Implement the Hungarian Algorithm in C++. Make sure to provide proper commenting that clearly shows what step is about to be taken. Also, please provide a complete write-down in full sentences to explain your implementation. Additionally, provide clear screenshots of the execution of your algorithm.

You may choose (not necessary) to refer to the following steps and outline of the Hungarian Algorithm:

The Hungarian algorithm consists of the four steps below. The first two steps are executed once, while Steps 3 and 4 are repeated until an optimal assignment is found. The input of the algorithm is an n by n square matrix with only nonnegative elements.

Step 1: Subtract row minima

For each row, find the lowest element and subtract it from each element in that row.

Step 2: Subtract column minima

Similarly, for each column, find the lowest element and subtract it from each element in that column.

Step 3: Cover all zeros with a minimum number of lines

Cover all zeros in the resulting matrix using a minimum number of horizontal and vertical lines. If n lines are required, an optimal assignment exists among the zeros. The algorithm stops.

If less than n lines are required, continue with Step 4.

Step 4: Create additional zeros

Find the smallest element (call it k) that is not covered by a line in Step 3. Subtract k from all uncovered elements, and add k to all elements that are covered twice.