,600 people died in the year 1635, among them 500
foreigners from Franconia who had taken refuge there. The cities
lying further east in Thuringia had been severely attacked in the
years 1632 and 1633, in consequence of the pestilences in Saxony; for
example, Gera, which had been infected in 1633 by Holk’s troops, the
near-by village of Untermhaus, which in the two years had 211 and
600 deaths respectively, and also many other villages in the
surrounding country. A plague in Schleiz carried away 600 persons
in the year 1632.
 In Rhineland and Westphalia pestilences broke out only
sporadically in the years 1630–4, but in 1635 they became more
general. In the year 1630 Münster was attacked, in 1631 Arnsberg,
and in 1632 a pestilence raged furiously in the Berg country—in
Lennep, for example, where the Imperialist troops were for a long
time quartered. In Mühlheim-on-the-Rhine a pestilential disease
broke out after the departure of the Nassau-Lorraine garrison in
1631. In the year 1632 the Imperialist and Swedish armies stood
facing each other in Westphalia for six weeks, and the result was an
outbreak of pestilence; 600 people succumbed to it in Bielefeld. In
1635 a pestilence raged furiously along the Rhine; in St. Goar 200
people died in the course of the summer. In that year Westphalia was
the scene of warlike events and pestilences; Arnsberg, the villages on
the Ruhr, Soest, Unna (near Hamm), Horstmar, and Kroesfeld were
attacked. The Governmental District of Düsseldorf (on the left bank
of the Rhine) was severely attacked by pestilence; many people died
in Geldern, while there were 389 deaths in Strälen, 256 in Nieukert,
and 700 in Lobberich.

2. South Germany

(a) Bavaria and Upper Swabia

After the battle of Breitenfeld (September 17, 1631) Gustavus

Adolphus passed through Halle and Erfurt to Würzburg,
Aschaffenburg, and Frankfurt-on-the-Main. Tilly had marched
through Halberstadt, Fulda, and Miltenberg to Würzburg, in order to
relieve that city, which had been captured by the Swedes, and then
turned south. Thus the principal scene of the war was transferred to
Bavaria, which from 1631 to 1634 suffered terribly from the ravages
of the soldiers passing back and forth. No part of the country was
spared. ‘The Thirty Years’ War’, says Lammert,[34] ‘was particularly
fatal and disastrous to Bavaria from the year 1632 on; it converted
the country into an uninhabited waste, especially because it was
followed by pestilence. Like the Imperialist army under Tilly in the
autumn of 1631, so the Swedish army on its marches consumed
everything it found, and wherever it went in the years 1632–5 it
spread ‘hunger typhus’ and ‘war typhus’ and bubonic plague; all the
places along the Main lost at least one-half of their population.’ In
September 1632, when Gustavus Adolphus withdrew from
Nuremberg, Wallenstein turned south, and there on November 6,
1632, Gustavus Adolphus was killed in the battle of Lützen. After that
Wallenstein returned to Bohemia, while the Swedes under Bernhard
von Weimar marched back into Bavaria. The acme of misery was
reached here in the year 1634. It is impossible to enumerate all the
places that were infected by the brutalized, wandering soldiers; the
most out-of-the-way and indigent regions, such as the Spessart and
the Odenwald, were visited by them, and inasmuch as they brought
pestilence wherever they went, the unfortunate villages were
subjected to merciless devastation.
1. The region of the Main. Since Gustavus Adolphus first had Horn
occupy the bishopric of Bamberg, and himself marched through
Aschaffenburg to Nuremberg, while Tilly returned to Ingolstadt and
later to Lech, the region of the Main, and later the region north of the
Danube, were the first to be attacked by typhus fever and bubonic
plague; not until later, from 1633 on, did the pestilences spread more
or less extensively in the country south of the Danube.
