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 want to write a function addArrays which will, as parameters, take two 2D arrays of type int and of dimensions 3x4, and it's job is to add individual elements of each index from the given arrays and display it in the console.
In main(), I created two 2D arrays arrA and arrB of appropriate sizes with intitialized members and check the functionality of the created function.
My code so far:
#include <iostream>
using namespace std;
void addArrays(int x[3][4], int y[3][4]);
int main()
{
int arrA[3][4] = { {7, 8, 13, 22}, {56, 4, 78, 3}, {22, 13, 46, 5} };
int arrB[3][4] = { {32, 47, 56, 14}, {33, 100, 19, 64}, {4, 18, 157, 84} };
}
void addArrays(int x[3][4], int y[3][4])
{
}
Honestly, I know how to work with 1D arrays, but not displaying the sum of all individual elements. I know I have to use a for loop, but again, I'm confused as to how to pass in a 2D array and use it.
You mention you know how to work with 1D arrays, it's the same for 2D arrays, only with one more dimension.
In a 1D array you use arrA[0] to access the first element of the array, in a 2D array you use arrA[0][0] to access the first element in the first line of the array, arrA[0][1] to access the second element in the first line of the array. To access the first element in the second line you would use arrA[1][0] and so on, you get the idea.
So to loop through all the elements in the array you can use nested loops like so:
void addArrays(int x[3][4], int y[3][4])
{
for( int i = 0; i < 3; i++){ // make sure to use the correct dimensions
for(int j = 0; j < 4; j++){ // 3 lines and 4 columns
// x[i][j] accesses elements in array x
// y[i][j] accesses elements in array y
}
}
}
I think you'll manage to do the math yourself. After that you just need to send data to the standard output, i.e. to print data in the console. For that, as you may know, you use std::cout.
Side notes:
In the function void addArrays(int x[3][4], int y[3][4]){...} you may omit the first dimension of the array i.e. int x[][4] or int (*x)[4] instead of int x[3][4], since the argument will decay to a pointer to array.
Since it seems that you are not to change the values of the passed arrays, using const is recommend. You would have void addArrays(const int (*x)[4], const int (*y)[4]);
As you are using C++, you can take advantage of the possibility of using references, something like void addArrays(const int (&x)[3][4], const int (&y)[3][4]){/*same code*/}, the benefit being you must pass a correct object to the function otherwise the program will fail to compile whereas in the previous versions if you pass, for example, NULL, i.e. addArrays(arrA, NULL); the program will compile fine but will result in undefined behavior when you run it. References are safer and you should use them when possible.
It's more or less consensual among more experienced C++ programmers that the usage of using namespace std; is not a good practice, you can read more about it, and find alternatives following the link.
I will start this for you and try to give you an idea of the general structure, but since you have not shown your attempt at the problem I won't fill things in for you.
The basic idea here when looping through 2D arrays (of size MxN) is that you can really just think about it in terms of looping through M arrays of length N.
void loopThroughArray(int arr[M][N])
{
// Loop over M arrays
for (int m = 0; m < M; ++m) {
// For each m'th array, loop over its N contents
for (int n = 0; n < N; ++n) {
// Doing work
arr[m][n] = 1234;
}
}
}
I need to create a lot of small 2-dimension arrays in C++ code.
The problem is that it's a lot of work to create even a simple array:
new int* [2]{
new int[2]{9, 9},
new int[2]{25, 19}
};
Is there any better way how to do that?
I wanted to avoid writing "new int[]..." every time.
If the dimensions are not decided at runtime, and all the inner arrays have the same dimensions, you do not need dynamic allocation here.
Just declare an array:
int myArray[2][2] = {
{9, 9},
{25, 19}
};
That's it!
I recommend allocating as a single dimension array. You can then treat the 1D array as a 2D array:
const unsigned int MAX_ROWS = 2U;
const unsigned int MAX_COLUMNS = 5U;
int example_array[MAX_ROWS * MAX_COLUMNS];
// Get value at [row][column]:
unsigned int one_dim_index = (row * MAX_COLUMNS) + column;
int value = example_array[one_dim_index];
For small array sizes, this would be more efficient since the processor can fit the entire contiguous array in the data cache. With your solution, an array of pointers, you have no idea where the sub-arrays are located and they may not be contiguous (thus requiring a refetch into the cache).
