2025年6月13日 星期五 4:17am

【动态规划】 【字典树】C++算法：472 连接词

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【动态规划】458:可怜的小猪

涉及知识点

动态规划 字典树

LeetCode472 连接词

给你一个 不含重复 单词的字符串数组 words ，请你找出并返回 words 中的所有 连接词 。
连接词 定义为：一个完全由给定数组中的至少两个较短单词（不一定是不同的两个单词）组成的字符串。
示例 1：
输入：words = [“cat”,“cats”,“catsdogcats”,“dog”,“dogcatsdog”,“hippopotamuses”,“rat”,“ratcatdogcat”]
输出：[“catsdogcats”,“dogcatsdog”,“ratcatdogcat”]
解释：“catsdogcats” 由 “cats”, “dog” 和 “cats” 组成;
“dogcatsdog” 由 “dog”, “cats” 和 “dog” 组成;
“ratcatdogcat” 由 “rat”, “cat”, “dog” 和 “cat” 组成。
示例 2：
输入：words = [“cat”,“dog”,“catdog”]
输出：[“catdog”]
提示：
1 <= words.length <= 104
1 <= words[i].length <= 30
words[i] 仅由小写英文字母组成。
words 中的所有字符串都是 唯一 的。
1 <= sum(words[i].length) <= 105

动态规划+字典树

分以下几步：
一，将所有单词存到字典树中。
二，枚举各单词s=word[i]，如果s[0,j)是字典树的叶子节点，则将j放到dp[i]中。
三，对dp[i]排序，出掉重复。
四，交换pre,dp。
五，如果pre[i]存在words[i].length，删除之。
六，循环处理pre，直到pre[i]全部为空。
七, for(j ;pre[i]) 如果字典树中存在words[i][j,k)且是叶子节点。将k加到dp[i]中。
八，对dp[i]排序，出掉重复。
九，交换pre,dp。
十,如果pre[i]存在wrods[i].length，将words[i]放到结果中，并清空pre[i]。

封装的字典树

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;
	}
	template<class IT>
	int Add(IT begin, IT end)
	{
		auto pNode = &m_root;
		for (; begin != end; ++begin)
		{
			pNode = pNode->AddChar(*begin,m_iMaxID);
		}
		if (-1 == pNode->m_iLeafIndex)
		{
			pNode->m_iLeafIndex = m_iLeafCount++;
		}
		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:	
	 int m_iMaxID = 0;
	 int m_iLeafCount = 0;	
};
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核心代码

class Solution {
public:
	vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
		CTrie preTrie;
		for (const auto& s : words)
		{
			preTrie.Add(s.begin(), s.end());	
		}
		vector<vector<int>> pre(words.size(),vector<int>(1));
		auto Do = [&]()
		{
			vector<vector<int>> dp(words.size());
			for (int i = 0; i < pre.size(); i++)
			{
				for (const auto& j : pre[i])
				{			
					auto p1 = &preTrie.m_root;
					for (int k = j; k < words[i].length(); k++)
					{
						p1 = p1->GetChild(words[i][k]);
						if (nullptr == p1)
						{
							break;
						}
						if (-1 != p1->m_iLeafIndex)
						{
							dp[i].emplace_back(k + 1);
						}
					}
				}
				sort(dp[i].begin(), dp[i].end());
				dp[i].erase(std::unique(dp[i].begin(), dp[i].end()), dp[i].end());
			}
			pre.swap(dp);
		};
		Do();
		for (int i = 0 ; i < pre.size(); i++ )
		{
			if (pre[i].size() && (pre[i].back() == words[i].length()))
			{
				pre[i].pop_back();
			}
		}
		vector<string> vRet;
		bool bDo = true;
		while (bDo)
		{
			Do();
			bDo = false;
			for (int i = 0; i < pre.size(); i++)
			{
				if (pre[i].size())
				{
					bDo = true;
				}
				if (pre[i].size() && (pre[i].back() == words[i].length()))
				{
					vRet.emplace_back(words[i]);
					pre[i].clear();
				}
			}
		}
		return vRet;
	}
};
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测试用例

