How to fill a 2D array with Every Possible Combination? C++ Logic - c++

Question

I can't figure out the logic behind this one... here's what I have so far:
#include <iostream>
using namespace std;
int thearray[4][4];
int NbPos = 4;
int main() {
int i2;
int q2;
for(int i = 1; i < 4; i++) {
for(int q = 1; q < 4; q++) {
for(int c = 0; c < NbPos; c++) {
thearray[i][q] = c;
}
}
}
}
This is filling the array up to the end is still:
3 3 3
3 3 3
3 3 3
but it's doing so without hitting anywhere near every possible combination.
Ideally once it gets to:
0 0 0
0 0 0
0 0 3
the next step SHOULD be:
0 0 0
0 0 0
0 1 0
so it hits a TON of combinations. Any ideas on how to make it hit them all? I'm stumped on the logic!

Answer 1

with the way you're iterating over this, a 1-dimensional array would make the looping simpler. you can still mentally treat it to have rows and columns, however they are just layed out end-to-end in the code.
you could try something like this; however if you want it in a 2D format specifically that challenge is left to you ;)
#include <iostream>
using namespace std;
#define rows 4
#define columns 4
int main() {
int thearray[rows * columns] = {0};
int NbPos = 4;
int lastPos = rows * columns - 1;
while (true) {
thearray[lastPos]++;
int pos = lastPos;
while (thearray[pos] == NbPos and pos >= 1) {
thearray[pos - 1]++;
thearray[pos] = 0;
pos--;
}
bool finished = true;
for (int i = 0; i < rows * columns; i++) {
if (thearray[i] != NbPos - 1) {
finished = false;
}
}
if (finished) {
break;
}
}
for (int i = 0; i < rows * columns; i++) {
std::cout << thearray[i] << " ";
if (i % rows == rows - 1) {
cout << endl; // makes it look like a 2D array
}
}
}

Answer 2

It makes sense to have the final form as all 3s , since you loop every element of the array and you assign it at the end with 3 .
So the next element will only take into account the combination with the final value of the previous element (which will be 3).
Thinking in math terms, your complexity is N^3 so to speak (actually is N^2 * 4 , but since your N is 3 ...).
Your approach is wrong, since you want to find permutations, which are defined by a factorial function , not a polinomial function.
The necessary complexity for the output doesn't match the complexity of your algorithm (your algorithm is incredbily fast for the amount of output needed).
What you are looking for is backtracking (backtacking will match the complexity needed for your output).
The recursion function should be something like this (thinking on a 1D array, with 9 elements):
RecursiveGeneratePermutations(int* curArray, int curIdx)
{
if (curIDX==9)
{
for (int i=0; i<9;i++)
{
// write the array
}
} else {
curArray[curIdx]=0;
RecursiveGeneratePermutations(curIdx+1);
curArray[curIdx]=1;
RecursiveGeneratePermutations(curIdx+1);
curArray[curIdx]=2;
RecursiveGeneratePermutations(curIdx+1);
curArray[curIdx]=3;
RecursiveGeneratePermutations(curIdx+1);
}
}
Now you only need to call the function for the index 0 :
RecursiveGeneratePermutations(arrayPtr,0);
Then wait...allot :).