code:

private void arbitrateCosts() {
        logMatrix(0);

        stepOne();
        stepTwo();

        // if stepThree returns true, done.
        // if stepThree returns false, do the process again
        while (!stepThree()) {

            // if stepFour returns true, go to step 6
            // if stepFour returns false, go to step 5
            while (stepFour()) {
                stepSix();
            }

            stepFive();
        }
    }

    /**
     * STEP 1.
     * 
     * For each row of the matrix, find the smallest element and subtract it from
     * every element in its row. Go to Step 2. We can define a local variable
     * called minval that is used to hold the smallest value in a row. Notice
     * that there are two loops over the index j appearing inside an outer loop
     * over the index i. The first inner loop over the index j searches a row
     * for the minval. Once minval has been found this value is subtracted from
     * each element of that row in the second inner loop over j. The value of
     * step is set to 2 just before stepone ends.
     * 
     */
    private void stepOne() {
        for (int i = 0; i < n; i++) {
            double minVal = Double.MAX_VALUE;

            for (int j = 0; j < m; j++) {
                minVal = Math.min(minVal, costMatrix[i][j].cost);
            }

            if (minVal > 0) {
                for (int j = 0; j < m; j++) {
                    costMatrix[i][j].cost -= minVal;
                }
            }
        }

        logMatrix(1);
    }