How to find Row and columns from box number on chessboard? - c++

Question

Example: chessboard has 64 fields, starting from 1 in top uppermost left box,
row 2, column 2 means its 10th box,
row 4, column 2 means its 26th box .....so on
Formula, trick to determine Row_column no from box number or vice versa?

Answer 1

I guess you mean that you have 8 boxes on each row?
This might do the trick:
#include <iostream>
#include <cmath>
const int totalNrOfBoxes = 64;
const float nrOfRows = std::sqrt(totalNrOfBoxes);
std::pair<int, int> getRowAndColumn(int boxNumber) {
int rowNumber = std::ceil(boxNumber / nrOfRows);
int columnNumber = (boxNumber - 1) % (int) nrOfRows; // we do -1 to avoid getting 0 when the boxNr is 8 or 16 or 32 for example
columnNumber += 1; // we add one number to the column number because we removed one from the box number
return std::make_pair(rowNumber, columnNumber);
}
int main()
{
std::pair<int, int> rowAndColumn = getRowAndColumn(11);
std::pair<int, int> rowAndColumn2 = getRowAndColumn(64);
std::pair<int, int> rowAndColumn3 = getRowAndColumn(1);
std::pair<int, int> rowAndColumn4 = getRowAndColumn(34);
std::pair<int, int> rowAndColumn5 = getRowAndColumn(7);
std::cout << rowAndColumn.first << " " << rowAndColumn.second << std::endl;
std::cout << rowAndColumn2.first << " " << rowAndColumn2.second << std::endl;
std::cout << rowAndColumn3.first << " " << rowAndColumn3.second << std::endl;
std::cout << rowAndColumn4.first << " " << rowAndColumn4.second << std::endl;
std::cout << rowAndColumn5.first << " " << rowAndColumn5.second << std::endl;
}
gives us the following output:
2 3
8 8
1 1
5 2
1 7
So basically what we do to determine the row number, is to divide the given box number by the number of rows, and take the ceil (finds the closest integer not less than n) out of that. Example: 26 / 8 = 3.25. We know that 26 is on the 4th row, so we need to take the closest integer not less than 3.25 which is 4.
For the column number we take the remainder. So for example with 12 it would return 4. The problem is that we start counting boxes at 1, so 16 % 8 would return 0, while we do want to get a value of 8. So that is why we say boxNumber - 1 (15 % 8 which returns 7) and add 1.