并查集--basic
public class UnionFind1 {
private int[] parent; //数组,表示并查集所有元素的集合号
private int size; //表示并查集元素个数
public UnionFind1(int size) { //并查集初始化
this.size = size;
parent = new int[size];
for (int i = 0; i < size; i++) {
parent[i] = i;
}
}
/**
* 查看元素所属集合
*
* @param element
* @return
*/
private int find(int element) {
return parent[element];
}
/**
* 判断两个集合是否在同一个集合
*
* @param firstElement
* @param secondElement
* @return
*/
public boolean isConnected(int firstElement, int secondElement) {
return find(firstElement) == find(secondElement);
}
/**
* 合并firstElement,secondElement两个元素所在集合
* 将firstElement集合中所有元素的集合号都变为secondElement,就是认为是将两个集合合并
*
* @param firstElement
* @param secondElement
*/
public void unionElements(int firstElement, int secondElement) {
int firstUnion = find(firstElement);
int secondUnion = find(secondElement);
if (firstUnion != secondUnion) {
for (int i = 0; i < size; i++) {
if (parent[i] == firstUnion) {
parent[i] = secondUnion;
}
}
}
}
private void printArray() {
for (int id : this.parent) {
System.out.print(id + "\t");
}
System.out.println();
}
public static void main(String[] args) {
int n = 10;
UnionFind1 union = new UnionFind1(n);
System.out.println("初始：");
union.printArray();
System.out.println("连接了5 6");
union.unionElements(5, 6);
union.printArray();
System.out.println("连接了1 2");
union.unionElements(1, 2);
union.printArray();
System.out.println("连接了2 3");
union.unionElements(2, 3);
union.printArray();
System.out.println("连接了1 4");
union.unionElements(1, 4);
union.printArray();
System.out.println("连接了1 5");
union.unionElements(1, 5);
union.printArray();
System.out.println("1 6 是否连接：" + union.isConnected(1, 6));
System.out.println("1 8 是否连接：" + union.isConnected(1, 8));
}
}
快速合并
public class UnionFind2 {
private int[] parent;
private int size;
public UnionFind2(int size) { //初始化并查集
this.size = size;
parent = new int[size];
for (int i = 0; i < size; i++) {
parent[i] = i;
}
}
/**
* 查找element集合的头结点
* element=parent[element]:说明element元素是一个集合的头结点或者是自己一个集合
*
* @param element
* @return
*/
public int find(int element) {
while (element != parent[element]) {//此时说明element已不是自己一个结点了,所以通过循环找寻element所属集合的头结点
element = parent[element];
}
return element; //
}
/**
* 判断两个元素是否是一个集合:只需要判断两个元素所属集合的头结点是否相同即可
*
* @param firstElement
* @param secondElement
* @return
*/
public boolean isConnected(int firstElement, int secondElement) {
int firstUnion = find(firstElement);
int secondUnion = find(secondElement);
return firstUnion == secondUnion;
}
/**
* 合并firstElement,secondElement所在的两个集合
* 将firstElement集合的头结点指向secondElement集合的头结点
*
* @param firstElement
* @param secondElement
*/
public void unionElements(int firstElement, int secondElement) {
int firstUnion = find(firstElement);
int secondUnion = find(secondElement);
if (firstUnion != secondUnion) {
parent[firstElement] = secondUnion;
}
}
/**
* 打印每个元素所属集合的小组号,即它的上一个结点号
*/
private void printArray() {
for (int parent : parent) {
System.out.print(parent + " ");
}
System.out.println();
}
public static void main(String[] args) {
int n = 10;
UnionFind2 union = new UnionFind2(n);
System.out.println("初始：");
union.printArray();
System.out.println("连接了5 6");
union.unionElements(5, 6);
union.printArray();
System.out.println("连接了1 2");
union.unionElements(1, 2);
union.printArray();
System.out.println("连接了2 3");
union.unionElements(2, 3);
union.printArray();
System.out.println("连接了1 4");
union.unionElements(1, 4);
union.printArray();
System.out.println("连接了1 5");
union.unionElements(1, 5);
union.printArray();
System.out.println("1 6 是否连接：" + union.isConnected(1, 6));
System.out.println("1 8 是否连接：" + union.isConnected(1, 8));
}
}
快速合并--weight
public class UnionFind3 {
private int[] parent;
private int[] weight;
private int size;
public UnionFind3(int size) {
this.parent = new int[size];
this.weight = new int[size];
this.size = size;
for (int i = 0; i < size; i++) {
this.parent[i] = i;
this.weight[i] = 1;
}
}
/**
* 查找元素所属集合的头结点
*
* @param element
* @return
*/
public int find(int element) {
