I am given a filled array of size WxH and need to create a new array by scaling both the width and the height by a power of 2. For example, 2x3 becomes 8x12 when scaled by 4, 2^2. My goal is to make sure all the old values in the array are placed in the new array such that 1 value in the old array fills up multiple new corresponding parts in the scaled array. For example:
old_array = [[1,2],
[3,4]]
becomes
new_array = [[1,1,2,2],
[1,1,2,2],
[3,3,4,4],
[3,3,4,4]]
when scaled by a factor of 2. Could someone explain to me the logic on how I would go about programming this?
It's actually very simple. I use a vector of vectors for simplicity noting that 2D matrixes are not efficient. However, any 2D matrix class using [] indexing syntax can, and should be for efficiency, substituted.
#include <vector>
using std::vector;
int main()
{
vector<vector<int>> vin{ {1,2},{3,4},{5,6} };
size_t scaleW = 2;
size_t scaleH = 3;
vector<vector<int>> vout(scaleH * vin.size(), vector<int>(scaleW * vin[0].size()));
for (size_t i = 0; i < vout.size(); i++)
for (size_t ii = 0; ii < vout[0].size(); ii++)
vout[i][ii] = vin[i / scaleH][ii / scaleW];
auto x = vout[8][3]; // last element s/b 6
}
Here is my take. It is very similar to #Tudor's but I figure between our two, you can pick what you like or understand best.
First, let's define a suitable 2D array type because C++'s standard library is very lacking in this regard. I've limited myself to a rather simple struct, in case you don't feel comfortable with object oriented programming.
#include <vector>
// using std::vector
struct Array2d
{
unsigned rows, cols;
std::vector<int> data;
};
This print function should give you an idea how the indexing works:
#include <cstdio>
// using std::putchar, std::printf, std::fputs
void print(const Array2d& arr)
{
std::putchar('[');
for(std::size_t row = 0; row < arr.rows; ++row) {
std::putchar('[');
for(std::size_t col = 0; col < arr.cols; ++col)
std::printf("%d, ", arr.data[row * arr.cols + col]);
std::fputs("]\n ", stdout);
}
std::fputs("]\n", stdout);
}
Now to the heart, the array scaling. The amount of nesting is … bothersome.
Array2d scale(const Array2d& in, unsigned rowfactor, unsigned colfactor)
{
Array2d out;
out.rows = in.rows * rowfactor;
out.cols = in.cols * colfactor;
out.data.resize(std::size_t(out.rows) * out.cols);
for(std::size_t inrow = 0; inrow < in.rows; ++inrow) {
for(unsigned rowoff = 0; rowoff < rowfactor; ++rowoff) {
std::size_t outrow = inrow * rowfactor + rowoff;
for(std::size_t incol = 0; incol < in.cols; ++incol) {
std::size_t in_idx = inrow * in.cols + incol;
int inval = in.data[in_idx];
for(unsigned coloff = 0; coloff < colfactor; ++coloff) {
std::size_t outcol = incol * colfactor + coloff;
std::size_t out_idx = outrow * out.cols + outcol;
out.data[out_idx] = inval;
}
}
}
}
return out;
}
Let's pull it all together for a little demonstration:
int main()
{
Array2d in;
in.rows = 2;
in.cols = 3;
in.data.resize(in.rows * in.cols);
for(std::size_t i = 0; i < in.rows * in.cols; ++i)
in.data[i] = static_cast<int>(i);
print(in);
print(scale(in, 3, 2));
}
This prints
[[0, 1, 2, ]
[3, 4, 5, ]
]
[[0, 0, 1, 1, 2, 2, ]
[0, 0, 1, 1, 2, 2, ]
[0, 0, 1, 1, 2, 2, ]
[3, 3, 4, 4, 5, 5, ]
[3, 3, 4, 4, 5, 5, ]
[3, 3, 4, 4, 5, 5, ]
]
To be honest, i'm incredibly bad at algorithms but i gave it a shot.
I am not sure if this can be done using only one matrix, or if it can be done in less time complexity.
Edit: You can estimate the number of operations this will make with W*H*S*S where Sis the scale factor, W is width and H is height of input matrix.
I used 2 matrixes m and r, where m is your input and r is your result/output. All that needs to be done is to copy each element from m at positions [i][j] and turn it into a square of elements with the same value of size scale_factor inside r.
