Bumped by Community user

occurred Aug 25 at 23:04

Bumped by Community user

occurred Apr 27 at 22:05

Bumped by Community user

occurred Dec 29, 2023 at 22:05

Bumped by Community user

occurred Aug 31, 2023 at 21:08

Bumped by Community user

occurred May 3, 2023 at 19:03

Bumped by Community user

occurred Jan 3, 2023 at 18:06

Bumped by Community user

occurred Sep 5, 2022 at 17:05

Bumped by Community user

occurred May 8, 2022 at 17:01

Bumped by Community user

occurred Jan 8, 2022 at 16:01

Add Java code environment

Source Link

edited Dec 9, 2021 at 15:36

John Kemeny

17.1k
3
43
67

public class WeightedQuickUnion {

int[] parent;   // parent[i] = parent of i  
int[] size;     // size[i] = number of sites in subtree rooted at i
int count;      // number of components

/**
 * Initializes an empty union–find data structure 
 * Each site is initially in its own 
 * component.
 * n is the number of sites
 */
public WeightedQuickUnion(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;
    }
}

/**
 * Return the number of components.
 *
 */
public int count() {
    return count;
}

/**
 * return the component identifier for the component containing p.
 * p the integer representing the item
 */
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));  
    }
}

/**
 * return true if the the item p and item q are in the same component.
 */
public boolean connected(int p, int q) {
    return find(p) == find(q);
}

/**
 * Merge the component containing p with the 
 * the component containing q.
 */
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--;
}

public class WeightedQuickUnion {

    int[] parent; // parent[i] = parent of i
    int[] size; // size[i] = number of sites in subtree rooted at i
    int count; // number of components

    /**
     * Initializes an empty union–find data structure
     * Each site is initially in its own
     * component.
     * n is the number of sites
     */
    public WeightedQuickUnion(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;
        }
    }

    /**
     * Return the number of components.
     *
     */
    public int count() {
        return count;
    }

    /**
     * return the component identifier for the component containing p.
     * p the integer representing the item
     */
    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));
        }
    }

    /**
     * return true if the the item p and item q are in the same component.
     */
    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    /**
     * Merge the component containing p with the
     * the component containing q.
     */
    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--;
    }

public class WeightedQuickUnion {

int[] parent;   // parent[i] = parent of i  
int[] size;     // size[i] = number of sites in subtree rooted at i
int count;      // number of components

/**
 * Initializes an empty union–find data structure 
 * Each site is initially in its own 
 * component.
 * n is the number of sites
 */
public WeightedQuickUnion(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;
    }
}

/**
 * Return the number of components.
 *
 */
public int count() {
    return count;
}

/**
 * return the component identifier for the component containing p.
 * p the integer representing the item
 */
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));  
    }
}

/**
 * return true if the the item p and item q are in the same component.
 */
public boolean connected(int p, int q) {
    return find(p) == find(q);
}

/**
 * Merge the component containing p with the 
 * the component containing q.
 */
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--;
}

public class WeightedQuickUnion {

    int[] parent; // parent[i] = parent of i
    int[] size; // size[i] = number of sites in subtree rooted at i
    int count; // number of components

    /**
     * Initializes an empty union–find data structure
     * Each site is initially in its own
     * component.
     * n is the number of sites
     */
    public WeightedQuickUnion(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;
        }
    }

    /**
     * Return the number of components.
     *
     */
    public int count() {
        return count;
    }

    /**
     * return the component identifier for the component containing p.
     * p the integer representing the item
     */
    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));
        }
    }

    /**
     * return true if the the item p and item q are in the same component.
     */
    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    /**
     * Merge the component containing p with the
     * the component containing q.
     */
    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--;
    }

Bumped by Community user

occurred Dec 9, 2021 at 15:08

Bumped by Community user

occurred Aug 11, 2021 at 14:07

Bumped by Community user

occurred Apr 13, 2021 at 13:08

Bumped by Community user

occurred Dec 14, 2020 at 12:04

Bumped by Community user

occurred Aug 16, 2020 at 10:04

Bumped by Community user

occurred Apr 18, 2020 at 9:05

Bumped by Community user

occurred Dec 20, 2019 at 9:01

Bumped by Community user

occurred Aug 22, 2019 at 8:03

Bumped by Community user

occurred Apr 24, 2019 at 6:01

Bumped by Community user

occurred Dec 25, 2018 at 5:02

Bumped by Community user

occurred Nov 25, 2018 at 5:00

Source Link

asked Oct 23, 2018 at 14:44

aky

85
6

communities problem with union and find

I am trying to solve the following problem:

Input is $2D$ array of integers, $M$, which corresponds to friendship relations. For example, if $M[1][2]=1$, $1$ and $2$ are friends (assuming symmetry it is also true that $M[2][1]=1$). If $M[2][3]=1$, then $\{1,2,3\}$ is a community. If all other entries are $0$, then $\{0\}$ is a community by itself, $\{4\}$ is a community by itself, etc. One can think of $M$ as representation of a graph with $V$ nodes, and $E$ edges. $M$ is $VxV$ matrix and the entries with value $1$ correspond to edges of an undirected graph. For the above example, the total number of communities is $V-2$.

I need to explain the following:

If we solve the above problem with union and find operations (weighted quick union), it will take $O(E+Vlog(V))$ time, explain.

I wrote the code for this. I am also including weighted union and find algorithm code as well below for completeness (but it is a standard known algorithm I guess). With the way I implement it, it does not look like this algorithm takes O(E+Vlog(V)) time. I need to understand how can this be done in O(E+Vlog(V)) time.

It is said that find operation takes O(log(V)) time because the tree is almost balanced with weighted quick union algorithm.

This is my code:

The code for weighted quick union and find (given):

public class WeightedQuickUnion {

int[] parent;   // parent[i] = parent of i  
int[] size;     // size[i] = number of sites in subtree rooted at i
int count;      // number of components

/**
 * Initializes an empty union–find data structure 
 * Each site is initially in its own 
 * component.
 * n is the number of sites
 */
public WeightedQuickUnion(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;
    }
}

/**
 * Return the number of components.
 *
 */
public int count() {
    return count;
}

/**
 * return the component identifier for the component containing p.
 * p the integer representing the item
 */
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));  
    }
}

/**
 * return true if the the item p and item q are in the same component.
 */
public boolean connected(int p, int q) {
    return find(p) == find(q);
}

/**
 * Merge the component containing p with the 
 * the component containing q.
 */
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--;
}

Stack Exchange Network

Return to Question

communities problem with union and find