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#include <vector>
bool gaussianElimination_binary(std::vector<std::vector<int>> &A) {
std::vector<std::vector<int>> B = A;
std::size_t max_col = B[0].size() - 1; //cols
std::size_t max_row = B.size() -1 ; //rows
std::size_t col_pivot = 0;
//perform "gaussian" elimination
for (std::size_t row = 0; row <= max_row; ++row) //for every column
{
if (col_pivot > max_col)
break;
// Search for first row having "1" in column "lead"
std::size_t i = row; //Start searching from row "i"=row
while (B[i][col_pivot] == 0)
{
++i;
if (i > max_row) // no "1" was found across rows
{
i = row; // set "i" back to "row"
++col_pivot; // move to next column
if (col_pivot > max_col) //if no more columns
break;
}
}
// swap "i" and "row" rows
if ((0 <= i) && (i <= max_row) && (0 <= row) && (row <= max_row)) {
for (std::size_t col = 0; col <= max_col; ++col) {
std::swap(B[i][col], B[row][col]);
}
}
// perform XOR in "k-th" row against "row-th" row
for (int k = 0; k <= max_row; ++k) //k=col_pivot?
{
if ( (k != row) ) // && (B[k][row] != 0) //Apply only to "1"s
{
int check_zero_row = 0;
for (std::size_t j = 0; j <= max_col; j++) {
B[k][j] = B[k][j] ^ B[row][j]; //XOR: Use "1" to set other "1" rows to 0 (and 0 to 1)
check_zero_row = check_zero_row | B[k][j]; //OR: Result will be "0" only if the entire row is "0"
}
if (check_zero_row == 0 )
{
return false;
}
}
}
}
return true;
}
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