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DATE 2017-02-01

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MESSAGE
DATE 2017-02-24
FROM Christopher League
SUBJECT Re: [Learn] decision making tree for a euler walk
From learn-bounces-at-nylxs.com Fri Feb 24 22:13:30 2017
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From: Christopher League
To: Ruben Safir , "learn\-at-nylxs.com"
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Subject: Re: [Learn] decision making tree for a euler walk
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Here's my Euler calculation, in my weird FP-influenced C++ style
(although it definitely uses mutable state). IMO it's usually a mistake
to make bunches of classes with elaborately interconnected pointers --
if the data structure can be represented in terms of maps and sets, then
just use maps and sets. Object-oriented programming is mostly a bankrupt
paradigm.

The referenced `assertions.hh` and `debug-log.hh` are available here:


Enjoy.

CL

~~~~ {.cpp}
#include
#include
#include
#include
#include
#include "assertions.hh"
#define LOG_LEVEL LOG_TRACE
#include "debug-log.hh"
using namespace std;

// Represent an undirected graph using hash maps and sets. The vertex
// type can be anything that supports equality and hashing.
template
struct graph {
void add_edge(vertex v1, vertex v2);
void remove_edge(vertex v1, vertex v2);
int degree(vertex v);
vector euler_path();
ostream& show(ostream&);
private:
typedef unordered_multiset neighbors;
typedef unordered_map> adjancency_map;
adjancency_map adjacency_map;
void add_directed(vertex v1, vertex v2);
void remove_directed(vertex v1, vertex v2);
};

// Print the graph's adjacency list
template
ostream& graph::show(ostream& out)
{
for(typename adjancency_map::iterator i =3D adjacency_map.begin();
i !=3D adjacency_map.end();
i++)
{
out << i->first << ':';
for(typename neighbors::iterator j =3D i->second.begin();
j !=3D i->second.end();
j++)
{
out << ' ' << *j;
}
out << '\n';
}
return out;
}

template
ostream& operator << (ostream& out, graph& g)
{
return g.show(out);
}

// Add an undirected edge.
template
void graph::add_edge(vertex v1, vertex v2)
{
add_directed(v1, v2);
add_directed(v2, v1);
}

// Add directed edge (private).
template
void graph::add_directed(vertex v1, vertex v2)
{
typename adjancency_map::iterator i =3D adjacency_map.find(v1);
if( adjacency_map.end() =3D=3D i) {
adjacency_map[v1] =3D neighbors{v2};
} else {
i->second.insert(v2);
}
}

// Remove undirected edge.
template
void graph::remove_edge(vertex v1, vertex v2)
{
remove_directed(v1, v2);
remove_directed(v2, v1);
}

// Remove directed edge (private). A little tricky because just doing
// .erase(v2) removes *all* the matching vertices from the multiset.
// Using find then .erase in the iterator solves that.
template
void graph::remove_directed(vertex v1, vertex v2)
{
typename neighbors::iterator i =3D adjacency_map.at(v1).find(v2);
adjacency_map.at(v1).erase(i);
}

// Return the degree of given vertex.
template
int graph::degree(vertex v)
{
return adjacency_map.at(v).size();
}

// Calculate and return an euler path. Algorithm basically taken from
// here: http://www.graph-magics.com/articles/euler.php
//
// NOTE: this is destructive -- it removes edges from the graph. So if
// you need the graph afterwards, make a copy.
template
vector graph::euler_path()
{
// If all vertices have even degree, choose any of them.
typename adjancency_map::iterator i =3D adjacency_map.begin();
vertex curr =3D i->first;
// If there are exactly 2 vertices having an odd degree: choose one
// of them. This will be the current vertex.
unsigned num_odd =3D 0;
for( ; i !=3D adjacency_map.end(); i++) {
if(degree(i->first) % 2 =3D=3D 1) {
num_odd++;
curr =3D i->first;
}
}
log(LOG_INFO, "There were " << num_odd << " odd-degree vertices.");
vector path;
stack stack;
if(num_odd !=3D 2 && num_odd !=3D 0) {
log(LOG_ERROR, "Sorry, no Euler path exists.");
return path;
}
log(LOG_DEBUG, "Starting at " << curr << '\n' << *this);
// Repeat until the current vertex has no more neighbors and the
// stack is empty.
while(degree(curr) > 0 || stack.size() > 0) {
// If current vertex has no neighbors,
if(degree(curr) =3D=3D 0) {
log(LOG_DEBUG, "* Adding " << curr << " to path.");
// Add it to path
path.push_back(curr);
// Remove the last vertex from the stack and set it as the
// current one.
curr =3D stack.top();
stack.pop();
log(LOG_DEBUG, " New curr is " << curr);
}
else {
// Add the vertex to the stack
log(LOG_DEBUG, "* Pushing " << curr << " to stack.");
stack.push(curr);
// Take any of its neighbors, remove the edge between selected
// neighbor and that vertex, and set that neighbor as the
// current vertex
typename neighbors::iterator n =3D adjacency_map.at(curr).begin();
log(LOG_DEBUG, " Removing " << curr << " <-> " << *n);
remove_edge(curr, *n);
curr =3D *n;
log(LOG_TRACE, *this);
}
}
path.push_back(curr);
return path;
}

// Grr why isn't this just in the standard library I have to write it
// every damn time.
template
ostream& operator << (ostream& out, const vector& vec)
{
for(unsigned i =3D 0; i < vec.size(); i++) {
if(i > 0) {
out << ", ";
}
out << vec.at(i);
}
return out;
}

graph rubensburg_demo()
{
// Set up graph
graph g;
g.add_edge('A','B');
g.add_edge('A','B');
g.add_edge('A','E');
g.add_edge('A','F');
g.add_edge('A','G');
g.add_edge('B','E');
g.add_edge('B','F');
g.add_edge('C','D');
g.add_edge('E','C');
g.add_edge('E','G');

assert_eq(5, g.degree('A'));
assert_eq(2, g.degree('G'));
assert_eq(1, g.degree('D'));

return g;
}

graph even_degree_demo()
{
graph g;
g.add_edge(13, 16);
g.add_edge(13, 18);
g.add_edge(16, 18);
assert_eq(2, g.degree(13));
assert_eq(2, g.degree(16));
assert_eq(2, g.degree(18));
return g;
}

// This is the actual K=C3=B6nigsberg graph, for which no Euler path
// exists.
graph impossible_demo()
{
graph g;
g.add_edge("austin", "baltimore");
g.add_edge("austin", "baltimore");
g.add_edge("austin", "dallas");
g.add_edge("baltimore", "chicago");
g.add_edge("baltimore", "chicago");
g.add_edge("baltimore", "dallas");
g.add_edge("chicago", "dallas");
return g;
}

int main()
{
cout << "=3D=3D=3D=3D=3D=3D=3D Even-degree test\n";
graph g0 =3D even_degree_demo();
cout << g0.euler_path() << '\n';

cout << "=3D=3D=3D=3D=3D=3D=3D Odd-degree test\n";
graph g1 =3D rubensburg_demo();
cout << g1.euler_path() << '\n';

cout << "=3D=3D=3D=3D=3D=3D=3D Impossible test\n";
graph g2 =3D impossible_demo();
cout << g2.euler_path() << '\n';

return 0;
}
~~~~

