本文涉及知识点

回溯 字典树（前缀树）

LeetCode212. 单词搜索 II

给定一个 m x n 二维字符网格 board 和一个单词（字符串）列表 words， 返回所有二维网格上的单词 。
单词必须按照字母顺序，通过 相邻的单元格 内的字母构成，其中“相邻”单元格是那些水平相邻或垂直相邻的单元格。同一个单元格内的字母在一个单词中不允许被重复使用。
示例 1：

输入：board = [[“o”,“a”,“a”,“n”],[“e”,“t”,“a”,“e”],[“i”,“h”,“k”,“r”],[“i”,“f”,“l”,“v”]], words = [“oath”,“pea”,“eat”,“rain”]
输出：[“eat”,“oath”]
示例 2：

输入：board = [[“a”,“b”],[“c”,“d”]], words = [“abcb”]
输出：[]

提示：

m == board.length
n == board[i].length
1 <= m, n <= 12
board[i][j] 是一个小写英文字母
1 <= words.length <= 3 * 10⁴
1 <= words[i].length <= 10
words[i] 由小写英文字母组成
words 中的所有字符串互不相同

回溯

用字典树存储所有words。
枚举起点，时间复杂度O(nm)。
最长的words[i]，除去第一个字符后，最多9个字符。后续字符4个。故处理每个起点的时间复杂是O(9ⁿ)
总时间复杂度$\approx$ 3$\times$10⁷ 超时边缘。
回溯部分一定要反复优化。

代码

核心代码

struct CVec
{
	int r;
	int c;
	CVec operator*(const int len)const
	{
		return { r * len,c * len };
	}
};

struct CPos
{	
	int r = 0, c = 0;
	CPos(int tr, int tc) {
		r = tr;
		c = tc;
	}
	int ToMask()const { return s_MaxC * r + c; };
	bool operator==(const CPos& o)const
	{
		return (r == o.r) && (c == o.c);
	}
	CPos operator+(const CVec& v)const
	{
		return { r + v.r, c + v.c };
	}
	CPos operator-(const CVec& v)const
	{
		return{ r - v.r, c - v.c };
	}
	CVec operator-(const CPos& o)const
	{
		return {r - o.r,c- o.c};
	}
	inline static  int s_MaxC = 10'000;
};

struct SPosHash {
	// 哈希函数的操作符重载，接受一个指针作为参数
	size_t operator()(const CPos& pos) const {
		// 简单的哈希函数示例，将指针地址转换为哈希值
		return (long long)100'000 * pos.r + pos.c;;
	}
};

class CRange
{
public:
	CRange(int rCount, int cCount, std::function<bool(int, int)> funVilidCur):m_r(rCount),m_c(cCount), m_funVilidCur(funVilidCur)
	{

	}
	bool Vilid(CPos pos)const
	{
		return (pos.r >= 0) && (pos.r < m_r) && (pos.c >= 0) && (pos.c < m_c) && m_funVilidCur(pos.r, pos.c);
	}
	const int m_r, m_c;
protected:
	std::function<bool(int, int)> m_funVilidCur;
};

template<class TData = char, int iTypeNum = 26, TData cBegin = 'a'>
class CTrieNode
{
public:
	CTrieNode* AddChar(TData ele, int& iMaxID)
	{
#ifdef _DEBUG
		if ((ele < cBegin) || (ele >= cBegin + iTypeNum))
		{
			return nullptr;
		}
#endif
		const int index = ele - cBegin;
		auto ptr = m_vPChilds[ele - cBegin];
		if (!ptr)
		{
			m_vPChilds[index] = new CTrieNode();
#ifdef _DEBUG
			m_vPChilds[index]->m_iID = ++iMaxID;
			m_childForDebug[ele] = m_vPChilds[index];
#endif
		}
		return m_vPChilds[index];
	}
	CTrieNode* GetChild(TData ele)const
	{
#ifdef _DEBUG
		if ((ele < cBegin) || (ele >= cBegin + iTypeNum))
		{
			return nullptr;
		}
#endif
		return m_vPChilds[ele - cBegin];
	}
protected:
#ifdef _DEBUG
	int m_iID = -1;
	std::unordered_map<TData, CTrieNode*> m_childForDebug;
#endif
public:
	int m_iLeafIndex = -1;
protected:
	CTrieNode* m_vPChilds[iTypeNum] = { nullptr };
};

