Closest distance between two points(disjoint set)

Question

This problem is a kind of closest pair between two disjoint set. Upperside picture

Answer 1

I worked on a similar problem where I had to find a nearest member to identify if a member belong to a cluster within a cluster. I was trying to identify clusters within clusters. Here is the code, This might help you get start.

/**
 * Find the nearest neighbor based on the distance threshold.
 * TODO:
 * @param currentPoint current point in the memory.
 * @param threshold dynamic distance threshold.
 * @return return the neighbor.
 */

private double nearestNeighbor(double currentPoint) {

    HashMap unsorted = new HashMap();
    TreeMap sorted = null; 
    double foundNeighbor = 0.0;

    for (int i = 0; i < bigCluster.length; i++) {
        if (bigCluster[i] != 0.0 && bigCluster[i] != currentPoint) {
            double shortestDistance = Math.abs(currentPoint - bigCluster[i]);
            if (shortestDistance <= this.getDistanceThreshold())
                unsorted.put(shortestDistance, bigCluster[i]);
        }
    }
    if (!unsorted.isEmpty()) {
        sorted = new TreeMap(unsorted);
        this.setDistanceThreshold(avgDistanceInCluster());
        foundNeighbor = sorted.firstEntry().getValue();
        return foundNeighbor;
    } else {
        return 0.0;
    }
} 


/**
 * Method will check if a point belongs to a cluster based on the dynamic 
 * threshold.
 */
public void isBelongToCluster() {


        for (int i=0; i < tempList.size(); i++) {

            double aPointInCluster = tempList.get(i);

            cluster.add(aPointInCluster);
            double newNeighbor = nearestNeighbor(aPointInCluster);
            if ( newNeighbor != 0.0) {
                cluster.add(newNeighbor);
                if (i + 1 > tempList.size() && (visited[i] != true)) {
                    isBelongToCluster();
                }
            }

        }

    for (int i=0; i < cluster.size(); i++) {
        if (cluster.get(i) != 0.0)
            System.out.println("whats in the cluster -> " + cluster.get(i)); 
    } 
}