算法14.并查集

算法|14.图相关算法

1.并查集（map版）

package greedy;

import java.util.HashMap;
import java.util.List;
import java.util.Stack;

public class UnionFind0 {
    public static class Node<V>{
        V value;
        public Node(V v){
            value=v;
        }
    }
    public static class UnionFind<V>{
        public HashMap<V,Node<V>> nodes;
        public HashMap<Node<V>,Node<V>> parents;
        public HashMap<Node<V>,Integer> sizeMap;

        public UnionFind(List<V> values) {
            nodes=new HashMap<>();
            parents=new HashMap<>();
            sizeMap=new HashMap<>();
            for (V cur:values) {
                Node<V> node=new Node<>(cur);
                nodes.put(cur,node);
                parents.put(node,node);
                sizeMap.put(node,1);
            }
        }
        public Node<V> findFather(Node<V> cur){
            Stack<Node<V>> path=new Stack<>();
            while(cur!=parents.get(cur)){
                path.push(cur);
                cur=parents.get(cur);
            }
            while(!path.isEmpty()){
                parents.put(path.pop(),cur);
            }
            return cur;
        }
        public boolean isSameSet(V a,V b){
            return findFather(nodes.get(a))==findFather(nodes.get(b));
        }
        public void union(V a,V b){
            Node<V> aHead=findFather(nodes.get(a));
            Node<V> bHead=findFather(nodes.get(b));
            if(aHead!=bHead){
                int aSetSize=sizeMap.get(aHead);
                int bSetSize=sizeMap.get(bHead);
                Node<V> big=aSetSize>=bSetSize?aHead:bHead;
                Node<V> small=big==aHead?bHead:aHead;
                parents.put(small,big);
                sizeMap.put(big,aSetSize+bSetSize);
                sizeMap.remove(small);
            }
        }
        public int sets(){
            return sizeMap.size();
        }
    }
}

2.并查集（数组版）

package greedy;

import java.io.*;

public class UnionFind1 {
    public static int MAXN=100001;
    public static int[] father=new int[MAXN];
    public static int[] size=new int[MAXN];
    public static int[] help=new int[MAXN];

    //初始化并查集
    public static void init(int n){
        for (int i = 0; i <= n; i++) {
            father[i]=i;
            size[i]=1;
        }
    }

    //从i开始寻找集合代表点
    public static int find(int i){
        int hi=0;
        while(i!=father[i]){
            help[hi++]=i;
            i=father[i];
        }
        //为什么是两次hi--
        for(hi--;hi>=0;hi--){
            father[help[hi]]=i;
        }
        return i;
    }

    //查询x和y是不是一个集合
    public static boolean isSameSet(int x,int y){
        return find(x)==find(y);
    }

    //x所在的集合和y所在的集合合并成一个集合
    public static void union(int x,int y){
        int fx=find(x);
        int fy=find(y);
        if(fx!=fy){
            if(size[fx]>=size[fy]){
                size[fx]+=size[fy];
                father[fy]=fx;
            }else{
                size[fy]+=size[fx];
                father[fx]=fy;
            }
        }
    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StreamTokenizer in = new StreamTokenizer(br);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        while (in.nextToken() != StreamTokenizer.TT_EOF) {
            int n = (int) in.nval;
            init(n);
            in.nextToken();
            int m = (int) in.nval;
            for (int i = 0; i < m; i++) {
                in.nextToken();
                int op = (int) in.nval;
                in.nextToken();
                int x = (int) in.nval;
                in.nextToken();
                int y = (int) in.nval;
                if (op == 1) {
                    out.println(isSameSet(x, y) ? "Yes" : "No");
                    out.flush();
                } else {
                    union(x, y);
                }
            }
        }
    }
}

3.朋友圈

package unionfind;

public class FriendCircle {
    public static class UnionFInd{
        //parent[i]=k:i的父亲是k
        private int[] parent;
        //size[i]=k:如果i是代表节点，size[i]才有意义，否则无意义
        //i所在的集合大小是多少
        private int[] size;
        //辅助结构
        private int[] help;
        //一共有多少个集合
        private int sets;
        public UnionFInd(int N){
            parent=new int[N];
            size=new int[N];
            help=new int[N];
            sets=N;
            for (int i = 0; i < N; i++) {
                parent[i]=i;
                size[i]=1;
            }
        }
        //从i开始一直往上，往上再往上，代表节点，返回
        //这个过程要做路径压缩
        private int find(int i){
            int hi=0;
            while(i!=parent[i]){
                help[hi++]=i;
                i=parent[i];
            }
            for(hi--;hi>=0;hi--){
                parent[help[hi]]=i;
            }
            return i;
        }

        public void union(int i,int j){
            int f1=find(i);
            int f2=find(j);
            if(f1!=f2){
                if(size[f1]>=size[f2]){
                    size[f1]+=size[f2];
                    parent[f2]=f1;
                }else{
                    size[f2]+=size[f1];
                    parent[f1]=f2;
                }
                sets--;
            }
        }
        public int sets(){
            return sets;
        }
    }
}

