Merge pull request kennyledet#421 from girishramnani/master

union find algorithm

union_find_algorithm/girishramnani/UF.java

@@ -0,0 +1,86 @@
+
+
+
+public class UF {
+    private int[] id;     // id[i] = parent of i
+    private byte[] rank;  // rank[i] = rank of subtree rooted at i (cannot be more than 31)
+    private int count;    // number of components
+
+    /**
+     * Initializes an empty union-find data structure with <tt>N</tt>
+     * isolated components <tt>0</tt> through <tt>N-1</tt>
+     * @throws java.lang.IllegalArgumentException if <tt>N &lt; 0</tt>
+     * @param N the number of sites
+     */
+    public UF(int N) {
+        if (N < 0) throw new IllegalArgumentException();
+        count = N;
+        id = new int[N];
+        rank = new byte[N];
+        for (int i = 0; i < N; i++) {
+            id[i] = i;
+            rank[i] = 0;
+        }
+    }
+
+    /**
+     * Returns the component identifier for the component containing site <tt>p</tt>.
+     * @param p the integer representing one object
+     * @return the component identifier for the component containing site <tt>p</tt>
+     * @throws java.lang.IndexOutOfBoundsException unless <tt>0 &le; p &lt; N</tt>
+     */
+    public int find(int p) {
+        if (p < 0 || p >= id.length) throw new IndexOutOfBoundsException();
+        while (p != id[p]) {
+            id[p] = id[id[p]];    // path compression by halving
+            p = id[p];
+        }
+        return p;
+    }
+
+    /**
+     * Returns the number of components.
+     * @return the number of components (between <tt>1</tt> and <tt>N</tt>)
+     */
+    public int count() {
+        return count;
+    }
+
+    /**
+     * Are the two sites <tt>p</tt> and <tt>q</tt> in the same component?
+     * @param p the integer representing one site
+     * @param q the integer representing the other site
+     * @return true if the two sites <tt>p</tt> and <tt>q</tt> are in the same component; false otherwise
+     * @throws java.lang.IndexOutOfBoundsException unless
+     *      both <tt>0 &le; p &lt; N</tt> and <tt>0 &le; q &lt; N</tt>
+     */
+    public boolean connected(int p, int q) {
+        return find(p) == find(q);
+    }
+
+
+    /**
+     * Merges the component containing site <tt>p</tt> with the 
+     * the component containing site <tt>q</tt>.
+     * @param p the integer representing one site
+     * @param q the integer representing the other site
+     * @throws java.lang.IndexOutOfBoundsException unless
+     *      both <tt>0 &le; p &lt; N</tt> and <tt>0 &le; q &lt; N</tt>
+     */
+    public void union(int p, int q) {
+        int i = find(p);
+        int j = find(q);
+        if (i == j) return;
+
+        // make root of smaller rank point to root of larger rank
+        if      (rank[i] < rank[j]) id[i] = j;
+        else if (rank[i] > rank[j]) id[j] = i;
+        else {
+            id[j] = i;
+            rank[i]++;
+        }
+        count--;
+    }
+
+
+}