Edit 1: Initializing
You can initialize the array by making the rows and columns pretty:
int example_array[MAX_ROWS * MAX_COLUMNS] =
{
/* row 0 */ 1, 2, 3, 4, 5,
/* row 1 */ 6, 7, 8, 9, 10,
};
Maybe you can use nested for loops to do the task
const int ARRAY_SIZE = 2;
int **create_array() {
int **array = new int*[ARRAY_SIZE];
if (array == nullptr) { return nullptr; }
for (int i=0; i<ARRAY_SIZE; i++) {
array[i] = new int[ARRAY_SIZE];
if (array[i] == nullptr) { return nullptr; }
}
return array;
}
If you want to assing the values you can do it directly in here. But they should come from a function of i. If you want some really specific values it will need to be a manual job
I have the following problem:
I have several partial (eigen) MatrixXds I want to concatenate to another, larger, MatrixXd variable I only have as a pointer. However, both the size of the smaller matrices and their number are dynamic, so I cannot use the << operator easily.
So I'm trying the following (the smaller matrices are stored in list_subdiagrams, obviously, and basis->cols() defines the number of matrices), using Eigen's MatrixXd block funtionality:
// sd[] contains the smaller matrices to be concatenated; all are of the same size
// col defines the total number of smaller matrices
MatrixXd* ret = new MatrixXd(sd[0]->rows(), col*sd[0]->cols());
for (int i=0; i<col; ++i){
ret->block(0, i*sd[0]->cols(), sd[0]->rows(), sd[0]->cols()) = *(sd[i]);
}
This, unfortunately, appears to somehow overwrite some part of the *ret variable - for before the assignment via the block, the size is (in my test-case) correctly shown as being 2x1. After the assignment it becomes 140736006011136x140736006011376 ...
Thank you for your help!
What do you mean you don't know the size? You can use the member functions cols()/rows() to get the size. Also, I assume by concatenation you mean direct sum? In that case, you can do something like
#include <iostream>
#include <Eigen/Dense>
int main()
{
Eigen::MatrixXd *A = new Eigen::MatrixXd(2, 2);
Eigen::MatrixXd *B = new Eigen::MatrixXd(3, 3);
*A << 1, 2, 3, 4;
*B << 5, 6, 7, 8, 9, 10, 11, 12, 13;
Eigen::MatrixXd *result = new Eigen::MatrixXd(A->rows() + B->rows(), A->cols() + B->cols());
result->Zero(A->rows() + B->rows(), A->cols() + B->cols());
result->block(0, 0, A->rows(), A->cols()) = *A;
result->block(A->rows(), A->cols(), B->rows(), B->cols()) = *B;
std::cout << *result << std::endl;
delete A;
delete B;
delete result;
}
So first make sure it works for 2 matrices, test it, then extend it to N.
I am writing code in c++ for a game in which a bucket controlled by the user collects raindrops with the same radius. I want to use an array to make each of the 16 raindrops a different size(radius). I have no clue how to change the variable into an array.
I am given a variable:
int radius = randomBetween( MARGIN / 4, MARGIN / 2 );
Here is an example that uses actual C++.
#include <algorithm>
#include <functional>
#include <random>
#include <vector>
std::mt19937 prng(seed);
std::uniform_int_distribution<> dist(MARGIN / 4, MARGIN / 2);
std::vector<int> radii(16);
std::generate(radii.begin(), radii.end(), std::bind(dist, std::ref(prng)));
You're probably going to want to use floats, but basically if I understand you correctly...
int size_in_elements = 16;
float *a= new float[size_in_elements];
float maxvalue = 100.0f; // this will be the maximum value to assign to each element
for(int i = 0; i < size_in_elements; i++)
{
a[i] = fmodf((float)rand(), maxvalue);
}
delete[] a; // Don't forget the brackets here... delete[] is used for deleting arrays.
Hope I helped some