Simply put:
int main()
{
Matrix<int> m(2, 2);
// initial values in your example
m[0][0] = 1;
m[0][1] = 2;
m[1][0] = 3;
m[1][1] = 4;
m.Print();
// pick some scale factor and create the new matrix
unsigned long scale = 2;
Matrix<int> r(m.rows*scale, m.columns*scale);
// i know this is bad but it is the most
// straightforward way of doing this
// it is also the only way i can think of :(
for(unsigned long i1 = 0; i1 < m.rows; i1++)
for(unsigned long j1 = 0; j1 < m.columns; j1++)
for(unsigned long i2 = i1*scale; i2 < (i1+1)*scale; i2++)
for(unsigned long j2 = j1*scale; j2 < (j1+1)*scale; j2++)
r[i2][j2] = m[i1][j1];
// the output in your example
std::cout << "\n\n";
r.Print();
return 0;
}
I do not think it is relevant for the question, but i used a class Matrix to store all the elements of the extended matrix. I know it is a distraction but this is still C++ and we have to manage memory. And what you are trying to achieve with this algorithm needs a lot of memory if the scale_factor is big so i wrapped it up using this:
template <typename type_t>
class Matrix
{
private:
type_t** Data;
public:
// should be private and have Getters but
// that would make the code larger...
unsigned long rows;
unsigned long columns;
// 2d Arrays get big pretty fast with what you are
// trying to do.
Matrix(unsigned long rows, unsigned long columns)
{
this->rows = rows;
this->columns = columns;
Data = new type_t*[rows];
for(unsigned long i = 0; i < rows; i++)
Data[i] = new type_t[columns];
}
// It is true, a copy constructor is needed
// as HolyBlackCat pointed out
Matrix(const Matrix& m)
{
rows = m.rows;
columns = m.columns;
Data = new type_t*[rows];
for(unsigned long i = 0; i < rows; i++)
{
Data[i] = new type_t[columns];
for(unsigned long j = 0; j < columns; j++)
Data[i][j] = m[i][j];
}
}
~Matrix()
{
for(unsigned long i = 0; i < rows; i++)
delete [] Data[i];
delete [] Data;
}
void Print()
{
for(unsigned long i = 0; i < rows; i++)
{
for(unsigned long j = 0; j < columns; j++)
std::cout << Data[i][j] << " ";
std::cout << "\n";
}
}
type_t* operator [] (unsigned long row)
{
return Data[row];
}
};
First of all, having a suitable 2D matrix class is presumed but not the question. But I don't know the API of yours, so I'll illustrate with something typical:
struct coord {
size_t x; // x position or column count
size_t y; // y position or row count
};
template <typename T>
class Matrix2D {
⋮ // implementation details
public:
⋮ // all needed special members (ctors dtor, assignment)
Matrix2D (coord dimensions);
coord dimensions() const; // return height and width
const T& cell (coord position) const; // read-only access
T& cell (coord position); // read-write access
// handy synonym:
const T& operator[](coord position) const { return cell(position); }
T& operator[](coord position) { return cell(position); }
};
I just showed the public members I need: create a matrix with a given size, query the size, and indexed access to the individual elements.
So, given that, your problem description is:
template<typename T>
Matrix2D<T> scale_pow2 (const Matrix2D& input, size_t pow)
{
const auto scale_factor= 1 << pow;
const auto size_in = input.dimensions();
Matrix2D<T> result ({size_in.x*scale_factor,size_in.y*scale_factor});
⋮
⋮ // fill up result
⋮
return result;
}
OK, so now the problem is precisely defined: what code goes in the big blank immediately above?
Each cell in the input gets put into a bunch of cells in the output. So you can either iterate over the input and write a clump of cells in the output all having the same value, or you can iterate over the output and each cell you need the value for is looked up in the input.
The latter is simpler since you don't need a nested loop (or pair of loops) to write a clump.
for (coord outpos : /* ?? every cell of the output ?? */) {
coord frompos {
outpos.x >> pow,
outpos.y >> pow };
result[outpos] = input[frompos];
}
Now that's simple!
