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POCycle finding algorithm
 

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    <p>I need do find a cycle beginning and ending at given point. It is not guaranteed that it exists. I use <code>bool[,] points</code> to indicate which point can be in cycle. Poins can be only on grid. <code>points</code> indicates if given point on grid can be in cycle. I need to find this cycle using as minimum number of points. One point can be used only once. Connection can be only vertical or horizontal.</p> <p>Let this be our points (red is starting point):</p> <p><em>removing dead ImageShack links</em></p> <p>I realized that I can do this:</p> <pre><code>while(numberOfPointsChanged) { //remove points that are alone in row or column } </code></pre> <p>So i have:</p> <p><em>removing dead ImageShack links</em></p> <p>Now, I can find the path.</p> <p><em>removing dead ImageShack links</em></p> <p>But what if there are points that are not deleted by this loop but should not be in path?</p> <p>I have written code:</p> <pre><code>class MyPoint { public int X { get; set; } public int Y { get; set; } public List&lt;MyPoint&gt; Neighbours = new List&lt;MyPoint&gt;(); public MyPoint parent = null; public bool marked = false; } private static MyPoint LoopSearch2(bool[,] mask, int supIndexStart, int recIndexStart) { List&lt;MyPoint&gt; points = new List&lt;MyPoint&gt;(); //here begins translation bool[,] to list of points points.Add(new MyPoint { X = recIndexStart, Y = supIndexStart }); for (int i = 0; i &lt; mask.GetLength(0); i++) { for (int j = 0; j &lt; mask.GetLength(1); j++) { if (mask[i, j]) { points.Add(new MyPoint { X = j, Y = i }); } } } for (int i = 0; i &lt; points.Count; i++) { for (int j = 0; j &lt; points.Count; j++) { if (i != j) { if (points[i].X == points[j].X || points[i].Y == points[j].Y) { points[i].Neighbours.Add(points[j]); } } } } //end of translating List&lt;MyPoint&gt; queue = new List&lt;MyPoint&gt;(); MyPoint start = (points[0]); //beginning point start.marked = true; //it is marked MyPoint last=null; //last point. this will be returned queue.Add(points[0]); while(queue.Count&gt;0) { MyPoint current = queue.First(); //taking point from queue queue.Remove(current); //removing it foreach(MyPoint neighbour in current.Neighbours) //checking Neighbours { if (!neighbour.marked) //in neighbour isn't marked adding it to queue { neighbour.marked = true; neighbour.parent = current; queue.Add(neighbour); } //if neighbour is marked checking if it is startig point and if neighbour's parent is current point. if it is not that means that loop already got here so we start searching parents to got to starting point else if(!neighbour.Equals(start) &amp;&amp; !neighbour.parent.Equals(current)) { current = neighbour; while(true) { if (current.parent.Equals(start)) { last = current; break; } else current = current.parent; } break; } } } return last; } </code></pre> <p>But it doesn't work. The path it founds contains two points: start and it's first neighbour.<br> What am I doing wrong?</p> <p><strong>EDIT:</strong> Forgot to mention... After horizontal connection there has to be vertical, horizontal, vertical and so on... What is more in each row and column there need to be max two points (two or none) that are in the cycle. But this condition is the same as "The cycle has to be the shortest one".</p>
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    1. COWhat you are calling a “loop” is usually called a “cycle” in graph theory (and it wasn’t at all clear what you meant by “loop” until I had looked at your pictures). I edited the question appropriately to make it comprehensible. Still, it’s not clear how your points are stored in in the two-dimensional boolean array.
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      1. USKonrad Rudolph
    2. COEdited to clarify how I store points.
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    3. COthis is not a C# question, is is only a question regarding algorithm.
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