4.岛问题

package unionfind;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Stack;

public class NumberOfIslands {
    public static int numIslands3(char[][] board) {
        int islands = 0;
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[0].length; j++) {
                if (board[i][j] == '1') {
                    islands++;
                    infect(board, i, j);
                }
            }
        }
        return islands;
    }

    // 从(i,j)这个位置出发，把所有练成一片的'1'字符，变成0
    public static void infect(char[][] board, int i, int j) {
        if (i < 0 || i == board.length || j < 0 || j == board[0].length || board[i][j] != '1') {
            return;
        }
        board[i][j] = 0;
        infect(board, i - 1, j);
        infect(board, i + 1, j);
        infect(board, i, j - 1);
        infect(board, i, j + 1);
    }

    public static int numIslands1(char[][] board) {
        int row = board.length;
        int col = board[0].length;
        Dot[][] dots = new Dot[row][col];
        List<Dot> dotList = new ArrayList<>();
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                if (board[i][j] == '1') {
                    dots[i][j] = new Dot();
                    dotList.add(dots[i][j]);
                }
            }
        }
        UnionFind1<Dot> uf = new UnionFind1<>(dotList);
        for (int j = 1; j < col; j++) {
            // (0,j)  (0,0)跳过了  (0,1) (0,2) (0,3)
            if (board[0][j - 1] == '1' && board[0][j] == '1') {
                uf.union(dots[0][j - 1], dots[0][j]);
            }
        }
        for (int i = 1; i < row; i++) {
            if (board[i - 1][0] == '1' && board[i][0] == '1') {
                uf.union(dots[i - 1][0], dots[i][0]);
            }
        }
        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                if (board[i][j] == '1') {
                    if (board[i][j - 1] == '1') {
                        uf.union(dots[i][j - 1], dots[i][j]);
                    }
                    if (board[i - 1][j] == '1') {
                        uf.union(dots[i - 1][j], dots[i][j]);
                    }
                }
            }
        }
        return uf.sets();
    }

    public static class Dot {

    }

    public static class Node<V> {

        V value;

        public Node(V v) {
            value = v;
        }

    }

    public static class UnionFind1<V> {
        public HashMap<V, Node<V>> nodes;
        public HashMap<Node<V>, Node<V>> parents;
        public HashMap<Node<V>, Integer> sizeMap;

        public UnionFind1(List<V> values) {
            nodes = new HashMap<>();
            parents = new HashMap<>();
            sizeMap = new HashMap<>();
            for (V cur : values) {
                Node<V> node = new Node<>(cur);
                nodes.put(cur, node);
                parents.put(node, node);
                sizeMap.put(node, 1);
            }
        }

        public Node<V> findFather(Node<V> cur) {
            Stack<Node<V>> path = new Stack<>();
            while (cur != parents.get(cur)) {
                path.push(cur);
                cur = parents.get(cur);
            }
            while (!path.isEmpty()) {
                parents.put(path.pop(), cur);
            }
            return cur;
        }

        public void union(V a, V b) {
            Node<V> aHead = findFather(nodes.get(a));
            Node<V> bHead = findFather(nodes.get(b));
            if (aHead != bHead) {
                int aSetSize = sizeMap.get(aHead);
                int bSetSize = sizeMap.get(bHead);
                Node<V> big = aSetSize >= bSetSize ? aHead : bHead;
                Node<V> small = big == aHead ? bHead : aHead;
                parents.put(small, big);
                sizeMap.put(big, aSetSize + bSetSize);
                sizeMap.remove(small);
            }
        }

