QuickFindUF.java
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/******************************************************************************
* Compilation: javac QuickFindUF.java
* Execution: java QuickFindUF < input.txt
* Dependencies: StdIn.java StdOut.java
* Data files: http://algs4.cs.princeton.edu/15uf/tinyUF.txt
* http://algs4.cs.princeton.edu/15uf/mediumUF.txt
* http://algs4.cs.princeton.edu/15uf/largeUF.txt
*
* Quick-find algorithm.
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code QuickFindUF} class represents a <em>union–find data type</em>
* (also known as the <em>disjoint-sets data type</em>).
* It supports the <em>union</em> and <em>find</em> operations,
* along with a <em>connected</em> operation for determining whether
* two sites are in the same component and a <em>count</em> operation that
* returns the total number of components.
* <p>
* The union–find data type models connectivity among a set of <em>n</em>
* sites, named 0 through <em>n</em>−1.
* The <em>is-connected-to</em> relation must be an
* <em>equivalence relation</em>:
* <ul>
* <li> <em>Reflexive</em>: <em>p</em> is connected to <em>p</em>.
* <li> <em>Symmetric</em>: If <em>p</em> is connected to <em>q</em>,
* then <em>q</em> is connected to <em>p</em>.
* <li> <em>Transitive</em>: If <em>p</em> is connected to <em>q</em>
* and <em>q</em> is connected to <em>r</em>, then
* <em>p</em> is connected to <em>r</em>.
* </ul>
* <p>
* An equivalence relation partitions the sites into
* <em>equivalence classes</em> (or <em>components</em>). In this case,
* two sites are in the same component if and only if they are connected.
* Both sites and components are identified with integers between 0 and
* <em>n</em>−1.
* Initially, there are <em>n</em> components, with each site in its
* own component. The <em>component identifier</em> of a component
* (also known as the <em>root</em>, <em>canonical element</em>, <em>leader</em>,
* or <em>set representative</em>) is one of the sites in the component:
* two sites have the same component identifier if and only if they are
* in the same component.
* <ul>
* <li><em>union</em>(<em>p</em>, <em>q</em>) adds a
* connection between the two sites <em>p</em> and <em>q</em>.
* If <em>p</em> and <em>q</em> are in different components,
* then it replaces
* these two components with a new component that is the union of
* the two.
* <li><em>find</em>(<em>p</em>) returns the component
* identifier of the component containing <em>p</em>.
* <li><em>connected</em>(<em>p</em>, <em>q</em>)
* returns true if both <em>p</em> and <em>q</em>
* are in the same component, and false otherwise.
* <li><em>count</em>() returns the number of components.
* </ul>
* <p>
* The component identifier of a component can change
* only when the component itself changes during a call to
* <em>union</em>—it cannot change during a call
* to <em>find</em>, <em>connected</em>, or <em>count</em>.
* <p>
* This implementation uses quick find.
* Initializing a data structure with <em>n</em> sites takes linear time.
* Afterwards, the <em>find</em>, <em>connected</em>, and <em>count</em>
* operations take constant time but the <em>union</em> operation
* takes linear time.
* For alternate implementations of the same API, see
* {@link UF}, {@link QuickUnionUF}, and {@link WeightedQuickUnionUF}.
*
* <p>
* For additional documentation, see <a href="http://algs4.cs.princeton.edu/15uf">Section 1.5</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class QuickFindUF {
private int[] id; // id[i] = component identifier of i
private int count; // number of components
/**
* Initializes an empty union–find data structure with {@code n} sites
* {@code 0} through {@code n-1}. Each site is initially in its own
* component.
*
* @param n the number of sites
* @throws IllegalArgumentException if {@code n < 0}
*/
public QuickFindUF(int n) {
count = n;
id = new int[n];
for (int i = 0; i < n; i++)
id[i] = i;
}
/**
* Returns the number of components.
*
* @return the number of components (between {@code 1} and {@code n})
*/
public int count() {
return count;
}
/**
* Returns the component identifier for the component containing site {@code p}.
*
* @param p the integer representing one site
* @return the component identifier for the component containing site {@code p}
* @throws IndexOutOfBoundsException unless {@code 0 <= p < n}
*/
public int find(int p) {
validate(p);
return id[p];
}
// validate that p is a valid index
private void validate(int p) {
int n = id.length;
if (p < 0 || p >= n) {
throw new IndexOutOfBoundsException("index " + p + " is not between 0 and " + (n-1));
}
}
/**
* Returns true if the the two sites are in the same component.
*
* @param p the integer representing one site
* @param q the integer representing the other site
* @return {@code true} if the two sites {@code p} and {@code q} are in the same component;
* {@code false} otherwise
* @throws IndexOutOfBoundsException unless
* both {@code 0 <= p < n} and {@code 0 <= q < n}
*/
public boolean connected(int p, int q) {
validate(p);
validate(q);
return id[p] == id[q];
}
/**
* Merges the component containing site {@code p} with the
* the component containing site {@code q}.
*
* @param p the integer representing one site
* @param q the integer representing the other site
* @throws IndexOutOfBoundsException unless
* both {@code 0 <= p < n} and {@code 0 <= q < n}
*/
public void union(int p, int q) {
validate(p);
validate(q);
int pID = id[p]; // needed for correctness
int qID = id[q]; // to reduce the number of array accesses
// p and q are already in the same component
if (pID == qID) return;
for (int i = 0; i < id.length; i++)
if (id[i] == pID) id[i] = qID;
count--;
}
/**
* Reads in a sequence of pairs of integers (between 0 and n-1) from standard input,
* where each integer represents some site;
* if the sites are in different components, merge the two components
* and print the pair to standard output.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
int n = StdIn.readInt();
QuickFindUF uf = new QuickFindUF(n);
while (!StdIn.isEmpty()) {
int p = StdIn.readInt();
int q = StdIn.readInt();
if (uf.connected(p, q)) continue;
uf.union(p, q);
StdOut.println(p + " " + q);
}
StdOut.println(uf.count() + " components");
}
}
/******************************************************************************
* Copyright 2002-2016, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/