--=-=-=
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable






1.0, user-scalable=3Dyes">




Here=E2=80=99s my Euler calculation, in my weird FP-influenced C++ style=
(although it definitely uses mutable state). IMO it=E2=80=99s usually a mi=
stake to make bunches of classes with elaborately interconnected pointers =
=E2=80=93 if the data structure can be represented in terms of maps and set=
s, then just use maps and sets. Object-oriented programming is mostly a ban=
krupt paradigm.


The referenced assertions.hh and debug-log.hh =
are available here: master/include" class=3D"uri">https://gitlab.liu.edu/cs691s17/public/tree/m=
aster/include


Enjoy.


CL


ceCode cpp">#include <iostr=
eam>

#include <unordered_map>=

#include <unordered_set>=

#include <vector>
#include <stack>
#include "assertions.hh&q=
uot;

#define LOG_LEVEL LOG_TRACE
#include "debug-log.hh&qu=
ot;

using namespace std;

// Represent an undirected graph using hash maps and set=
s. The vertex

// type can be anything that supports equality and hashi=
ng.

template<typename ve=
rtex>
struct graph {
void add_edge(vertex v1, vertex v2);
void remove_edge(vertex v1, vertex v2);
int degree(vertex v);
vector<vertex> euler_path();
ostream& show(ostream&);
private:
typedef unordered_multiset<vertex> neighb=
ors;
typedef unordered_map<vertex, unordered_mult=
iset<vertex>> adjancency_map;
adjancency_map adjacency_map;
void add_directed(vertex v1, vertex v2);
void remove_directed(vertex v1, vertex v2);
};