        public int sets() {
            return sizeMap.size();
        }

    }

    public static int numIslands2(char[][] board) {
        int row = board.length;
        int col = board[0].length;
        UnionFind2 uf = new UnionFind2(board);
        for (int j = 1; j < col; j++) {
            if (board[0][j - 1] == '1' && board[0][j] == '1') {
                uf.union(0, j - 1, 0, j);
            }
        }
        for (int i = 1; i < row; i++) {
            if (board[i - 1][0] == '1' && board[i][0] == '1') {
                uf.union(i - 1, 0, i, 0);
            }
        }
        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                if (board[i][j] == '1') {
                    if (board[i][j - 1] == '1') {
                        uf.union(i, j - 1, i, j);
                    }
                    if (board[i - 1][j] == '1') {
                        uf.union(i - 1, j, i, j);
                    }
                }
            }
        }
        return uf.sets();
    }

    public static class UnionFind2 {
        private int[] parent;
        private int[] size;
        private int[] help;
        private int col;
        private int sets;

        public UnionFind2(char[][] board) {
            col = board[0].length;
            sets = 0;
            int row = board.length;
            int len = row * col;
            parent = new int[len];
            size = new int[len];
            help = new int[len];
            for (int r = 0; r < row; r++) {
                for (int c = 0; c < col; c++) {
                    if (board[r][c] == '1') {
                        int i = index(r, c);
                        parent[i] = i;
                        size[i] = 1;
                        sets++;
                    }
                }
            }
        }

        // (r,c) -> i
        private int index(int r, int c) {
            return r * col + c;
        }

        // 原始位置 -> 下标
        private int find(int i) {
            int hi = 0;
            while (i != parent[i]) {
                help[hi++] = i;
                i = parent[i];
            }
            for (hi--; hi >= 0; hi--) {
                parent[help[hi]] = i;
            }
            return i;
        }

        public void union(int r1, int c1, int r2, int c2) {
            int i1 = index(r1, c1);
            int i2 = index(r2, c2);
            int f1 = find(i1);
            int f2 = find(i2);
            if (f1 != f2) {
                if (size[f1] >= size[f2]) {
                    size[f1] += size[f2];
                    parent[f2] = f1;
                } else {
                    size[f2] += size[f1];
                    parent[f1] = f2;
                }
                sets--;
            }
        }

        public int sets() {
            return sets;
        }

    }

    // 为了测试
    public static char[][] generateRandomMatrix(int row, int col) {
        char[][] board = new char[row][col];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                board[i][j] = Math.random() < 0.5 ? '1' : '0';
            }
        }
        return board;
    }

    // 为了测试
    public static char[][] copy(char[][] board) {
        int row = board.length;
        int col = board[0].length;
        char[][] ans = new char[row][col];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                ans[i][j] = board[i][j];
            }
        }
        return ans;
    }

    // 为了测试
    public static void main(String[] args) {
        int row = 0;
        int col = 0;
        char[][] board1 = null;
        char[][] board2 = null;
        char[][] board3 = null;
        long start = 0;
        long end = 0;

        row = 1000;
        col = 1000;
        board1 = generateRandomMatrix(row, col);
        board2 = copy(board1);
        board3 = copy(board1);

        System.out.println("感染方法、并查集(map实现)、并查集(数组实现)的运行结果和运行时间");
        System.out.println("随机生成的二维矩阵规模 : " + row + " * " + col);

        start = System.currentTimeMillis();
        System.out.println("感染方法的运行结果: " + numIslands3(board1));
        end = System.currentTimeMillis();
        System.out.println("感染方法的运行时间: " + (end - start) + " ms");

        start = System.currentTimeMillis();
        System.out.println("并查集(map实现)的运行结果: " + numIslands1(board2));
        end = System.currentTimeMillis();
        System.out.println("并查集(map实现)的运行时间: " + (end - start) + " ms");

        start = System.currentTimeMillis();
        System.out.println("并查集(数组实现)的运行结果: " + numIslands2(board3));
        end = System.currentTimeMillis();
        System.out.println("并查集(数组实现)的运行时间: " + (end - start) + " ms");

        System.out.println();

        row = 10000;
        col = 10000;
        board1 = generateRandomMatrix(row, col);
        board3 = copy(board1);
        System.out.println("感染方法、并查集(数组实现)的运行结果和运行时间");
        System.out.println("随机生成的二维矩阵规模 : " + row + " * " + col);

        start = System.currentTimeMillis();
        System.out.println("感染方法的运行结果: " + numIslands3(board1));
        end = System.currentTimeMillis();
        System.out.println("感染方法的运行时间: " + (end - start) + " ms");

        start = System.currentTimeMillis();
        System.out.println("并查集(数组实现)的运行结果: " + numIslands2(board3));
        end = System.currentTimeMillis();
        System.out.println("并查集(数组实现)的运行时间: " + (end - start) + " ms");

    }
}