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

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]);
	}
}


int main()
{
	vector<string> words;
	{
		Solution sln;
		words = { "cat","dog","catdog" };
		auto res = sln.findAllConcatenatedWordsInADict(words);
		Assert(vector<string>{"catdog"}, res);
	}
	{
		Solution sln;
		words = { "cat","cats","catsdogcats","dog","dogcatsdog","hippopotamuses","rat","ratcatdogcat" };
		auto res = sln.findAllConcatenatedWordsInADict(words);
		Assert(vector<string>{"catsdogcats", "dogcatsdog", "ratcatdogcat"}, res);
	}
	{
		Solution sln;
		words = { "vhsgzvwiixxaob","fso","qnebmfl","ooetjiz","lq","msxphqdgz","mqhoggvrvjqrp","xbhkkfg","zxjegsyovdrmw","jav","mshoj","ax","biztkfomz","hujdmcyxdqteqja","gqgsomonv","reqqzzpw","lihdnvud","lznfhbaokxvce","fhxbldylqqewdnj","rlbskqgfvn","lfvobeyolyy","v","iwh","fpbuiujlolnjl","gvwxljbo","ypaotdzjxxrsc","mwrvel","umzpnoiei","ogwilaswn","yw","egdgye","hsrznlzrf","mwdgxaigmxpy","yaqgault","dtlg","cyvfiykmkllf","zxqyhvizqmamj","lvvgoifltzywueyp","abinmy","ppzaecvmx","qsmzc","iddymnl","uskihek","evxtehxtbthq","jvtfzddlgch","czohpyewf","ufzazyxtqxcu","brxpfymuvfvs","xrrcfuusicc","aqhlswbzievij","rv","udvmara","upityz","fecd","suxteeitxtg","dfuydrtbfypbn","cypqodxr","wikfuxwjht","jrliuaifpp","vkmxys","wvpfyfpkvgthq","rmajxis","jncxgviyu","av","nmhskodmidaj","lkfrimprrhen","uip","hstyopbvuiqc","p","vwduwmjpblqo","fnxwgqtvwztje","xwnbcuggl","iehimvoymyjasin","spsqiu","flhyfac","mqrbq","pstsxhplrrmbeddv","hnegtuxx","alsyxezjwtlwmxv","jtxytykkcku","bhhlovgcx","xhhivxnutkx","had","aysulvk","m","anhsyxli","jdkgfc","potn","lcibpxkidmwexp","gwoxjicdkv","tltienw","ngiutnuqbzi","o","tzlyb","vumnwehj","os","np","lhv","uzvgyeette","ipfvr","lpprjjalchhhcmh","k","pciulccqssaqgd","tp","dmzdzveslyjad","wtsbhgkd","eouxbldsxzm","vhtonlampljgzyve","xhnlcrldtfthul","xhflc","upgei","rlaks","yfqvnvtnqspyjbxr","phouoyhvls","voibuvbhhjcdflvl","rgorfbjrofokggaf","dqhqats","zchpicyuawpovm","yzwfor","koat","pybf","fhdzsbiyjld","gznfnqydisn","xz","po","tcjup","wygsnxk","kqlima","fgxnuohrnhg","publurhztntgmimc","zuufzphd","iucrmmmjqtcey","wnnbq","rghzyz","ukjqsjbmp","mdtrgv","vyeikgjdnml","kxwldnmi","apzuhsbssaxj","tkbkoljyodlipof","nkq","ktwtj","vgmkgjwle","t","agylw","vomtuy","jbtvitkqn","vtdxwrclpspcn","rdrls","yxfeoh","upj","myctacn","fdnor","ahqghzhoqprgkym","phiuvdv","jp","fdgpouzjwbq","hqoyefmugjvewhxu","qfzwuwe","fnsbijkeepyxry","oja","qthkcij","zpmqfbmnr","ybaibmzonzqlnmd","svo","gjftyfehik","jfrfgznuaytvaegm","aljhrx","odjq","ogwaxrssjxgvnka","zaqswwofedxj","lugpktauixp","dc","odknlbvxrs","jeobu","vqythyvzxbcgrlbg","hwc","erpbaxq","ujxcxck","rrklkb","wlrwyuy","zmg","yyhga","xwdbycdu","htedgvsrhchox","wr","suhesetv","jonqwhkwezjvjgg","sqqyrxtjkcalswq","hvyimhe","pjzdkmoue","zbphmgoxq","lbdlcumdgixjbcq","ztzdjqmadthtdmv","qcagsyqggcf","if","jpjxcjyi","chyicqibxdgkqtg","iwpdklhum","wljmg","micmun","npdbamofynykqv","ijsnfkpfy","lmq","oyjmeqvhcrvgm","mqopusqktdthpvz","fz","r","qbsqtipq","nxtsnason","xbpipyhh","topsuqomfjrd","islif","gbndakaq","bwnkxnwpzeoohlx","hrtbfnq","fguvomeepxoffg","mat","dzfpfnwbfuj","onlvy","cwcchvsasdylb","rxfcztzqopdi","ybrhodjn","oqkijy","ncvrjo","dphbfaal","xgtpdtkz","sebevsopjvciwljf","rcumyacqdapwczen","mabkapuoud","pbozezeygljfftvy","bvazmzbndl","vl","qiaixdtbhqvlzd","ffjfb","svthrfmkoxbho","cvet","ucgqyvopafyttrh","lbgihet","naiqyufxffdw","vruh","uz","ukffmudygjavem","dccamymhp","wofwgjkykm","fbuujzxhln","kmm","lzandlltowjpwsal","fapfvrmezbsjxs","wiw","sc","soqlh","hzaplclkwl","gcdqbcdwbwa","gadgt","pgowefka","juffuguqepwnfh","nbuinl","cpdxf","sox","fq","lfnrhgsxkhx","xrcorfygjxpi","mwtqjwbhgh","loc","fkglorkkvx","nlzdhucvayrz","azefobxutitrf","rlrstkcbtikklmh","ggk","sbphcejuylh","nraoenhd","zngyodiqlchxyycx","rrbhfwohfv","krzolrglgn","cpjesdzy","yoifoyg","hqqevqjugi","ahmv","xgaujnyclcjq","evhyfnlohavrj","byyvhgh","hyw","kedhvwy","ysljsqminajfipds","rglnpxfqwu","cibpynkxg","su","mbntqrlwyampdg","nig","ldhlhqdyjcfhu","jfymrbafmyoc","tyjmnhlfnrtz","dlazixtlxyvm","fbiguhsfuqo","rhymsno","rkbdlchs","ocbbwwd","astaiamnepwkya","mplirup","edkxjq","g","exlwulswtvot","tlnc","vnrrzerz","ygeraoozbtt","yyifkin","eo","ua","qgztvqdolf","rlzddjzcshvd","khxkdxflwxme","kk","zylbhoaac","cw","iizic","gcdxstpz","kjwdqeg","earjrncmmkdel","kbesuhquepj","nrzbllldgdmyrpgl","hllwnqozf","djpchowhwevbqvjj","zsmhylnjpktb","pxnktxkm","fxwiaqqb","qjwufmwresfsfaok","aa","d","iobioqm","svjgzk","khbzp","euexyudhrioi","yqsj","ngrwqpoh","rwuvd","eruffmlg","bxzovyew","faz","pmvfvyguqdi","jlxnoixsy","hyfrdngjf","ly","eibcapetpmeaid","tpnwwiif","pfgsp","kvhhwkzvtvlhhb","pjxurgqbtldims","rncplkeweoirje","akyprzzphew","wyvfpjyglzrmhfqp","ubheeqt","rmbxlcmn","taqakgim","apsbu","khwnykughmwrlk","vtdlzwpbhcsbvjno","tffmjggrmyil","schgwrrzt","mvndmua","nlwpw","glvbtkegzjs","piwllpgnlpcnezqs","xkelind","urtxsezrwz","zechoc","vfaimxrqnyiq","ybugjsblhzfravzn","btgcpqwovwp","zgxgodlhmix","sfzdknoxzassc","wgzvqkxuqrsqxs","dwneyqisozq","fg","vhfsf","uspujvqhydw","eadosqafyxbmzgr","tyff","blolplosqnfcwx","uwkl","puenodlvotb","iizudxqjvfnky","cjcywjkfvukvveq","jrxd","igwb","dftdyelydzyummmt","uvfmaicednym","oai","higfkfavgeemcgo","naefganqo","iqebfibigljbc","ulicojzjfrc","igxprunj","cymbrl","fqmwciqtynca","zjyagi","mzuejrttefhdwqc","zyiurxvf","wrjxffzbjexsh","wrxw","mhrbdxjwi","htknfa","wfrvxqdkhbwwef","vqsghhhutdget","cwupzrts","hbjnb","wpccoa","nx","howbzhaoscgyk","bilt","wqqatye","zceuuwg","jxzon","kkfj","bwsezd","ifdegsyjtswselk","xweimxlnzoh","tqthlftjblnpht","ww","ss","b","jmruuqscwjp","nxbk","wd","cqkrtbxgzg","xhppcjnq","cfq","tkkolzcfi","wblxki","ijeglxsvc","kcqjjwcwuhvzydm","gubqavlqffhrzz","hiwxrgftittd","caybc","ncsyjlzlxyyklc","poxcgnexmaajzuha","dhaccuualacyl","mtkewbprs","oncggqvr","sqqoffmwkplsgbrp","ioajuppvqluhbdet","dzwwzaelmo","afumtqugec","wglucmugwqi","zveswrjevfz","nxlbkak","pzcejvxzeoybb","fd","vewj","ivws","zjhudtpqsfc","zcmukotirrxx","zksmx","umofzhhowyftz","zbotrokaxaryxlk","ueolqk","dxmzhoq","zvu","cjl","esfmqgvxwfy","npbep","vbgjtbv","poeugoqynkbfiv","fewjjscjrei","yqssxzsydgllfzmo","urxkwcypctjkabi","wqtldwhjouas","tovdtkr","onzgeyddkqwuhnim","ffxviyvsktqrfa","qujhd","pvcz","hiyjlkxmeplnrvxg","hdykehkefp","vepcxhozpjxtreyn","liguhuxudbnh","f","ordxzm","klgohcmmbukz","yrmooliaobbnlap","dutnbetocxylcey","ywdsjegd","cr","blbxhjsgcuoxmqft","ngzdc","srfyjjumcbxole","dazwzwtdjoyuqeqj","xazjarqgfm","fxyfqbeoktcc","qrsjchxp","iltaqzawhgu","sgenjcfxr","yfikp","dvwhbyumthkiktb","walsx","jyajrkcvysicisab","brdeumb","tviihjwxdcz","dnrrgmem","ydgxlrjzucxyid","cdvdpvjlagwmg","ngnpxjkxims","gvyhnchlimsxc","w","jtizpezjl","qe","rjzv","vhnqvi","qm","iedzqswrsnfmnn","lt","utqfcqyrrwm","wtelvsqrru","fjwrhjcrtbcytn","qmqxceuohpiffaq","rmoybqjjgdyo","pmxttqftypfexlv","tg","qa","iqbqjlnpbf","kgaynkddbzllecd","tccvslp","curkxfoimnw","fvnyqkzlheruxr","iiygnzfov","coqs","oa","eiu","vzemmxtklis","lxu","nrwsjaxzwmh","tdayz","oxbbemejgosgcynf","ykbcn","hesvnctfvdsp","ku","rjhykpadahbhj","at","sxlngbtxmqr","wqrom","qzyabzrco","rbbyklndcqdj","cnsmgmwmpbgjq","krvnaf","qrwfajnfahyqocdb","fnlaozmff","vmoymbmytjvfcgt","cijyy","jdgwjbztl","swmalgbgpaplqgz","hfl","typttkrpfvx","tkzpzrscwbx","bwfqqvjcukjbsg","nxqmxr","x","eyavnz","il","dhthp","eyelg","npsoqsw","reogbmveofvusdsx","jvdrjkhxkq","qzjbrpljwuzpl","czqeevvbvcwh","vzuszqvhlmapty","yu","yldwwgezlqur","vorxwgdtgjilgydq","pknt","bgihl","ckorgrm","ixylxjmlfv","bpoaboylced","zea","igfagitkrext","ipvqq","dmoerc","oqxbypihdv","dtjrrkxro","rexuhucxpi","bvmuyarjwqpcoywa","qwdmfpwvamisns","bhopoqdsref","tmnm","cre","ktrniqwoofoeenbz","vlrfcsftapyujmw","updqikocrdyex","bcxw","eaum","oklsqebuzeziisw","fzgyhvnwjcns","dybjywyaodsyw","lmu","eocfru","ztlbggsuzctoc","ilfzpszgrgj","imqypqo","fump","sjvmsbrcfwretbie","oxpmplpcg","wmqigymr","qevdyd","gmuyytguexnyc","hwialkbjgzc","lmg","gijjy","lplrsxznfkoklxlv","xrbasbznvxas" };
		auto res = sln.findAllConcatenatedWordsInADict(words);
		Assert(vector<string>{"rv", "tp", "koat", "po", "mdtrgv", "wr", "mat", "kmm", "ggk", "kk", "fg", "wrxw", "bilt", "ww", "nxbk", "wd", "fd", "tovdtkr", "ordxzm", "tg", "nxqmxr"}, res);
	}