Calculating the from position for a given output must match the way the scale was defined: you will have pow bits giving the position relative to this clump, and the higher bits will be the index of where that clump came from
Now, we want to set outpos to every legal position in the output matrix indexes. That's what I need. How to actually do that is another sub-problem and can be pushed off with top-down decomposition.
a bit more advanced
Maybe nested loops is the easiest way to get that done, but I won't put those directly into this code, pushing my nesting level even deeper. And looping 0..max is not the simplest thing to write in bare C++ without libraries, so that would just be distracting. And, if you're working with matrices, this is something you'll have a general need for, including (say) printing out the answer!
So here's the double-loop, put into its own code:
struct all_positions {
coord current {0,0};
coord end;
all_positions (coord end) : end{end} {}
bool next() {
if (++current.x < end.x) return true; // not reached the end yet
current.x = 0; // reset to the start of the row
if (++current.y < end.y) return true;
return false; // I don't have a valid position now.
}
};
This does not follow the iterator/collection API that you could use in a range-based for loop. For information on how to do that, see my article on Code Project or use the Ranges stuff in the C++20 standard library.
Given this "old fashioned" iteration helper, I can write the loop as:
all_positions scanner {output.dimensions}; // starts at {0,0}
const auto& outpos= scanner.current;
do {
⋮
} while (scanner.next());
Because of the simple implementation, it starts at {0,0} and advancing it also tests at the same time, and it returns false when it can't advance any more. Thus, you have to declare it (gives the first cell), use it, then advance&test. That is, a test-at-the-end loop. A for loop in C++ checks the condition before each use, and advances at the end, using different functions. So, making it compatible with the for loop is more work, and surprisingly making it work with the ranged-for is not much more work. Separating out the test and advance the right way is the real work; the rest is just naming conventions.
As long as this is "custom", you can further modify it for your needs. For example, add a flag inside to tell you when the row changed, or that it's the first or last of a row, to make it handy for pretty-printing.
summary
You need a bunch of things working in addition to the little piece of code you actually want to write. Here, it's a usable Matrix class. Very often, it's prompting for input, opening files, handling command-line options, and that kind of stuff. It distracts from the real problem, so get that out of the way first.
Write your code (the real code you came for) in its own function, separate from any other stuff you also need in order to house it. Get it elsewhere if you can; it's not part of the lesson and just serves as a distraction. Worse, it may be "hard" in ways you are not prepared for (or to do well) as it's unrelated to the actual lesson being worked on.
Figure out the algorithm (flowchart, pseudocode, whatever) in a general way before translating that to legal syntax and API on the objects you are using. If you're just learning C++, don't get bogged down in the formal syntax when you are trying to figure out the logic. Until you naturally start to think in C++ when doing that kind of planning, don't force it. Use whiteboard doodles, tinkertoys, whatever works for you.
Get feedback and review of the idea, the logic of how to make it happen, from your peers and mentors if available, before you spend time coding. Why write up an idea that doesn't work? Fix the logic, not the code.
Finally, sketch the needed control flow, functions and data structures you need. Use pseudocode and placeholder notes.
Then fill in the placeholders and replace the pseudo with the legal syntax. You already planned it out, so now you can concentrate on learning the syntax and library details of the programming language. You can concentrate on "how do I express (some tiny detail) in C++" rather than keeping the entire program in your head. More generally, isolate a part that you will be learning; be learning/practicing one thing without worrying about the entire edifice.
To a large extent, some of those ideas translate to the code as well. Top-Down Design means you state things at a high level and then implement that elsewhere, separately. It makes code readable and maintainable, as well as easier to write in the first place. Functions should be written this way: the function explains how to do (what it does) as a list of details that are just one level of detail further down. Each of those steps then becomes a new function. Functions should be short and expressed at one semantic level of abstraction. Don't dive down into the most primitive details inside the function that explains the task as a set of simpler steps.
Good luck, and keep it up!
I am trying to create an array of X pointers referencing matrices of dimensions Y by 16. Is there any way to accomplish this in C++ without the use of triple pointers?
Edit: Adding some context for the problem.
There are a number of geometries on the screen, each with a transform that has been flattened to a 1x16 array. Each snapshot represents the transforms for each of number of components. So the matrix dimensions are 16 by num_components by num_snapshots , where the latter two dimensions are known at run-time. In the end, we have many geometries with motion applied.
I'm creating a function that takes a triple pointer argument, though I cannot use triple pointers in my situation. What other ways can I pass this data (possibly via multiple arguments)? Worst case, I thought about flattening this entire 3D matrix to an array, though it seems like a sloppy thing to do. Any better suggestions?
