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/******************************************************************************
* Compilation: javac WeightedQuickUnionUF.java
* Execution: java WeightedQuickUnionUF < input.txt
* Dependencies: StdIn.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/15uf/tinyUF.txt
* https://algs4.cs.princeton.edu/15uf/mediumUF.txt
* https://algs4.cs.princeton.edu/15uf/largeUF.txt
*
* Weighted quick-union (without path compression).
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code WeightedQuickUnionUF} class represents a union–find data type
* (also known as the disjoint-sets data type).
* It supports the union and find operations,
* along with a connected operation for determining whether
* two sites are in the same component and a count operation that
* returns the total number of components.
*
* The union–find data type models connectivity among a set of n
* sites, named 0 through n–1.
* The is-connected-to relation must be an
* equivalence relation:
*
* - Reflexive: p is connected to p.
*
- Symmetric: If p is connected to q,
* then q is connected to p.
*
- Transitive: If p is connected to q
* and q is connected to r, then
* p is connected to r.
*
*
* An equivalence relation partitions the sites into
* equivalence classes (or components). 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
* n–1.
* Initially, there are n components, with each site in its
* own component. The component identifier of a component
* (also known as the root, canonical element, leader,
* or set representative) 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.
*
* - union(p, q) adds a
* connection between the two sites p and q.
* If p and q are in different components,
* then it replaces
* these two components with a new component that is the union of
* the two.
*
- find(p) returns the component
* identifier of the component containing p.
*
- connected(p, q)
* returns true if both p and q
* are in the same component, and false otherwise.
*
- count() returns the number of components.
*
*
* The component identifier of a component can change
* only when the component itself changes during a call to
* union—it cannot change during a call
* to find, connected, or count.
*
* This implementation uses weighted quick union by size (without path compression).
* Initializing a data structure with n sites takes linear time.
* Afterwards, the union, find, and connected
* operations take logarithmic time (in the worst case) and the
* count operation takes constant time.
* For alternate implementations of the same API, see
* {@link UF}, {@link QuickFindUF}, and {@link QuickUnionUF}.
*
*
* For additional documentation, see Section 1.5 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class WeightedQuickUnionUF {
private int[] parent; // parent[i] = parent of i
private int[] size; // size[i] = number of sites in subtree rooted at 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 WeightedQuickUnionUF(int n) {
count = n;
parent = new int[n];
size = new int[n];
for (int i = 0; i < n; i++) {
parent[i] = i;
size[i] = 1;
}
}
/**
* 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 object
* @return the component identifier for the component containing site {@code p}
* @throws IllegalArgumentException unless {@code 0 <= p < n}
*/
public int find(int p) {
validate(p);
while (p != parent[p])
p = parent[p];
return p;
}
// validate that p is a valid index
private void validate(int p) {
int n = parent.length;
if (p < 0 || p >= n) {
throw new IllegalArgumentException("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 IllegalArgumentException unless
* both {@code 0 <= p < n} and {@code 0 <= q < n}
*/
public boolean connected(int p, int q) {
return find(p) == find(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 IllegalArgumentException unless
* both {@code 0 <= p < n} and {@code 0 <= q < n}
*/
public void union(int p, int q) {
int rootP = find(p);
int rootQ = find(q);
if (rootP == rootQ) return;
// make smaller root point to larger one
if (size[rootP] < size[rootQ]) {
parent[rootP] = rootQ;
size[rootQ] += size[rootP];
}
else {
parent[rootQ] = rootP;
size[rootP] += size[rootQ];
}
count--;
}
/**
* Reads in a sequence of pairs of integers (between 0 and n-1) from standard input,
* where each integer represents some object;
* 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();
WeightedQuickUnionUF uf = new WeightedQuickUnionUF(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 2002-2018, 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.
******************************************************************************/