// Print the graph's adjacency list
template<typename ve=
rtex>
ostream& graph<vertex>::show(ostream& out)
{
for(typename adjancen=
cy_map::iterator i =3D adjacency_map.begin();
i !=3D adjacency_map.end();
i++)
{
out << i->first << ':'n>;
for(typename neig=
hbors::iterator j =3D i->second.begin();
j !=3D i->second.end();
j++)
{
out << ' ' << *j;
}
out << '\nan>';
}
return out;
}

template<typename ve=
rtex>
ostream& operator << (ostream& out,=
graph<vertex>& g)
{
return g.show(out);
}

// Add an undirected edge.
template<typename ve=
rtex>
void graph<vertex>::add_edge(vertex v1, ver=
tex v2)
{
add_directed(v1, v2);
add_directed(v2, v1);
}

// Add directed edge (private).
template<typename ve=
rtex>
void graph<vertex>::add_directed(vertex v1,=
vertex v2)
{
typename adjancency_map::iterator i =3D adjacen=
cy_map.find(v1);
if( adjacency_map.end() =3D=3D i) {
adjacency_map[v1] =3D neighbors{v2};
} else {
i->second.insert(v2);
}
}

// Remove undirected edge.
template<typename ve=
rtex>
void graph<vertex>::remove_edge(vertex v1, =
vertex v2)
{
remove_directed(v1, v2);
remove_directed(v2, v1);
}

// Remove directed edge (private). A little tricky becau=
se just doing

// .erase(v2) removes *all* the matching vertices from t=
he multiset.

// Using find then .erase in the iterator solves that.span>
template<typename ve=
rtex>
void graph<vertex>::remove_directed(vertex =
v1, vertex v2)
{
typename neighbors::iterator i =3D adjacency_ma=
p.at(v1).find(v2);
adjacency_map.at(v1).erase(i);
}

// Return the degree of given vertex.
template<typename ve=
rtex>
int graph<vertex>::degree(vertex v)
{
return adjacency_map.at(v).size();
}

// Calculate and return an euler path. Algorithm basical=
ly taken from

// here: http://www.graph-magics.com/articles/euler.php<=
/span>
//
// NOTE: this is destructive -- it removes edges from th=
e graph. So if

// you need the graph afterwards, make a copy.
template<typename ve=
rtex>
vector<vertex> graph<vertex>::euler_path()
{
// If all vertices have even degree, choose any of the=
m.

typename adjancency_map::iterator i =3D adjacen=
cy_map.begin();
vertex curr =3D i->first;
// If there are exactly 2 vertices having an odd degre=
e: choose one

// of them. This will be the current vertex.
unsigned num_odd =3D 0>;
for( ; i !=3D adjacency_map.end(); i++) {
if(degree(i->first) % 2=
=3D=3D 1) {
num_odd++;
curr =3D i->first;
}
}
log(LOG_INFO, "There were " << =
num_odd << " odd-degree vertices.">);
vector<vertex> path;
stack<vertex> stack;
if(num_odd !=3D 2 &am=
p;& num_odd !=3D 0) {
log(LOG_ERROR, "Sorry, no Euler path exists.&qu=
ot;
);
return path;
}
log(LOG_DEBUG, "Starting at " <<=
; curr << '\n=
' << *this);
// Repeat until the current vertex has no more neighbo=
rs and the

// stack is empty.
while(degree(curr) > 0pan> || stack.size() > 0) {
// If current vertex has no neighbors,
if(degree(curr) =3D=3D 0span>) {
log(LOG_DEBUG, "* Adding " <&l=
t; curr << " to path.");
// Add it to path
path.push_back(curr);
// Remove the last vertex from the stack and set i=
t as the

// current one.
curr =3D stack.top();
stack.pop();
log(LOG_DEBUG, " New curr is " &=
lt;< curr);
}
else {
// Add the vertex to the stack
log(LOG_DEBUG, "* Pushing " <&=
lt; curr << " to stack.");
stack.push(curr);
// Take any of its neighbors, remove the edge betw=
een selected

// neighbor and that vertex, and set that neighbor=
as the

// current vertex
typename neighbors::iterator n =3D adjacenc=
y_map.at(curr).begin();
log(LOG_DEBUG, " Removing " <=
< curr << " <-> " <&l=
t; *n);
remove_edge(curr, *n);
curr =3D *n;
log(LOG_TRACE, *this);
}
}
path.push_back(curr);
return path;
}