What I have now:
function(..., double ***snapshot_transforms, ...)
What I want to accomplish:
function (..., <1+ non-triple pointer parameters>, ...)
Below isn't the function I'm creating that takes the triple pointer, but shows what the data is all about.
static double ***snapshot_transforms_function (int num_snapshots, int num_geometries)
{
double component_transform[16];
double ***snapshot_transforms = new double**[num_snapshots];
for (int i = 0; i < num_snapshots; i++)
{
snapshot_transforms[i] = new double*[num_geometries];
for (int j = 0; j < num_geometries; j++)
{
snapshot_transforms[i][j] = new double[16];
// 4x4 transform put into a 1x16 array with dummy values for each component for each snapshot
for (int k = 0; k < 16; k++)
snapshot_transforms[i][j][k] = k;
}
}
return snapshot_transforms;
}
Edit2: I cannot create new classes, nor use C++ features like std, as the exposed function prototype in the header file is getting put into a wrapper (that doesn't know how to interpret triple pointers) for translation to other languages.
Edit3: After everyone's input in the comments, I think going with a flattened array is probably the best solution. I was hoping there would be some way to split this triple pointer and organize this complex data across multiple data pieces neatly using simple data types including single pointers. Though I don't think there is a pretty way of doing this given my caveats here. I appreciate everyone's help =)
It is easier, better, and less error prone to use an std::vector. You are using C++ and not C after all. I replaced all of the C-style array pointers with vectors. The typedef doublecube makes it so that you don't have to type vector<vector<vector<double>>> over and over again. Other than that the code basically stays the same as what you had.
If you don't actually need dummy values I would remove that innermost k loop completely. reserve will reserve the memory space that you need for the real data.
#include <vector>
using std::vector; // so we can just call it "vector"
typedef vector<vector<vector<double>>> doublecube;
static doublecube snapshot_transforms_function (int num_snapshots, int num_geometries)
{
// I deleted component_transform. It was never used
doublecube snapshot_transforms;
snapshot_transforms.reserve(num_snapshots);
for (int i = 0; i < num_snapshots; i++)
{
snapshot_transforms.at(i).reserve(num_geometries);
for (int j = 0; j < num_geometries; j++)
{
snapshot_transforms.at(i).at(j).reserve(16);
// 4x4 transform put into a 1x16 array with dummy values for each component for each snapshot
for (int k = 0; k < 16; k++)
snapshot_transforms.at(i).at(j).at(k) = k;
}
}
return snapshot_transforms;
}
Adding a little bit of object-orientation usually makes the code easier to manage -- for example, here's some code that creates an array of 100 Matrix objects with varying numbers of rows per Matrix. (You could vary the number of columns in each Matrix too if you wanted to, but I left them at 16):
#include <vector>
#include <memory> // for shared_ptr (not strictly necessary, but used in main() to avoid unnecessarily copying of Matrix objects)
/** Represents a (numRows x numCols) 2D matrix of doubles */
class Matrix
{
public:
// constructor
Matrix(int numRows = 0, int numCols = 0)
: _numRows(numRows)
, _numCols(numCols)
{
_values.resize(_numRows*_numCols);
std::fill(_values.begin(), _values.end(), 0.0f);
}
// copy constructor
Matrix(const Matrix & rhs)
: _numRows(rhs._numRows)
, _numCols(rhs._numCols)
{
_values.resize(_numRows*_numCols);
std::fill(_values.begin(), _values.end(), 0.0f);
}
/** Returns the value at (row/col) */
double get(int row, int col) const {return _values[(row*_numCols)+col];}
/** Sets the value at (row/col) to the specified value */
double set(int row, int col, double val) {return _values[(row*_numCols)+col] = val;}
/** Assignment operator */
Matrix & operator = (const Matrix & rhs)
{
_numRows = rhs._numRows;
_numCols = rhs._numCols;
_values = rhs._values;
return *this;
}
private:
int _numRows;
int _numCols;
std::vector<double> _values;
};
int main(int, char **)
{
const int numCols = 16;
std::vector< std::shared_ptr<Matrix> > matrixList;
for (int i=0; i<100; i++) matrixList.push_back(std::make_shared<Matrix>(i, numCols));
return 0;
}
As part of a larger program I need to generate every possible set of 3D coordinate points contained within the rectangular prism formed by the origin and point (Y1, Y2, Y3), given the number of points, n, that will be in the set, and the value by which the x/y/z values are to be incremented by.
