Added examples

Author: mlazaric

README.md

@@ -1 +1,38 @@
-# Hanoi-Matlab
+# Hanoi Matlab
+
+A simple function that generates a graph object of the possible moves in a game of Hanoi with `numOfPegs` pegs and `numOfDisks` disks.
+
+## Explanation of the graph
+Each node represents a possible state of the Hanoi game and each node is represented by a string with `numOfDisks` characters where the `k`-th element represents the position of the `k`-th biggest disk, so ABC means the biggest disk is on the first peg, the second biggest is on the second one and the smallest one is on the third peg.
+
+Each edge represents a valid move in the game.
+
+## Examples
+
+### 2D Graph
+```
+G = hanoi(3, 3);
+plot(G);
+```
+
+![3_3.jpg](images/3_3.jpg)
+
+### 3D Graph
+```
+G = hanoi(2, 4);
+p = plot(G);
+layout(p, 'force3');
+view(3);
+```
+
+![2_4_3d.jpg](images/2_4_3d.jpg)
+
+### Shortest path
+```
+G = hanoi(3, 3);
+p = plot(G);
+path = shortestpath(G, 'AAA', 'CCC');
+highlight(p, path, 'NodeColor', 'r', 'EdgeColor', 'r');
+```
+
+![3_3_shortest.jpg](images/3_3_shortest.jpg)

hanoi.m

@@ -1,3 +1,13 @@
+% Returns a graph object representing the possible moves in a game of Hanoi
+% with numOfDisks disks and numOfPegs pegs.
+%
+% Each node is a state of the Hanoi game and each edge is a move.
+%
+% A state is represented with a vector whreich has numOfDisks elements and
+% the k-th element represents the current position of (numOfDisks - k)-th
+% disk. So if we have a game of 3 disks and 3 pegs and the state is [1 2
+% 3], the smallest disk is on the third peg and the biggest is on the first
+% peg.
 function G = hanoi(numOfDisks, numOfPegs)
     numOfNodes = numOfPegs^numOfDisks;
     numOfEdges = 0;
@@ -12,7 +22,6 @@
             toVector = numberToVectorInBase(to - 1);
 
             if isValidEdge(fromVector, toVector)
-                %disp([getNameOfNode(fromVector), ' ', getNameOfNode(toVector)]);
                 beginEdge(numOfEdges + 1) = from;
                 endEdge(numOfEdges + 1) = to;
                 numOfEdges = numOfEdges + 1;
@@ -24,6 +33,15 @@
 
     G = graph(beginEdge, endEdge, ones(1, numOfEdges), names);
 
+    % Checks if an edge is a valid move in Hanoi
+    % For it to be valid, it needs to satisfy three conditions:
+    %
+    % 1) Only one disk can be moved in one move
+    % 2) You cannot move a disk which has a smaller disk on it
+    % 3) You cannot move a disk to a peg which already has a smaller disk
+    % on it
+    %
+    % Returns 1 if it is valid, 0 if it is invalid
     function validEdge = isValidEdge(fromVector, toVector)
         numOfChanges = 0;
         firstChanged = -1;