算法笔记_148:有向图欧拉回路求解(Java)

Posted 2020-09-14 舞动的心

目录

1 问题描述

2 解决方案

 

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1 问题描述

Description

A catenym is a pair of words separated by a period such that the last letter of the first word is the same as the last letter of the second. For example, the following are catenyms: 

dog.gopher

gopher.rat

rat.tiger

aloha.aloha

arachnid.dog

A compound catenym is a sequence of three or more words separated by periods such that each adjacent pair of words forms a catenym. For example, 

aloha.aloha.arachnid.dog.gopher.rat.tiger 

Given a dictionary of lower case words, you are to find a compound catenym that contains each of the words exactly once.

Input

The first line of standard input contains t, the number of test cases. Each test case begins with 3 <= n <= 1000 - the number of words in the dictionary. n distinct dictionary words follow; each word is a string of between 1 and 20 lowercase letters on a line by itself.

Output

For each test case, output a line giving the lexicographically least compound catenym that contains each dictionary word exactly once. Output "***" if there is no solution.

Sample Input

2
6
aloha
arachnid
dog
gopher
rat
tiger
3
oak
maple
elm

Sample Output

aloha.arachnid.dog.gopher.rat.tiger
***

Source

Waterloo local 2003.01.25

题目链接：http://poj.org/problem?id=2337

 

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2 解决方案

具体代码如下：

 

package com.liuzhen.practice;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    public static int MAX = 30;   //英文字母共26个
    @SuppressWarnings("unchecked")
    public static ArrayList<edge>[] map = new ArrayList[MAX];
    public static String[] path;
    public static int count;  //统计DFS遍历访问的边数目，即检测图的连通性
    public static int start;
    public static int[] inDegree = new int[MAX];
    public static int[] outDegree = new int[MAX];
    public static ArrayList<String> result = new ArrayList<String>();
    
    class MyComparator implements Comparator<edge> {

        public int compare(edge arg0, edge arg1) {
            String A = arg0.word;
            String B = arg1.word;
            int judge = A.compareTo(B);
            if(judge > 0)
                return 1;
            else if(judge < 0)
                return -1;
            return 0;
        }
        
    }
    
    static class edge {
        public int a; //单词的第一个字母序号
        public int b; //单词最后一个字母序号
        public String word;  //具体单词
        public boolean used;     //判断单词是否被访问
        
        public edge(int a, int b, String word) {
            this.a = a;
            this.b = b;
            this.word = word;
            used = false;
        }
    }
    
    public void init(int k) {
        start = MAX;
        for(int i = 0;i < MAX;i++) {
            map[i] = new ArrayList<edge>();
            inDegree[i] = 0;
            outDegree[i] = 0;
        }
        path = new String[k];
        for(int i = 0;i < k;i++)
            path[i] = "";
        count = 0;
    }
    
    public boolean judgeDegree() {
        int in = 0, out = 0;
        for(int i = 1;i < map.length;i++) {  //对map[i]中单词进行字典序排序
            if(map[i].size() > 1) 
                Collections.sort(map[i], new MyComparator());
        }
        
        for(int i = 0;i < inDegree.length;i++) {
            if(inDegree[i] == outDegree[i])
                continue;
            else if(inDegree[i] - outDegree[i] == 1)
                in++;
            else if(outDegree[i] - inDegree[i] == 1) {
                out++;
                start = i;   //此时，可能存在欧拉路径，必须从入度小于出度的点开始遍历
            } else 
                return false;
        }
        if(in == out && (in == 0 || in == 1))
            return true;
        return false;
    }
    
    public void dfs(int begin) {
        for(int i = 0;i < map[begin].size();i++) {
            edge temp = map[begin].get(i);
            if(temp.used == false) {
                temp.used = true;
                path[count++] = temp.word;
                dfs(temp.b);
            }
        }
    }
    
    public static void main(String[] args) {
        Main test = new Main();
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t > 0) {
            t--;
            int k = in.nextInt();
            test.init(k);
            for(int i = 0;i < k;i++) {
                String A = in.next();
                int a = A.charAt(0) - ‘a‘;
                int b = A.charAt(A.length() - 1) - ‘a‘;
                start = Math.min(start, Math.min(a, b));
                map[a].add(new edge(a, b, A));
                outDegree[a]++;
                inDegree[b]++;
            }
            StringBuilder temp = new StringBuilder("");
            if(test.judgeDegree()) {  //满足欧拉回路或者欧拉路径对顶点度的要求
                test.dfs(start);
                if(count == k) {  //图连通
                    for(int i = 0;i < k;i++) {
                        temp.append(path[i]);
                        if(i != k - 1)
                            temp.append(".");
                    }
                } else {
                    temp.append("***");
                }
            } else {
                temp.append("***");
            }
            result.add(temp.toString());
        }
        for(int i = 0;i < result.size();i++)
            System.out.println(result.get(i));
    }
}

 

运行结果：

2
6
aloha
arachnid
dog
gopher
rat
tiger
3
oak
maple
elm
aloha.arachnid.dog.gopher.rat.tiger
***

 

 

 

 

 

参考资料：

   1. 欧拉回路