POJ 1386 Play on Words-优快云博客

本文链接：https://blog.youkuaiyun.com/bobten2008/article/details/4721086

本文介绍了一种使用并查集判断连通性的方法，并通过构建字母节点图来解决欧拉路径问题。该方法首先定义了字母节点的出入度，并通过一系列操作确保图的连通性和欧拉路径的存在。

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欧拉路径

并查集判断连通性

建图:小写字母作为结点，对于单词hello，为h的出度增加1，为o的入度增加1

#include <iostream>
#include <cstring>
#include <cmath>
using namespace std;

int caseNum, wordNum, letterNum;
char temp[1002];

struct letter
{
    char type;
    int rank, setId, inDeg, outDeg;
}letters[26];

int getIndex(char c)
{
    for(int i = 0; i < letterNum; i++)
        if(letters[i].type == c)
            return i;
    return -1;
}
void init()
{
    int i;
    letterNum = 0;
    for(i = 0; i < 26; i++)
    {
        letters[i].rank = 0;
        letters[i].setId = i;
        letters[i].inDeg = letters[i].outDeg = 0;
    }
}
int find(int id)
{
    if(letters[id].setId == id) return id;
    else return letters[id].setId = find(letters[id].setId);
}
void join(int id1, int id2)
{
    int sid1 = find(id1), sid2 = find(id2);
    if(sid1 == sid2) return;
    if(letters[sid1].rank < letters[sid2].rank)
        letters[sid1].setId = sid2;
    else
    {
        letters[sid2].setId = sid1;
        if(letters[sid1].rank == letters[sid2].rank)
            letters[sid1].rank++;
    }
}

int main()
{
    int c, w, wordNum;
    char head, tail;
    scanf("%d", &caseNum);
    for(c = 1; c <= caseNum; c++)
    {
        scanf("%d", &wordNum);
        init();
        for(w = 0; w < wordNum; w++)
        {
            scanf("%s", temp);
            head = temp[0];
            tail = temp[strlen(temp) - 1];
            int indexH = getIndex(head);
            if(indexH == -1)
            {
                letterNum++;
                indexH = letterNum - 1;
                letters[indexH].type = head;
            }
            int indexT = getIndex(tail);
            if(indexT == -1)
            {
                letterNum++;
                indexT = letterNum - 1;
                letters[indexT].type = tail;
            }
            letters[indexH].outDeg++;
            letters[indexT].inDeg++;

            join(indexH, indexT);

        }
        bool can = true;
        bool connect = true;
        int setId0 = find(0);
        for(w = 1; w < letterNum; w++)
        {
            if(find(w) != setId0)
            {
                connect = false;
                break;
            }
        }
        if(!connect) can = false;
        if(can)
        {
            int oddNum = 0;
            for(w = 0; w < 26; w++)
            {
                int sub = abs(letters[w].inDeg - letters[w].outDeg);
                if(sub >= 2) {can = false; break;}
                else if(sub == 1) oddNum++;
            }
            if(can)
            {
                if(!(oddNum == 0 || oddNum == 2))
                    can = false;
            }
        }
        if(can) printf("Ordering is possible./n");
        else printf("The door cannot be opened./n");
    }
    return 0;
}