while (element != parent[element]) {
element = parent[element];
}
return element;
}
/**
* 判断两个元素是否是一个集合
*
* @param firstElement
* @param secondElement
* @return
*/
public boolean isConnected(int firstElement, int secondElement) {
return find(firstElement) == find(secondElement);
}
public void unionElements(int firstElement, int secondElement) {
int firstRoot = find(firstElement);
int secondRoot = find(secondElement);
if (firstRoot == secondRoot) {//已经是同一个集合的元素就不用再合并了
return;
}
//集合的子元素多的头结点,合并之后仍然做头结点
if (weight[firstRoot] > weight[secondRoot]) {
parent[secondRoot] = firstRoot;
weight[firstRoot] += weight[secondRoot];
} else {
parent[firstRoot] = secondRoot;
weight[secondRoot] += weight[firstRoot];
}
}
/**
* 打印parent数组
*/
public void printArray(int[] arr) {
for (int parent : arr) {
System.out.print(parent + "\t");
}
System.out.println();
}
public static void main(String[] args) {
int n = 10;
UnionFind3 union = new UnionFind3(n);
System.out.println("初始parent：");
union.printArray(union.parent);
System.out.println("初始weight：");
union.printArray(union.weight);
System.out.println("连接了5 6 之后的parent：");
union.unionElements(5, 6);
union.printArray(union.parent);
System.out.println("连接了5 6 之后的weight：");
union.printArray(union.weight);
System.out.println("连接了1 2 之后的parent：");
union.unionElements(1, 2);
union.printArray(union.parent);
System.out.println("连接了1 2 之后的weight：");
union.printArray(union.weight);
System.out.println("连接了2 3 之后的parent：");
union.unionElements(2, 3);
union.printArray(union.parent);
System.out.println("连接了2 3 之后的weight：");
union.printArray(union.weight);
System.out.println("连接了1 4 之后的parent：");
union.unionElements(1, 4);
union.printArray(union.parent);
System.out.println("连接了1 4 之后的weight：");
union.printArray(union.weight);
System.out.println("连接了1 5 之后的parent：");
union.unionElements(1, 5);
union.printArray(union.parent);
System.out.println("连接了1 5 之后的weight：");
union.printArray(union.weight);
System.out.println("1 6 是否连接：" + union.isConnected(1, 6));
System.out.println("1 8 是否连接：" + union.isConnected(1, 8));
}
}
快速合并--height
public class UnionFind4 {
private int[] parent;
private int[] height;
int size;
public UnionFind4(int size) {
this.size = size;
this.parent = new int[size];
this.height = new int[size];
for (int i = 0; i < size; i++) {
parent[i] = i;
height[i] = 1;
}
}
public int find(int element) {
while (element != parent[element]) {
element = parent[element];
}
return element;
}
public boolean isConnected(int firstElement, int secondElement) {
return find(firstElement) == find(secondElement);
}
public void unionElements(int firstElement, int secondElement) {
int firstRoot = find(firstElement);
int secondRoot = find(secondElement);
if (firstRoot == secondRoot) {
return;
}
if (height[firstRoot] > height[secondRoot]) {
parent[secondRoot] = firstRoot;
} else if (height[firstRoot] < height[secondRoot]) {
parent[firstRoot] = secondRoot;
} else {
parent[firstRoot] = secondRoot;
height[secondRoot] += 1;
}
}
private void printArray(int[] arr) {
for (int parent : arr) {
System.out.print(parent + " ");
}
System.out.println();
}
public static void main(String[] args) {
int n = 10;
UnionFind4 union = new UnionFind4(n);
System.out.println("初始parent：");
union.printArray(union.parent);
System.out.println("初始height：");
union.printArray(union.height);
System.out.println("连接了5 6 之后的parent：");
union.unionElements(5, 6);
union.printArray(union.parent);
System.out.println("连接了5 6 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 2 之后的parent：");
union.unionElements(1, 2);
union.printArray(union.parent);
System.out.println("连接了1 2 之后的height：");
union.printArray(union.height);
System.out.println("连接了2 3 之后的parent：");
union.unionElements(2, 3);
union.printArray(union.parent);
System.out.println("连接了2 3 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 4 之后的parent：");
union.unionElements(1, 4);
union.printArray(union.parent);
System.out.println("连接了1 4 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 5 之后的parent：");