}
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优化

b[j] 表示words[i][0,j) 是否能由一个或多个单词拼接。
Do(j) 的功能： b[j]为true，words[i][j,x)能和那些单词匹配。
Do(0)后，b[s.length()] = 0;是因为至少要拼接两次。

class Solution {
public:
	vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
		CTrie preTrie;
		for (const auto& s : words)
		{
			preTrie.Add(s.begin(), s.end());	
		}
		int b[31] = { 0 };
		vector<string> vRet;
		for (const auto& s : words)
		{			
			auto Do = [&](int inx)
			{
				auto p1 = &preTrie.m_root;
				for (int k = inx; k < s.length(); k++)
				{
					p1 = p1->GetChild(s[k]);
					if (nullptr == p1)
					{
						break;
					}
					if (-1 != p1->m_iLeafIndex)
					{
						b[k + 1] = true;
					}					
				}
			};
			memset(b, 0, sizeof(b));
			Do(0);
			b[s.length()] = 0;
			for (int i = 1; i < s.length(); i++)
			{
				if (b[i])
				{
					Do(i);
				}
			}
			if (b[s.length()])
			{
				vRet.emplace_back(s);
			}
		}		
		return vRet;
	}
};
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2023年1月

class Solution {
public:
vector findAllConcatenatedWordsInADict(vector& words) {
std::unordered_set setHas;
for (const auto& s : words)
{
setHas.insert(s);
}
vector vRet;
for (const auto& s : words)
{
if (Test(s, setHas))
{
vRet.push_back(s);
}
}
return vRet;
}
bool Test(const string& s, const std::unordered_set& setHas)
{
std::vector preLens;
preLens.push_back(0);
while (preLens.size())
{
std::vector lens;
for (const auto& pos : preLens)
{
for (int len = 1; pos + len - 1 < s.length(); len++)
{
if (setHas.count(s.substr(pos, len)))
{
if ((0 == pos) && (s.length() == len))
{
continue;
}
if (pos + len == s.length())
{
return true;
}
lens.push_back(pos + len);
}
}
}
preLens.swap(lens);
}

	 return false;
 }
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};

扩展阅读

视频课程

有效学习：明确的目标 及时的反馈 拉伸区（难度合适），可以先学简单的课程，请移步CSDN学院，听白银讲师（也就是鄙人）的讲解。
https://edu.csdn.net/course/detail/38771

如何你想快

速形成战斗了，为老板分忧，请学习C#入职培训、C++入职培训等课程
https://edu.csdn.net/lecturer/6176

相关

下载

想高屋建瓴的学习算法，请下载《喜缺全书算法册》doc版
https://download.csdn.net/download/he_zhidan/88348653

我想对大家说的话
闻缺陷则喜是一个美好的愿望，早发现问题，早修改问题，给老板节约钱。
子墨子言之：事无终始，无务多业。也就是我们常说的专业的人做专业的事。
如果程序是一条龙，那算法就是他的是睛

测试环境

操作系统：win7 开发环境： VS2019 C++17
或者 操作系统：win10 开发环境： VS2022 **C+

+17**
如无特殊说明，本算法用**C++**实现。

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注：本文转载自blog.csdn.net的闻缺陷则喜何志丹的文章"https://blog.csdn.net/he_zhidan/article/details/135487820"。版权归原作者所有，此博客不拥有其著作权，亦不承担相应法律责任。如有侵权，请联系我们删除。
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