In Aschaffenburg and vicinity a plague broke out in the summer of
1632 and almost wiped out several villages; the city of Aschaffenburg
itself, which lost a large percentage of its inhabitants, was revisited in
the year 1635. In Würzburg the pestilence began in August 1632, and
in the last part of July of the following year another serious
pestilence broke out there, in consequence of which 489 bodies were
buried in the cathedral parish alone. The prolonged quartering of
troops, notwithstanding all the precautionary measures that were
adopted, caused the pestilence to rage with extraordinary fury; not
until September did it begin to abate. In the year 1635, when infected
soldiers were transferred from Schweinfurt to the stronghold of
Marienburg, it appeared once more. In 1632 Schweinfurt lost ‘several
hundred people’ in consequence of ‘pestilential purple-spots’ (typhus
fever). The total number of deaths was 1,055. In December of the
following year another rather large pestilence broke out, and again in
August 1635; in the latter year it reached a climax in September and
came to an end in December. In Bamberg many people succumbed in
1632 to Hungarian disease, which the Swedes had borne thither in
the spring. This disease was also very widespread throughout the
entire vicinity. In the year 1634 the Swedes came several times into
the region around Bamberg and plundered the country, so that
famine and plague caused great misery. In the summer of 1635
Bamberg was once more attacked by an infectious disease (typhus
fever), and only two houses in the city were spared. In Kulmbach the
plague raged extensively in the first part of the year 1633; the
number of the dead was so large that the bodies could not all be
buried in Kulmbach, and some had to be taken to the churchyards of
near-by villages. In the following year the plague broke out anew,
carrying away 60 persons in a single day. In Bayreuth 400 persons
succumbed to a pestilence in the year 1632, and in the following year
360 died; it raged even more furiously after the city was plundered
by the Master of Ordnance, von der Waal, on August 19, 1634. From
July to October 1,927 out of 7,000 inhabitants died, while the
average number of deaths amounted to only 167 per annum.
2. The region between the Main and the Danube suffered no less.
Nuremberg and vicinity was severely attacked by pestilence in the
year 1632. In the summer of that year Wallenstein encamped near
Fürth, and Gustavus Adolphus near Nuremberg; they watched each
other for a long time without venturing a battle. The country people
had all fled to the city. In the Swedish army and in the overcrowded
city, which had some 50,000 inhabitants, scurvy and typhus fever
carried away many thousands.[35] Only 4,522 bodies were buried by
the Church, but many more thousands died. Two weeks after his
disastrous attack on Wallenstein’s camp on September 4, Gustavus
Adolphus marched south, while Wallenstein turned into Saxony. The
plague continued to rage in the vicinity of Nuremberg, and many
people contracted the disease by visiting the deserted camp of the
Imperialist army and appropriating the left-behind implements,
weapons, and kitchen utensils. Scurvy was still raging in Nuremberg
in the following year. In the year 1634 the plague broke out and
carried away 18,000 persons. In December 1631 Forchheim was
besieged by the Swedes under General Horn, and the result was that
a pestilence broke out in the year 1632 and carried away 578
inhabitants; the average number of deaths per annum was 45. In
March of that year the Swedes had deserted the city, and in June
1634, when they reappeared there, the mortality increased again. In
the years 1631–2 Uffenheim suffered a great deal from the predatory
raids of the Swedes and also from plague, which in the year 1634
became very widespread there as in all Bavaria, carrying away one-
half of the inhabitants of the town. While the Swedes and
Imperialists were establishing their camps near Nuremberg, many
people from Ansbach and other places fled to Windsheim, which
thus became greatly overcrowded; the consequence was that people
died there by the hundred, and their bodies were buried, thirty or
forty at a time, in large ditches. When the Swedes left Nuremberg
and appeared in Windsheim, they left behind them 450 men who
were infected with disease; in the entire year 1,564 bodies were
counted. In the following year the city was besieged by the
Imperialists (October 12–23, 1633), and during this time 360
persons succumbed to a pestilential disease; the number of deaths in
the entire year, including the outsiders, was 1,600. Windsheim also
suffered greatly in the two following years; at the end of the year
1635 there were only 50 inhabitants left. In near-by Burgbernheim,
where typhus fever raged in the year 1630, 155 persons died in the
year 1632, 165 in 1634, and 107 in 1636. In Schwabach, which had
been plundered by the Imperialists in the latter part of July, 1632,
various diseases broke out—‘Hungarian disease, dysentery, and even
bubonic plague.’ In the year 1633 there were 298 deaths in
Weissenburg; in 1634, on the other hand, there were 642. Eichstätt
had 494 deaths in the year 1632, 827 in 1633, and 982 in 1634; in the
last year the town was besieged and captured by the Swedes, and for
a few days thereafter pestilences raged furiously. The country
districts throughout Central Franconia, like these cities, were almost
completely depopulated by flight and pestilence.