// Grr why isn't this just in the standard library I=
have to write it

// every damn time.
template<typename T&=
gt;
ostream& operator << (ostream& out,=
const vector<T>& vec)
{
for(unsigned i =3D pan class=3D"dv">0
; i < vec.size(); i++) {
if(i > 0) {
out << ", ";
}
out << vec.at(i);
}
return out;
}

graph<char> rubensburg_demo()
{
// Set up graph
graph<char> g;
g.add_edge('A','=
B'
);
g.add_edge('A','=
B'
);
g.add_edge('A','=
E'
);
g.add_edge('A','=
F'
);
g.add_edge('A','=
G'
);
g.add_edge('B','=
E'
);
g.add_edge('B','=
F'
);
g.add_edge('C','=
D'
);
g.add_edge('E','=
C'
);
g.add_edge('E','=
G'
);

assert_eq(5, g.degree('A=
'
));
assert_eq(2, g.degree('G=
'
));
assert_eq(1, g.degree('D=
'
));

return g;
}

graph<int> even_degree_demo()
{
graph<int> g;
g.add_edge(13, 16);
g.add_edge(13, 18);
g.add_edge(16, 18);
assert_eq(2, g.degree(13an>));
assert_eq(2, g.degree(16an>));
assert_eq(2, g.degree(18an>));
return g;
}

// This is the actual K=C3=B6nigsberg graph, for which n=
o Euler path

// exists.
graph<string> impossible_demo()
{
graph<string> g;
g.add_edge("austin", t">"baltimore");
g.add_edge("austin", t">"baltimore");
g.add_edge("austin", t">"dallas");
g.add_edge("baltimore", =3D"st">"chicago");
g.add_edge("baltimore", =3D"st">"chicago");
g.add_edge("baltimore", =3D"st">"dallas");
g.add_edge("chicago", st">"dallas");
return g;
}

int main()
{
cout << "=3D=3D=3D=3D=3D=3D=3D Even-degree =
test
\n";
graph<int> g0 =3D even_degree_demo();
cout << g0.euler_path() << 'an class=3D"sc">\n
';

cout << "=3D=3D=3D=3D=3D=3D=3D Odd-degree t=
est
\n";
graph<char> g1 =3D rubensburg_demo();
cout << g1.euler_path() << 'an class=3D"sc">\n
';

cout << "=3D=3D=3D=3D=3D=3D=3D Impossible t=
est
\n";
graph<string> g2 =3D impossible_demo();
cout << g2.euler_path() << 'an class=3D"sc">\n
';

return 0;
}




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  28. 2017-02-16 ruben <ruben-at-mrbrklyn.com> Subject: [Learn] chew on this
  29. 2017-02-16 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] ct scan
  30. 2017-02-16 Christopher League <league-at-contrapunctus.net> Subject: [Learn] Should I name "makefile" or "Makefile"?
  31. 2017-02-20 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] overloading operator== and casting
  32. 2017-02-20 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Vector Documentation
  33. 2017-02-22 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Network Patterns
  34. 2017-02-24 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] decision making tree for a euler walk
  35. 2017-02-24 Christopher League <league-at-contrapunctus.net> Re: [Learn] decision making tree for a euler walk
  36. 2017-02-24 Christopher League <league-at-contrapunctus.net> Re: [Learn] decision making tree for a euler walk
  37. 2017-02-24 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] decision making tree for a euler walk
  38. 2017-02-27 Ruben Safir <ruben-at-mrbrklyn.com> Subject: [Learn] Computational Phylogenies and fossil scanning
  39. 2017-02-28 Christopher League <league-at-contrapunctus.net> Re: [Learn] decision making tree for a euler walk
  40. 2017-02-28 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] decision making tree for a euler walk
  41. 2017-02-28 Nicholas Rodin <nikbbwil-at-icloud.com> Re: [Learn] thesis update
  42. 2017-02-28 Ruben Safir <mrbrklyn-at-panix.com> Re: [Learn] thesis update
  43. 2017-02-28 Don Brinkman <Don.Brinkman-at-gov.ab.ca> Re: [Learn] visit
  44. 2017-02-28 Ruben Safir <ruben-at-mrbrklyn.com> Re: [Learn] [Hangout-NYLXS] Peer Review

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