union.unionElements(1, 5);
union.printArray(union.parent);
System.out.println("连接了1 5 之后的height：");
union.printArray(union.height);
System.out.println("1 6 是否连接：" + union.isConnected(1, 6));
System.out.println("1 8 是否连接：" + union.isConnected(1, 8));
}
}
路径压缩
public class UnionFind5 {
private int[] parent;
private int[] height;
int size;
public UnionFind5(int size) {
this.size = size;
this.parent = new int[size];
this.height = new int[size];
for (int i = 0; i < size; i++) {
parent[i] = i;
height[i] = 1;
}
}
public int find(int element) {
while (element != parent[element]) {
parent[element]=parent[parent[element]];//对于height比较大的,可以压缩路径
element = parent[element];
}
return element;
}
public boolean isConnected(int firstElement, int secondElement) {
return find(firstElement) == find(secondElement);
}
public void unionElements(int firstElement, int secondElement) {
int firstRoot = find(firstElement);
int secondRoot = find(secondElement);
if (firstRoot == secondRoot) {
return;
}
if (height[firstRoot] > height[secondRoot]) {
parent[secondRoot] = firstRoot;
} else if (height[firstRoot] < height[secondRoot]) {
parent[firstRoot] = secondRoot;
} else {
parent[firstRoot] = secondRoot;
height[secondRoot] += 1;
}
}
private void printArray(int[] arr) {
for (int parent : arr) {
System.out.print(parent + " ");
}
System.out.println();
}
public static void main(String[] args) {
int n = 10;
UnionFind5 union = new UnionFind5(n);
System.out.println("初始parent：");
union.printArray(union.parent);
System.out.println("初始height：");
union.printArray(union.height);
System.out.println("连接了5 6 之后的parent：");
union.unionElements(5, 6);
union.printArray(union.parent);
System.out.println("连接了5 6 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 2 之后的parent：");
union.unionElements(1, 2);
union.printArray(union.parent);
System.out.println("连接了1 2 之后的height：");
union.printArray(union.height);
System.out.println("连接了2 3 之后的parent：");
union.unionElements(2, 3);
union.printArray(union.parent);
System.out.println("连接了2 3 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 4 之后的parent：");
union.unionElements(1, 4);
union.printArray(union.parent);
System.out.println("连接了1 4 之后的height：");
union.printArray(union.height);
System.out.println("连接了1 5 之后的parent：");
union.unionElements(1, 5);
union.printArray(union.parent);
System.out.println("连接了1 5 之后的height：");
union.printArray(union.height);
System.out.println("1 6 是否连接：" + union.isConnected(1, 6));
System.out.println("1 8 是否连接：" + union.isConnected(1, 8));
}
}
例题
例题:How Many Tables
public class Main {
private int[] parent;
private int[] weight;
private int size;
private int groups;
public Main(int size) {
this.size = size;
this.groups = size;
this.parent = new int[size];
this.weight = new int[size];
for (int i = 0; i < size; i++) {
parent[i] = i;
weight[i] = 1;
}
}
public int find(int element) {
while (element != parent[element]) {
element = parent[element];
}
return element;
}
public boolean isConnected(int firstElement, int secondElement) {
return find(firstElement) == find(secondElement);
}
public void unionElement(int firstElement, int secondElement) {
int firstRoot = find(firstElement);
int secondRoot = find(secondElement);
if (firstRoot == secondRoot) {
return;
}
if (weight[firstRoot] < weight[secondRoot]) {
parent[firstRoot] = secondRoot;
weight[secondRoot] += weight[firstRoot];
} else {
parent[secondRoot] = firstRoot;
weight[firstRoot] += weight[secondRoot];
}
this.groups--;
}
public int getGroups() {
return this.groups;
}
public void printArray(int[] arr) {
for (int parent : arr) {
System.out.print(parent + " ");
}
System.out.println();
}
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int n = scan.nextInt();
for (int i = 0; i < n; i++) {
int N = scan.nextInt();
Main m = new Main(N);
int M = scan.nextInt();
for (int j = 0; j < M; j++) {
int a = scan.nextInt()-1;
int b = scan.nextInt()-1;
m.unionElement(a, b);
}
System.out.println(m.getGroups());
}
}
}