The Upper Palatinate was also severely attacked by pestilence
(typhus fever and bubonic plague), which spread far into the
Bavarian Forest. In Amberg an epidemic of typhus fever and
dysentery broke out in the year 1633, and in April of the following
year bubonic plague appeared; the latter disease carried away from
15 to 20 persons on many days of that month, while in July and
August as many as 40 people died every day. In the spring of 1634
Weiden became infected with typhus fever and shortly after that with
bubonic plague; from August 17 to November 6, some 1,800 people
died. The bodies were corded up like piles of wood, placed in ditches
in groups of 200 and 300, and covered with quick-lime. In
Schwandorf (north of Regensburg) the Imperialists had encamped in
the summer of 1634; after their departure a pestilence characterized
by ‘swellings and large unknown spots’ broke out and carried away
almost one-third of the inhabitants. In Hemau (north-west of
Regensburg), after the Swedes had passed through the town, ‘the
malignant pestilence’ (typhus fever) had broken out in the year 1633;
and in 1634, after the devastations committed by the troops of
Bernhard von Weimar, bubonic plague appeared and carried away
one-half of the inhabitants.
3. The cities on the Danube. In the year 1632 Neuburg was
occupied by the Swedes; after their departure, on October 18, an
epidemic of Hungarian head-disease broke out and carried away
many soldiers and citizens (more than 900 in eight months). Again
in the two following years pestilence caused great devastation. On
April 29, 1632, the Swedes appeared before Ingolstadt, but in a few
days withdrew; there was a strong garrison in the city, however, and
many fugitives had gathered there. In this overcrowded population
typhus fever broke out and carried away large numbers of people. In
the following year the disease became even more widespread, and
1,039 people succumbed to it before the end of November. In the
first part of the year 1635 the pestilence abated. In the second half of
the year 1634 Regensburg was attacked by bubonic plague, and
despite all measures of precaution it carried away two-thirds of the
population (according to other reports there were 3,125 deaths). The
entire vicinity suffered from the plague. The mortality in Straubing
during the siege of the Imperialists (March 1634) increased greatly;
even in the year before it had been very high (294 deaths). The total
number of deaths in the year 1634 is not known, but of three
parishes St. Jacob’s alone had 631 burials. Deggendorf and Passau
fared similarly.
4. Upper Bavaria and Lower Bavaria south of the Danube. On May
17, 1632, Gustavus Adolphus had occupied Munich, and during his
short sojourn of three weeks apparently no epidemic diseases made
their appearance among the Swedes. But since typhus fever had
broken out everywhere in the vicinity, strict measures of precaution
were adopted by the city authorities. According to G. von Suttner[36]
124 people in the quarantine-house before the Schwabinger Tor
succumbed to ‘burning fever and headache’ between August and the
end of the year. According to a report published in 1632 the poor
people suffered in particular, while red spots, continual headache,
and later on diarrhoea, characterized the disease. A very severe
pestilence broke out in Munich in the year 1634. ‘The epidemic was
caused’, says Seitz,[37] ‘by the arrival of 4,000 Spanish soldiers in July
of the year 1634; they were called there from Tölz and Weilheim
when the Duke of Saxe-Weimar and General Horn were threatening
the city. Although shortly after that, in August, a few evidences of
disease were noticed, it was not regarded as infectious. Finally,
however, a real plague broke out with such fury that four lazarets and
a garden outside of the city had to be made ready for the care of the
sick. It raged most furiously in the months of October and
November, when from 200 to 250 dwellings, among them entire
houses, were quarantined every week. Thus it went on until the end
of December.’ Unfortunately there exists no medical description of
the disease, the most important characteristics of which were chills,
accompanied by internal fever, violent headaches, great lassitude,
haemorrhage, plague-spots, and swellings. All told, some 15,000
persons are said to have died in the year 1634—about one-half of the
total population of the city. The bodies of victims became so
numerous that they were piled up in the streets and houses, without
attempt to keep a record of the names, and buried in ditches forty at
a time. Strict isolation of the patients by closing up the houses was
enforced, and the use of the clothes and bedding of the dead was
forbidden under severe penalties; such effects were burned outside
of the gates. Only two gates remained open, and in front of one of
them a garden was made ready to receive strangers who were denied
admittance into the city. In February 1635, the pestilence had almost
entirely ceased, but in September it broke out anew and did not
disappear until February 1637.