template<class TData = char, int iTypeNum = 26, TData cBegin = 'a'>
class CTrie
{
public:
	int GetLeadCount()
	{
		return m_iLeafCount;
	}
	CTrieNode<TData, iTypeNum, cBegin>* AddA(CTrieNode<TData, iTypeNum, cBegin>* par,TData curValue)
	{
		auto curNode =par->AddChar(curValue, m_iMaxID);
		FreshLeafIndex(curNode);
		return curNode;
	}
	template<class IT>
	int Add(IT begin, IT end)
	{
		auto pNode = &m_root;
		for (; begin != end; ++begin)
		{
			pNode = pNode->AddChar(*begin, m_iMaxID);
		}
		FreshLeafIndex(pNode);
		return pNode->m_iLeafIndex;
	}	
	template<class IT>
	CTrieNode<TData, iTypeNum, cBegin>* Search(IT begin, IT end)
	{
		auto ptr = &m_root;
		for (; begin != end; ++begin)
		{
			ptr = ptr->GetChild(*begin);
			if (nullptr == ptr)
			{
				return nullptr;
			}
		}
		return ptr;
	}
	CTrieNode<TData, iTypeNum, cBegin> m_root;
protected:
	void FreshLeafIndex(CTrieNode<TData, iTypeNum, cBegin>* pNode)
	{
		if (-1 == pNode->m_iLeafIndex)
		{
			pNode->m_iLeafIndex = m_iLeafCount++;
		}
	}
	int m_iMaxID = 0;
	int m_iLeafCount = 0;
};

class Solution {
public:
	vector<string> findWords(vector<vector<char>>& board, vector<string>& words) {
		const int R = board.size();
		const int C = board[0].size();
		for (const auto& s : words) {
			m_trie.Add(s.begin(), s.end());
		}		
		vector<bool> vHas(m_trie.GetLeadCount());
		int hasVisit[12][12] ;
		memset(hasVisit, 0, sizeof(hasVisit));
		CRange rang(R, C, [&](int r, int c) {return !hasVisit[r][c]; });
		int move[][2] = { {0,1},{0,-1},{1,0},{-1,0}};
		std::function<void(CTrieNode<>* par, int r, int c)> BackTrack = [&](CTrieNode<>* par, int r, int c)
		{
			auto p = par->GetChild(board[r][c]);
			if (nullptr == p) { return; }
			if (-1 != p->m_iLeafIndex) {
				vHas[p->m_iLeafIndex] = true;
			}
			hasVisit[r][c]=true;
			for (int i = 0; i < 4; i++) {
				const int r1 = r + move[i][0];
				const int c1 = c + move[i][1];
				if(!rang.Vilid(CPos(r1,c1 ))){continue;}
				BackTrack(p, r1, c1);
			}
			hasVisit[r][c] = false;
		};
		for (int r = 0; r < R; r++) {
			for (int c = 0; c < C; c++) {
				BackTrack(&m_trie.m_root, r, c);
			}
		}
		vector<string> vRet;
		for (const auto& s : words) {
			auto p = m_trie.Search(s.begin(), s.end());
			if (vHas[p->m_iLeafIndex]) {
				vRet.emplace_back(s);
			}
		}
		return vRet;
	}	
	CTrie<> m_trie;
};