This was what I initially wrote, which does the job of cycling through all possible coordinates correctly for an individual point, but does not correctly generate all the overall combinations of points needed.
In the program I created a point object, and created a vector of point objects with default x/y/z values of zero.
void allPoints(double Y1, double Y2, double Y3, double increment, vector<Point> pointset)
{
int count = pointset.size()-1;
while (count>=0)
{
while (pointset.at(count).getX()<Y1)
{
while (pointset.at(count).getY()<Y2)
{
while (pointset.at(count).getZ()<Y3)
{
//insert intended statistical test to be run on each possible set here
}
pointset.at(count).setZ(0);
pointset.at(count).incY(increment);
}
pointset.at(count).setY(0);
pointset.at(count).incX(increment);
}
count--;
}
}
I am new to coding and may be approaching this entirely wrong, and am just looking for help getting in the right direction. If using a point object isn't the way to go, it's not needed in the rest of the program - I could use 3d arrays instead.
Thanks!
Lets assume you have class Point3d which represents a point, Vec3d which represents a vector which can translate points (proper operators are defined).
In such case this should go like this:
std::vector<Point3d> CrystalNet(
size_t size,
const Point3d& origin,
const Vec3d& a = { 1, 0, 0 },
const Vec3d& b = { 0, 1, 0 },
const Vec3d& c = { 0, 0, 1 })
{
std::vector<Point3d> result;
result.reserve(size * size * size);
for (int i = 0; i < size; ++i)
for (int j = 0; j < size; ++j)
for (int k = 0; k < size; ++k) {
result.empalce_back(origin + a * i + b * j + c * k);
}
return result;
}
Defining Point3d and Vec3d is quite standard and I'm sure there is ready library which can do it.
The chief problem appears to be that your textual description is about creating a pointset. The count isn't known up front. The example code takes an already created pointset. That just doesn't work.
That's also why you end up with the // insert test here - that's not the location for a test, that's where you would add a new point to the pointset you have to create.
I have a bunch of 3d arrays generated using boost::multi_array in a function. I would not want to use all these arrays in another code of mine is there any way to do this?
When I had a 2d case what I did was
typedef boost::numeric::ublas::matrix<double> fils;
boost::array<fils,5> filter1(unsigned width, unsigned height)
{
matrix<double>l,m,n,o,p;
//perform other steps//
boost::array<fils,5> t={l,m,n,o,p};
return t;
}
main.cpp
int main()
{
boost::array<fils,5> z;
z= t(w,h);
}
for the 2d case this method works fine. I now want to do the same with a 3D case where
typedef boost::multi_array<double,3>x;
boost::array<x,12>x1(unsigned w,unsigned h,unsigned s)
{
typedef boost::multi_array<double,3>M;
typedef M::index Mi;
m l(boost::extents[w][h][s]),m(boost::extents[w][h][s]),n(boost::extents[w][h][s]),o(boost::extents[w][h][s]);
//perform steps//
}
how do I get the matrices l,m,n,o,p so that I can use them as source in other bits of code.
In my opinion the most elegant solution is to declare a 4-D multi_array like so :
typedef boost::multi_array<double,4> FloatArray4D;
typedef M::index Mi;
function create4dArray()
{
FloatArray4D returnValue(boost::extents[w][h][s][4]);
// Populate the array as you please here is an example.
for (int i = 0; i < 4; i++) {
for (int j = 0; j < w; j++) {
for (int k = 0; k < h; k++) {
for (int x = 0; x < s; x++) {
returnValue[j][k][x][i] = i+j*10+k*100+x*1000;
}
}
}
}
return returnValue;
}
Then you can access the subarray by indexing on the last coordinate. It might be more efficient to index them by the first coordinate (in terms of localization of the data) but I don't know the implementation details of boost::multi_array (can someone weight in on this in comments ?)
To extract a view (no-copy) of your 3-D data from the 4-D multi_array created you can use this :
typedef boost::multi_array_types::index_range range;
FloatArray4D::index_gen indices;
FloatArray4D my4DArray = create4dArray();
// Create a new view with 3 dimentions (corresponding to your l) fixing the 4th dimention to 0
FloatArray4D::array_view<3>::type l = [indices[range()][range()][range()][0];
then you can use l as if it was your 3-D array.