In the years 1633–4 typhus fever and bubonic plague were spread
throughout all Upper and Lower Bavaria by the continued
marauding of the Swedes. The Imperialists, no less than the Swedes,
helped to devastate the country, while the Spanish soldiers had the
worst reputation of all. Again in the year 1635, especially in the
autumn, the pestilence appeared. A plague broke out in Freising after
the town was plundered by the Swedes on July 16, 1634 (Landshut
had already been captured by them on May 10, 1632), and after their
departure they left behind them an infectious disease which was
diagnosed by the town-physician as Hungarian fever. A pestilence
broke out in the city when it was plundered by the soldiers under
Bernhard von Weimar, on July 10, 1634, and carried away one-third
of the inhabitants; according to a list furnished by the court the
number of deaths was 738, but there were many more with whose
legacies the court had nothing to do. The bodies were piled up on
wagons and conveyed to cemeteries, while the dwellings of diseased
persons were closed. In Dingolfing, which was occupied by the
Swedes from July 22, 1633, to June 1634, a plague raged with such
fury that it was thought the city would be completely wiped out.
Simbach-on-the-Inn and the near-by market-town of Thann suffered
greatly from a plague in the year 1634. In Thann many bodies lay for
a long time in the houses unburied, while entire families among the
poorer population were wiped out of existence. The plague also raged
in the surrounding localities, and many bodies lay in the streets as
food for scavenger birds. A plague raged in the years 1633–4 in
Traunstein, which had already had a few isolated cases of disease in
the previous year; 123 people died terrible deaths in the two years
mentioned, and also in the years 1635–6. In the year 1634 a
pestilence caused 500 deaths in Rosenheim, while severe outbreaks
of pestilence were reported from many surrounding places—Aibling,
Miesbach, Wasserburg, and Tegernsee.
In Tölz twenty-seven adults succumbed in May and June 1633, to
Hungarian disease; a pestilence also broke out in the spring of 1634
and carried away hundreds of people in the months of May, June,
and July. From July on, the church-registers contain no more
entries; the patients with black swellings usually had but a few hours
to live. In Oberammergau ‘wild headache’ raged in the years 1631
and 1633, and many people succumbed to it. In September 1634, the
town became infected with bubonic plague, and up to October 28,
eighty-four people succumbed to the disease—about one-fifth of the
population. The epidemic caused the people to vow that they would
produce the Passion Play there every ten years. Murnau, Weilheim,
and other places were severely attacked in the year 1634. In Andechs
the mortality was increased in the year 1634 by an outbreak of
dysentery and typhus fever, and on July 27 bubonic plague also
appeared and remained until November, carrying away 200 of the
500 inhabitants of the town. In Landsberg typhus fever broke out
very seriously in the year 1630. ‘All over the bodies of the people who
contracted the disease’, says Lammert,[38] ‘red spots appeared, and
then the victims lost control of themselves and knocked their heads
against the walls. Many who seemed scarcely to have contracted the
disease died suddenly. Dead bodies were found everywhere, even in
public squares.’ In the following year the disease spread even further;
the vicinity of Landsberg was infected by the soldiers, who were
constantly marching back and forth. After the terrible plundering of
the city in April and September of the year 1633, a plague broke out
and carried away a large proportion of the few inhabitants that were
left.
5. The governmental district of Swabia fared no better than the
aforesaid Bavarian countries, while the region on the northern side
of the Lake of Constance suffered terribly from the predatory raids of
the Swedes and the consequent epidemics. In Augsburg, which from
April 1632 to 1635 was occupied by the Swedes, the suffering began
when the city was besieged by the Imperialists. During a siege of
seven months (September 1634 to March 1635) famine and
pestilence did a great deal more damage among the population than
the bullets and swords of the enemies. Whereas this population
numbered from 70,000 to 80,000 in the year 1624, by October 12,
1635, it had dwindled to 16,422. After the city had surrendered to the
Imperialists, people still continued to die in consequence of
pestilential diseases; the town council therefore gave orders on July
7, 1635, that all refuse should be removed from the city. Not until the
winter did the pestilence disappear. In Memmingen there were 1,200
deaths in 1633, and 1,400 deaths in the following year; the worst year
was 1635, when the pestilence is said to have carried away 3,000
persons. The towns surrounding the city were also severely attacked.
In Kempten, which was oppressed by the Swedes and Imperialists in
the years 1632–3, a pestilence broke out in the year 1634 and lasted
well into the next year, carrying away 3,000 people. In the
surrounding country, pestilence raged so furiously that many places
were completely wiped out. In the near-by towns of Kaufbeuren,
Immenstadt, Pfronten, Füssen, &c., the pestilence was likewise very
widespread; in 1635 there were 1,600 deaths in Füssen—about one-
quarter of the inhabitants.
The predatory incursions of the Swedes extended even to the Lake
of Constance. In the year 1634 the number of deaths in Lindau was
800; at the beginning of the year 1633 Weingarten, Wangen, and