As a homework, I have a problem which sounds like this:
We have a n*n square matrix. It is called 'subdiagonal'
if all the elements above the main diagonal are null.
a) Copy the useful elements (the ones which are not null, so basically all the elements
from the main diagonal and below) to an array. (I've done that)
b) Write an algorithm which takes two subdiagonal matrix A, B as an input.
Those are transformed into arrays V_a and V_b with the algorithm from a),
then they calculate C = A*B only using only V_a and V_b
e.g.
Let's say A =
1 0 0 0 0
2 3 0 0 0
4 1 3 0 0
1 9 0 2 0
1 0 1 2 2
B =
2 0 0 0 0
1 1 0 0 0
0 1 2 0 0
1 1 2 3 0
2 0 0 1 2
after this input, V_a = 1,2,3,4,1,3,1,9,0,2,1,0,1,2,2; V_b = 2,1,1,0,1,2,1,1,2,3,2,0,0,1,2
and the product V_c will be 2,7,3,9,4,6,13,11,4,6,8,3,6,8,4
so the matrix will look like
2 0 0 0 0
7 3 0 0 0
9 4 6 0 0
13 11 4 6 0
8 3 6 8 4
Here's the code that I've been working on for a while:
#include <iostream>
#include <algorithm>
void read(int& a, int**& matrix)
{
std::cin >> a;
matrix = new int*[a];
for (int i = 0; i < a; i++)
{
for (int j = 0; j < a; j++)
{
matrix[i] = new int[a];
}
}
for (int i = 0; i < a; i++)
{
for (int j = 0; j < a; j++)
{
std::cin >> matrix[i][j];
}
}
}
void showMatrix(int a, int** matrix)
{
for (int i = 0; i < a; i++)
{
for (int j = 0; j < a; j++)
{
std::cout << matrix[i][j] << " ";
}
std::cout << std::endl;
}
}
void showArray(int a, int* array)
{
for (int i = 0; i < a; i++)
{
std::cout << array[i] << " ";
}
}
void createArray(int a, int& arrayLength, int** matrix, int*& array)
{
int nrDeElemente = a*a - (a * (a - 1)) / 2;
array = new int[nrDeElemente+1];
arrayLength = 0;
for (int i = 0; i < a; i++)
{
for (int j = 0; j < i+1; j++)
{
array[arrayLength++] = matrix[i][j];
}
}
}
int* multiplyArrays(int a, int arrayLength, int* array1, int* array2)
{
int* array3 = new int[arrayLength + 1];
for (int i = 0; i < a; i++)
{
array3[i] = 0;
}
int t = 1;
for (int i = 0; i < arrayLength; ++i)
{
for (int j = 0; j < t; ++j)
{
for (int p = j; p < a; p++)
{
array3[i] += array1[j] * array2[p];
}
}
++t;
}
return array3;
}
int main()
{
int **matrix1, **matrix2;
int *array1, *array2, *multiplyResult;
int a, arrayLength;
read(a, matrix1);
read(a, matrix2);
createArray(a, arrayLength, matrix1, array1);
createArray(a, arrayLength, matrix2, array2);
multiplyResult = multiplyArrays(a, arrayLength, array1, array2);
showArray(arrayLength, multiplyResult);
}
I've done a), but I don't know how to do b)
I think I understood it (after many hours of trials) conceptually, but I don't really know how to implement it.
I need 3 for loops, as such:
->the most outer one has to be responsible for the position we calculate on the new array
->the next one has to choose which elements from the second array will be multiplied. (choose the multiplier) That's one of the loops I don't know how to implement. It somehow has to stop when the line (from the matrix) ended and start where it stopped + 1 element.
->the most inner one has to choose the second term of the multiplication (the multiplicand). I also don't know how I should implement this one. It should choose as many elements as there multipliers are and also, the looping is quite strange (because I need to select all the elements from the same row every time).
Can anybody help me solve point b and also explain their thinking?
I struggled a lot and I really feel like I need help.
BTW the 3 for loops from multiplyArrays make no sense, you can just write something else instead of them. Those 3 for loops are basically the only things that my program needs (I think).
Thanks :)
