Every possible path from 2D array? (Cross Product) - c

Question

Let's suppose I have this array
int diml = 3;
int dims = 3;
int time [diml][dims] ={
(10, 3, 5),
( 4, 7, 2),
( 2, 8, 1)
};
How can I get every combination like:
(10, 3, 5)
(10, 3, 2)
(10, 3, 1)
(10, 7, 5)
(10, 7, 2)
(10, 7, 1)
...
(2, 8, 5)
(2, 8, 2)
(2, 8, 1)
*Is this possible without saving all the combinations in a new array, but just a 1D local array that can store the current combination on every cycle?
*I'd prefer cycles over recursion. And at the end of each cycle I need the pattern (like 10, 3, 2) so I can elaborate it.
*The dimensions of the 2D array are MxN (3x3 is just an example).
*A solution with binary trees is accepted (but I want to save the indexes too).
I should do this in C. I have found similar solutions in StackOverflow but they work by column and they save the data in a 2D array, but that's not what I need.
Thanks in advance! (:

Answer 1

For this example codes, The first one was built so it would be easier to understand example 2. Example 1 was built for only 3x3 matrixes. Example 2 was built so that it can accommodate a matrix with 8 columns at maximum. I didn't use malloc or return an array. It will print back all the possible combinations for you. It doesn't deal with returning the data but it wouldn't be hard to incorporate that into the code.
For the method of calculation all the possible combination, I would use a 3x3 matrix as an example.
In a 3x3 matrix, there are 3 rows and 3 columns. I treated each column as a set of number that I can pick and the rows as the possible of numbers that I can pick from. So in that example, I can pick 012 for my first, second, and third set of number.
So to get all the possible combinations, I have 3 arrays, [0] [1] [2]. They all start at 0. I first save the possible combination of 0 0 0. Then I increase array 2 by 1. Then I would get 0 0 1. I then save that combination. I will keep on doing that and one the [2] array == 2. I turn that to 0 and add a 1 to the array to the left of it. So it become 0 1 0. When I reach a loop where my values of my arrays are 0 2 2, the loop after that, I will get 1 0 0. I will keep on doing that until all the value turn to zero then I am done.
For how the data is store, I store them continually in an array. To read back the value properly. Say for example in a 2x5 matrix. Each combination will have 5 numbers. Thus, the first combination is the first five indexes, the next combination, is the next five numbers after that one.
To calculate how much array length you would need before calculating the combinations, you can just base the calculation on rows and columns. Think of this like the lottery. If there are 3 columns, it like you can pick 3 numbers. Each column have 3 rows, so that mean for each time you pick a number there are 3 possible numbers to pick from. For you to hit a jackpot the chances are 1:3 x 1:3 x 1:3 or 1:27 because there are 27 possibilities if picking 3 numbers like this (123 123 123) and matching them in the correct order. Thus, for a 3x3 matrix, it is 3x3x3, 4x4 = 4x4x4x4, 1x3 = 1, 3x1 = 3, 2x5 = 2x2x2x2x2 = 32.
Thus, the amount of possible combinations is "the amount of rows" to the power of "the amount of columns".
The size is the amount of possible combinations multiply by the amount of numbers per combination. Of which would be "possibilities multiply column count = array size needed.
Example 1:
#include <stdio.h>
void printMatrixCombo(int row, int col, int matrix[row][col]);
int main(){
const int m1 = 3;
const int m2 = 3;
int matrix[m1][m2] = {
{10, 3, 5},
{4, 7, 2},
{2, 8, 1}
};
printMatrixCombo(m1, m2, matrix);
return 0;
}
// Only use this for a 3x3
void printMatrixCombo(int row, int col, int matrix[row][col]){
int oi = 0;
int output[81] = {0};
for (int group1 = 0; group1 < 3; group1++){
for (int group2 = 0; group2 < 3; group2++ ){
for (int group3 = 0; group3 < 3; group3++ ){
output[oi++] = matrix[group1][0];
output[oi++] = matrix[group2][1];
output[oi++] = matrix[group3][2];
}
}
}
printf("There were %d combination in the matrix of %d x %d\n", oi / col, row, col );
for ( int i = 0; i < oi ; ){
printf("(");
for ( int j = 0; j < col; j++ ){
printf("%d", output[i+j]);
if ( j != col - 1 ) printf(", ");
}
printf(")\n");
i = i + col;
}
}
Example 2:
#include <stdio.h>
void printMatrixCombo(int row, int col, int matrix[row][col]);
int main(){
const int row = 4;
const int col = 4;
/*// 3x3
int matrix[row][col] = {
{10, 3, 5},
{4, 7, 2},
{2, 8, 1}
};//*/
// 4 x 4
int matrix[row][col] = {
{10, 3, 5, 7},
{4, 7, 2, 3},
{2, 8, 1, 9},
{9, 4, 8, 11}
};//*/
/*// 5 x 5
int matrix[row][col] = {
{10, 3, 5, 7, 25},
{4, 7, 2, 87, 42},
{2, 8, 1, 85, 39},
{9, 4, 8, 94, 57},
{10, 3, 5, 7, 93},
};//*/
/*// 2 x 2
int matrix[row][col] = {
{10, 3},
{4, 7},
};//*/
/*// 1 x 1
int matrix[row][col] = {
{10},
};//*/
/* // 3 x 1
int matrix[row][col] = {
{10},
{4},
{1}
}; //*/
/*// 1 x 3
int matrix[row][col] = {
{10, 4, 1},
};// */
printMatrixCombo(row, col, matrix);
return 0;
}
void printMatrixCombo(int row, int col, int matrix[row][col]){
int oi = 0;
int allZ = 0;
// This is the maximum for a 5x5
// Change to fit usage case
int output[15625] = {0};
int colCount[8] = {0};
int lastCol = col - 1;
int lastRow = row - 1;
while (1){
for ( int i = 0; i < col; i++ )
output[oi++] = matrix[colCount[i]][i];
if ( colCount[lastCol] == lastRow ){
colCount[lastCol] = 0;
for (int i = lastCol - 1; i > -1; i--){
if ( colCount[i] == lastRow ){
colCount[i] = 0;
} else {
colCount[i]++;
break;
}
}
} else {
colCount[lastCol]++;
}
allZ = 1;
for ( int i = 0; i < col; i++ ){
if ( colCount[i] != 0 ){
allZ = 0;
break;
}
}
if (allZ == 1) break;
}
printf("There were %d combination in the matrix of %d x %d\n", oi / col, row, col );
printf("Array's length(indexes) is %d\n", oi );
for ( int i = 0; i < oi ; ){
printf("(");
for ( int j = 0; j < col; j++ ){
printf("%d", output[i+j]);
if ( j != col - 1 ) printf(", ");
}
printf(")\n");
i = i + col;
}
}