有向图的转置算法

Question

I am trying to write a simple algorithm to represent a reverse directed adjacency matrix. I want this in in-place, with running time of Theta(n^2).

At first I had this:

for i=1 to n
         for k=1 to n
               //Reverse the edges and update the new adjacency list
                  A_new[k][i] = A_old[i][k]
return A_new

However, I realized the inner for loop would cause a problem because if first loop is going 1..n and second going form 1..n, you will need to swap everything twice.

What would the inner for loop have to be to avoid this?

Answer 1

Your code is fine if you're returning a new matrix. If you want to flip the matrix in place, then you iterate over the upper triangle, and swap each element with the lower triangle like this:

for i=1 to n-1
    for j=i+1 to n
        temp = A[i][j];
        A[i][j] = A[j][i];
        A[j][i] = temp;