PS: NEVER name something x or M, especially not a type. Yes long names are a pain to type, but get a decent text editor with auto-completion and it won't be a problem.
Knowing what an object is by its name however, will always be great. It improves readability, for you and for anyone else who has to read your code.
Also do not typedef inside a function. If you want to define a custom type do it in a header file that is shared.
You don't want to have to declare that type everywhere.
And actually don't overuse typedef, only use it if it improves readability.
This is a constructor for a class called Graph. In the constructor I am trying to initialise somethings and here is the contructor that works i.e. it runs and finishes:
Graph(const float density, const int numVertex = 50): numEdges(0) {
graph.resize(numVertex, vector<Vertex>(numVertex));
for (int s = 0; s < numVertex; ++s) {
for (int k = 0; k < s; ++k )
if (edge_exist(density)) {
graph[s][k].visited = graph[k][s].visited = false;
graph[s][k].distance = graph[k][s].distance = _MAX;
++numEdges;
int distance = rand() % 10 + 1;
graph[s][k].edges.emplace_back(piiv(distance, graph[k][s]));
graph[k][s].edges.emplace_back(piiv(distance, graph[s][k]));
}
}
}
typedef pair<int, Vertex> piiv;
vector<vector<Vertex> > graph;
The class has a field called graph which is a vector of vector of struct called Vertex.
typedef struct vert {
std::list<std::pair<int, vert> > edges;
int distance;
bool visited;
} Vertex;
Now if I leave the vertex struct the way it is and instead make the vector just a one dimensional vector
vector<Vertex> graph;
And change the constructor to be like so:
Graph(const float density, const int numVertex = 50): numEdges(0) {
graph.resize(numVertex);
for (int s = 0; s < numVertex; ++s) {
for (int k = 0; k < s; ++k )
if (edge_exist(density)) {
graph[s].visited = graph[k].visited = false;
graph[s].distance = graph[k].distance = _MAX;
++numEdges;
int distance = rand() % 10 + 1;
graph[s].edges.emplace_back(piiv(distance, graph[k]));
graph[k].edges.emplace_back(piiv(distance, graph[s]));
}
}
}
Now this change causes the code to run far longer than it usually does when the vector was 2 dimensional. I have not had the patience to figure out how long it runs, but I know it runs unreasonably slower than the first one and for no apparent reason. Well not apparent to me, but I bet someone here has some insight as to why this is.
So my question is, what is causing this seemingly unnecessary delay in the program?
If it helps, this is how the constructor is called:
Graph G(0.4);
I have tracked the problem to be coming from these last 2 lines in the second constructor implementation:
graph[s].edges.emplace_back(piiv(distance, graph[k]));
graph[k].edges.emplace_back(piiv(distance, graph[s]));
So I guess the real question is how is the above different from what is being done in the first constructor?
EDIT
Bingo!
As I was debugging I decided to change the Vertex struct to be declared like so:
typedef struct vert {
std::list<std::pair<int, vert&> > edges;
int distance;
bool visited;
} Vertex;
This seemed to fix the problem, but why?? Why is passing in the Vertex object by value not working as compared to pass by reference?
The reason why this was happening was nicely summarized by #Joe Z.
std::list<std::pair<int, vert> > edges;
By declaring the Vertex edges to be a list of other that contains other Vertex by value, this meant that each time a new vertex is added to the list, the copy constructor immediately kicks in and starts making a copy of all of that vert's edges which also means making a copy of all any children of that Vertex and so on and so forth...
As you can see, this insatiable copying means that as the graph gets denser, we the copying takes progressively more time and God help us if we decide to introduce a cycle in the graph because this means we will run out of memory before this program finishes.
Changing the edges property to have this type:
std::list<std::pair<int, vert&> > edges;
Now this means that each time we add a new edge to the graph, we simply maintain a reference to the other vertices rather than copying them. This also means we can actually be able to detect when an edge has been removed from another vertex.
Furthermore, I would actually define this edge to be:
std::list<std::pair<int, const vert&> > edges;
This is just a matter of good practice because we want to ensure that edges are immutable and having a reference to another vertex does not mean being able to change it's properties.