Bit-wise shift for Matrix iteration?

Question

Ok some background

I have been working on this project, which I had started back in college, (no longer in school but want to expand on it to help me improve my understanding of C++). I digress... The problem is to find the Best path through a matrix. I generate a matrix filled with a set integer value lets say 9. I then create a path along the outer edge (Row 0, Col length-1) so that all values along it are 1.

The goal is that my program will run through all the possible paths and determine the best path. To simplify the problem I decide to just calculate the path SUM and then compare that to what the SUM computed by the application.

(The title is miss leading S=single-thread P=multi-threads)

OK so to my question.

In one section the algorithm does some simple bit-wise shifts to come up with the bounds for iteration. My question is how exactly do these shifts work so that the entire matrix (or MxN array) is completely traversed?

void AltitudeMapPath::bestPath(unsigned int threadCount, unsigned int threadIndex) {
    unsigned int tempPathCode;
    unsigned int toPathSum, toRow, toCol;
    unsigned int fromPathSum, fromRow, fromCol;

    Coordinates startCoord, endCoord, toCoord, fromCoord;

    // To and From split matrix in half along the diagonal
    unsigned int currentPathCode = threadIndex;
    unsigned int maxPathCode = ((unsigned int)1 << (numRows - 1));
    while (currentPathCode < maxPathCode) {
        tempPathCode = currentPathCode;

        // Setup to path iteration
        startCoord = pathedMap(0, 0);
        toPathSum = startCoord.z;
        toRow = 0;
        toCol = 0;

        // Setup from path iteration 
        endCoord = pathedMap(numRows - 1, numCols - 1);
        fromPathSum = endCoord.z;
        fromRow = numRows - 1;
        fromCol = numCols - 1;

        for (unsigned int index = 0; index < numRows - 1; index++) {
            if (tempPathCode % 2 == 0) {
                toCol++;
                fromCol--;
            }
            else {
                toRow++;
                fromRow--;
            }
            toCoord = pathedMap(toRow, toCol);
            toPathSum += toCoord.z;
            fromCoord = pathedMap(fromRow, fromCol);
            fromPathSum += fromCoord.z;
            tempPathCode = tempPathCode >> 1;
        }

        if (toPathSum < bestToPathSum[threadIndex][toRow]) {
            bestToPathSum[threadIndex][toRow] = toPathSum;
            bestToPathCode[threadIndex][toRow] = currentPathCode;
        }

        if (fromPathSum < bestFromPathSum[threadIndex][fromRow]) {
            bestFromPathSum[threadIndex][fromRow] = fromPathSum;
            bestFromPathCode[threadIndex][fromRow] = currentPathCode;
        }
        currentPathCode += threadCount;
    }
}

I simplified the code since all the extra stuff just detracts from the question. Also if people are wondering I wrote most of the application but this idea of using the bit-wise operators was given to me by my past instructor.

Edit:

I added the entire algorithm for which each thread executes on. The entire project is still a work a progress but here is the source code for the whole thing if any one is interested [GITHUB]

Answer 1

A right bit shift is equivalent to dividing by 2 to the power of the number of bits shifted. IE 1 >> 2 = 1 / (2 ^ 2) = 1 / 4

A left bit shift is equivalent to multiplying by 2 to the power of the number of bits shifted. IE 1 << 2 = 1 * 2 ^ 2 = 1 * 4

I'm not entirely sure what that algorithm does and why it needs to multiply by 2^ (num rows - 1) and then progressively divide by 2.