重新排列单词顺序，使第一个和最后一个字母匹配

Question

如何编写 C++ 代码来重新排列词序，使每个单词的第一个字母（第一个除外）等于前一个单词的最后一个字母？

细节：

输入单词列表，每行一个单词，所有字母小写 a 到 z

输出一个有序的单词列表，每个单词的第一个字母（第一个除外）等于前一个单词的最后一个字母。必须使用列表中的所有单词，每个单词恰好出现一次。多次提到的词必须使用该次数。

Answer 1

这是进行匹配的代码

#include <string>
#include <fstream>
#include <sstream>
#include <iostream>
#include <vector>
#include <set>
#include <algorithm>

class cGraph;

/// @brief Spanning tree
class cTree
{
    cGraph &myGraph;

    /// @brief  links in spanning tree
    std::vector<std::pair<int, int>> myLink;

    std::vector<bool> myVisited;

    /// @brief links arranged so last matched next first
    std::vector<std::pair<int, int>> myArrange;

public:
    cTree(cGraph &g)
        : myGraph(g)
    {
    }

    void add(int n1, int n2)
    {
        myLink.push_back(std::make_pair(n1, n2));
    }
    int nodeCount();

    std::string text();

    /// @brief Depth first search starting at a link
    /// @param link
    /// @return true if every word was reached
    bool dfs(
        const std::pair<int, int> &link);

    /// @brief arrange words into required order
    ///
    /// The last letter of each word must be the
    /// same as the first letter of the next word
    std::vector<std::pair<int, int>> arrange();
};

class cGraph
{
    std::vector<std::string> myWord;
    std::vector<std::vector<bool>> myAdj;
    std::vector<std::pair<int, int>> myArrange;

public:
    void setSize(int s)
    {
        myAdj.resize(s, std::vector<bool>(s, false));
    }
    void addLink(int n1, int n2)
    {
        myAdj[n1][n2] = true;
    }

    void read(const std::string &fname);

    void constructAdjacencyMatrix();

    int wordCount() const
    {
        return myWord.size();
    }
    std::string word(int idx) const
    {
        return myWord[idx];
    }

    std::vector<int> sources(int n);
    std::vector<int> targets(int n);

    void arrange();

    void displayArrange();

private:
    cTree spanningTree();
};

int cTree::nodeCount()
{
    std::set<int> nodes;
    for (auto &l : myLink)
    {
        nodes.insert(l.first);
        nodes.insert(l.second);
    }
    return nodes.size();
}

std::string cTree::text()
{
    std::stringstream ss;
    for (auto &l : myLink)
        ss << myGraph.word(l.first)
           << " -> "
           << myGraph.word(l.second)
           << " ";
    return ss.str();
}

std::vector<int> cGraph::sources(int n)
{
    std::vector<int> ret;
    int n1idx = -1;
    for (auto &vl : myAdj)
    {
        n1idx++;
        int n2idx = -1;
        for (bool l : vl)
        {
            n2idx++;
            if (n2idx == n)
                if (l)
                    ret.push_back(n1idx);
        }
    }
    return ret;
}
std::vector<int> cGraph::targets(int n)
{
    std::vector<int> ret;
    int n2idx = -1;
    for (bool l : myAdj[n])
    {
        n2idx++;
        if (l)
            ret.push_back(n2idx);
    }

    return ret;
}

cTree cGraph::spanningTree()
{
    cTree mySpanningTree(*this);
    std::vector<bool> visited(myAdj.size(), false);

    // add initial arbitrary link
    int v, w;
    for (v = 0; v < myAdj.size(); v++)
    {
        auto vt = targets(v);
        if (vt.size())
        {
            w = vt[0];
            mySpanningTree.add(v, w);
            break;
        }
    }
    if (v == myAdj.size())
        throw std::runtime_error("no links");

    visited[v] = true;
    visited[w] = true;

    // while nodes remain outside of span
    bool fdone = false;
    while (!fdone)
    {
        // loop over nodes in span
        for (v = 0; v < myAdj.size(); v++)
        {
            if (!visited[v])
                continue;

            // loop over nodes not in span
            fdone = true;
            for (w = 0; w < myAdj.size(); w++)
            {
                if (visited[w])
                    continue;

                fdone = false;

                if (myAdj[v][w])
                {
                    mySpanningTree.add(v, w);
                    visited[w] = true;
                }
                if (myAdj[w][v])
                {
                    mySpanningTree.add(w, v);
                    visited[w] = true;
                }
            }
        }
        if (v == myAdj.size())
            fdone = true;
    }

    if (mySpanningTree.nodeCount() < myAdj.size())
        throw std::runtime_error(
            "Spanning tree incomplete: no solution available
");

    // std::cout << "
"
    //           << mySpanningTree.text() << "
";

    return mySpanningTree;
}

void cGraph::arrange()
{
    // Find a spanning tree and search it for a matching word arrangement
    // throw exception if no arrangement possible
    myArrange = spanningTree().arrange();
}

void cGraph::displayArrange()
{
    // display the arrangement found
    std::cout << "arrange into "
              << word(myArrange[0].first) << " ";
    for (auto &l : myArrange)
        std::cout << word(l.second) << " ";
    std::cout << "
";
}

void cGraph::read(const std::string &fname)
{
    std::ifstream ifs(fname);
    if (!ifs.is_open())
    {
        std::cout << "cannot open input
";
        exit(1);
    }
    std::string word;
    ifs >> word; // skip count
    while (ifs.good())
    {
        ifs >> word;
        myWord.push_back(word);
        std::cout << word << "
";
    }
    setSize(myWord.size());
}

void cGraph::constructAdjacencyMatrix()
{
    int widx = -1;
    for (auto &w : myWord)
    {
        widx++;
        char first = w[0];
        char last = w[w.length() - 1];
        int sidx = -1;
        for (auto &src : myWord)
        {
            sidx++;
            if (sidx == widx)
                continue;
            if (src[src.length() - 1] == first)
            {
                addLink(sidx, widx);
            }
            if (src[0] == last)
            {
                addLink(widx, sidx);
            }
        }
    }
}

bool cTree::dfs(
    const std::pair<int, int> &l)
{
    myVisited[l.first] = true;
    myVisited[l.second] = true;
    bool fdone = true;
    for (bool v : myVisited)
    {
        if (!v)
        {
            fdone = false;
            break;
        }
    }
    if (fdone)
    {
        myArrange.push_back(l);
        return true;
    }

    auto visited_save = myVisited;
    for (const auto &lnext : myLink)
    {
        if (lnext.first == l.second)
        {
            myVisited = visited_save;
            if (dfs(lnext))
            {
                myArrange.push_back(l);
                return true;
            }
        }
    }
    return false;
}

std::vector<std::pair<int, int>> cTree::arrange()
{
    // loop over links in spanning tree
    for (const auto &l : myLink)
    {
        // do a depth fist search through the tree
        // starting from this link
        myVisited.clear();
        myVisited.resize(myGraph.wordCount(), false);
        if (dfs(l))
        {
            // the dfs reached every word
            // reverse the order in which the words were found
            // which gives an arrangement of words in required order
            std::reverse(myArrange.begin(), myArrange.end());

            // done
            return myArrange;
        }
    }
}

main()
{
    cGraph graph;

    // read word list from file
    graph.read("input.txt");

    // connect matching words
    graph.constructAdjacencyMatrix();

    // arrange words, matching first and last letters
    graph.arrange();

    // output results
    graph.displayArrange();

    return 0;
}