Edited highlights

An Example induction argument

An Example induction argument: Closed Form First Order Recurrence Relation

• A small example, to illustrate the recursive nature of Dijkstra's algorithm, and to illustrate the graphs resulting from the procedure.
• A larger graph example of Dijkstra's, carried out with the arrays and style suggested by our author.
• An illustration of Bellman-Ford, in which we seek shortest paths by paths of successively larger length.

  A tree provides a useful means of doing the accounting of the algorithm. In the end, a variety of rooted minimal spanning tree results, with the starting node as the root.

• An illustration of the Floyd sweep: we sweep across the adjacency matrix, checking for shortcuts: \[ d(i,x) + d(x,j) \le d(i,j) \] By the time we've swept all columns and rows, the original adjacency matrix is replaced by a matrix containing all shortest path distances.

  We don't know, however, exactly what path produces those values between any two given nodes.