测试用例

template<class T>
void Assert(const vector<T>& v1, const vector<T>& v2)
{
	if (v1.size() != v2.size())
	{
		assert(false);
		return;
	}
	for (int i = 0; i < v1.size(); i++)
	{
		assert(v1[i] == v2[i]);
	}
}

template<class T>
void Assert(const T& t1, const T& t2)
{
	assert(t1 == t2);
}

int main()
{
	vector<vector<char>> board;
	vector<string> words;
	{
		Solution slu;
		board= { {'o','a','a','n'},{'e','t','a','e'},{'i','h','k','r'},{'i','f','l','v'} },words= { "oath","pea","eat","rain" };
		auto res = slu.findWords(board, words);
		Assert({ "oath","eat" }, res);
	}
	{
		Solution slu;
		board = { {'a','b'},{'c','d'} }, words = { "abcb" };
		auto res = slu.findWords(board, words);
		Assert({  }, res);
	}	
	
}

2023年4月版

class Solution {
public:
	vector<string> findWords(vector<vector<char>>& board, vector<string>& words) {
		m_r = board.size();
		m_c = board[0].size();
		m_iMaskNum = m_r*m_c;
		m_vMove.resize(m_iMaskNum);
		
		for (int r = 0; r < m_r; r++)
		{
			for (int c = 0; c < m_c; c++)
			{
				int iMask = m_c*r + c;
				if (r > 0)
				{
					m_vMove[iMask].emplace_back(iMask - m_c);
				}
				if (r + 1 < m_r)
				{
					m_vMove[iMask].emplace_back(iMask + m_c);
				}
				if ( c > 0 )
				{
					m_vMove[iMask].emplace_back(iMask - 1);
				}
				if (c + 1 < m_c)
				{
					m_vMove[iMask].emplace_back(iMask + 1);
				}
			}
		}
		for (const auto& s : words)
		{
			long long llRet = 0;
			for (const auto& ch : s)
			{
				llRet = llRet * 27 + ch - 'a'+1;
				m_setNeedSub.emplace(llRet);
			}
			m_setNeed.emplace(llRet);
		}
		int v[12] = { 0 };
		bool bPre[12 * 12] = { 0 };
		for (int i = 0; i < m_iMaskNum; i++)
		{			
			const char& ch = board[i / m_c][i%m_c];
			v[0] = i;
			bPre[i] = true;
			dfs(v, 1,bPre, ch - 'a' + 1, board);
			
			bPre[i] = false;
		}


		vector<string> vRet;
		for (const auto& s : words)
		{
			const long long llMask = Mask(s);
			if (!m_setNeed.count(llMask))
			{
				vRet.emplace_back(s);
			}
		}
		return vRet;
	}

	void dfs(int* v,int iSize, bool* vPre, const long long llMask, vector<vector<char>>& board)
	{
		if (iSize > 10)
		{
			return;
		}
		
		if (m_setNeed.count(llMask))
		{
			m_setNeed.erase(llMask);
			auto tmp = llMask;
			while (tmp > 0)
			{
				auto it = m_setNeedSub.find(tmp);
				m_setNeedSub.erase(it);
				tmp /= 27;
			}
		}

		if (!m_setNeedSub.count(llMask))
		{
			return;
		}
		//const int iSize = v.size();
		const int iCur = v[iSize-1];
		for (const auto& next : m_vMove[iCur])
		{
			if (vPre[next])
			{
				continue;
			}
			v[iSize] = next;
			vPre[next] = true;
			dfs(v, iSize+1,vPre, llMask * 27 + board[next / m_c][next%m_c] - 'a' + 1, board);
		
			vPre[next] = false;
		}

	}
	long long Mask(const std::string& str)
	{
		long long llRet = 0;
		for (const auto& ch : str)
		{
			llRet = llRet * 27 + ch - 'a'+1;
		}
		return llRet;
	}
	int m_r, m_c;
	int m_iMaskNum;
	vector<vector<int>> m_vMove;
	std::unordered_multiset<long long> m_setNeedSub;
	std::unordered_set<long long> m_setNeed;
};