LeetCode928. 尽量减少恶意软件的传播 II

给定一个由 n 个节点组成的网络，用 n x n 个邻接矩阵 graph 表示。在节点网络中，只有当 graph[i][j] = 1 时，节点 i 能够直接连接到另一个节点 j。
一些节点 initial 最初被恶意软件感染。只要两个节点直接连接，且其中至少一个节点受到恶意软件的感染，那么两个节点都将被恶意软件感染。这种恶意软件的传播将继续，直到没有更多的节点可以被这种方式感染。
假设 M(initial) 是在恶意软件停止传播之后，整个网络中感染恶意软件的最终节点数。
我们可以从 initial 中删除一个节点，并完全移除该节点以及从该节点到任何其他节点的任何连接。
请返回移除后能够使 M(initial) 最小化的节点。如果有多个节点满足条件，返回索引 最小的节点 。
示例 1：
输入：graph = [[1,1,0],[1,1,0],[0,0,1]], initial = [0,1]
输出：0
示例 2：
输入：graph = [[1,1,0],[1,1,1],[0,1,1]], initial = [0,1]
输出：1
示例 3：
输入：graph = [[1,1,0,0],[1,1,1,0],[0,1,1,1],[0,0,1,1]], initial = [0,1]
输出：1
提示：
n == graph.length
n == graph[i].length
2 <= n <= 300
graph[i][j] 是 0 或 1.
graph[i][j] == graph[j][i]
graph[i][i] == 1
1 <= initial.length < n
0 <= initial[i] <= n - 1
initial 中每个整数都不同

割点

时间复杂度O(nn)，无提升。原理见： 【图论】【并集查找】【C++算法】928. 尽量减少恶意软件的传播 II

代码

class CNeiBo
{
public:	
	static vector<vector<int>> Two(int n, vector<vector<int>>& edges, bool bDirect, int iBase = 0) 
	{
		vector<vector<int>>  vNeiBo(n);
		for (const auto& v : edges)
		{
			vNeiBo[v[0] - iBase].emplace_back(v[1] - iBase);
			if (!bDirect)
			{
				vNeiBo[v[1] - iBase].emplace_back(v[0] - iBase);
			}
		}
		return vNeiBo;
	}	
	static vector<vector<std::pair<int, int>>> Three(int n, vector<vector<int>>& edges, bool bDirect, int iBase = 0)
	{
		vector<vector<std::pair<int, int>>> vNeiBo(n);
		for (const auto& v : edges)
		{
			vNeiBo[v[0] - iBase].emplace_back(v[1] - iBase, v[2]);
			if (!bDirect)
			{
				vNeiBo[v[1] - iBase].emplace_back(v[0] - iBase, v[2]);
			}
		}
		return vNeiBo;
	}
	static vector<vector<int>> Grid(int rCount, int cCount, std::function<bool(int, int)> funVilidCur, std::function<bool(int, int)> funVilidNext)
	{
		vector<vector<int>> vNeiBo(rCount * cCount);
		auto Move = [&](int preR, int preC, int r, int c)
		{
			if ((r < 0) || (r >= rCount))
			{
				return;
			}
			if ((c < 0) || (c >= cCount))

			{
				return;
			}
			if (funVilidCur(preR, preC) && funVilidNext(r, c))
			{
				vNeiBo[cCount * preR + preC].emplace_back(r * cCount + c);
			}
		};

		for (int r = 0; r < rCount; r++)
		{
			for (int c = 0; c < cCount; c++)
			{
				Move(r, c, r + 1, c);
				Move(r, c, r - 1, c);
				Move(r, c, r, c + 1);
				Move(r, c, r, c - 1);
			}
		}
		return vNeiBo;
	}
	static vector<vector<int>> Mat(vector<vector<int>>& neiBoMat)
	{
		vector<vector<int>> neiBo(neiBoMat.size());
		for (int i = 0; i < neiBoMat.size(); i++)
		{
			for (int j = i + 1; j < neiBoMat.size(); j++)
			{
				if (neiBoMat[i][j])
				{
					neiBo[i].emplace_back(j);
					neiBo[j].emplace_back(i);
				}
			}
		}
		return neiBo;
	}
};

class CCutPoint
{
public:
	CCutPoint(const vector<vector<int>>& vNeiB) : m_iSize(vNeiB.size())
	{
		m_vNodeToTime.assign(m_iSize, -1);
		m_vCutNewRegion.resize(m_iSize);		
	}
	void Init(const vector<vector<int>>& vNeiB)
	{
		for (int i = 0; i < m_iSize; i++)
		{
			if (-1 == m_vNodeToTime[i])
			{
				m_vRegionFirstTime.emplace_back(m_iTime);
				dfs(vNeiB, i, -1);
			}
		}
	}	
	const int m_iSize;
	const vector<int>& Time()const { return m_vNodeToTime; }//各节点的时间戳
	const vector<int>& RegionFirstTime()const { return m_vRegionFirstTime; }//各连通区域的最小时间戳
	vector<bool> CalCut()const { 
		vector<bool> ret;
		for (int i = 0; i < m_iSize; i++)
		{
			ret.emplace_back(m_vCutNewRegion[i].size());
		}
		return ret; }//
	const vector < vector<pair<int, int>>>& NewRegion()const { return m_vCutNewRegion; };
protected:
	int dfs(const vector<vector<int>>& vNeiB, const int cur, const int parent)
	{
		int iMinTime = m_vNodeToTime[cur] = m_iTime++;
		OnBeginDFS(cur);
		int iRegionCount = (-1 != parent);//根连通区域数量
		for (const auto& next : vNeiB[cur]) {
			if (next == parent)
			{
				continue;
			}
			if (-1 != m_vNodeToTime[next]) {
				iMinTime = min(iMinTime, m_vNodeToTime[next]);
				continue;
			}
			const int childMinTime = dfs(vNeiB, next, cur);
			iMinTime = min(iMinTime, childMinTime);
			if (childMinTime >= m_vNodeToTime[cur]) {
				iRegionCount++;
				m_vCutNewRegion[cur].emplace_back(m_vNodeToTime[next], m_iTime);
			}
			OnVisitNextEnd(childMinTime,cur, next);
		}
		if (iRegionCount < 2)
		{
			m_vCutNewRegion[cur].clear();
		}
		return iMinTime;
	}
	virtual void OnVisitNextEnd(int childMinTime,int cur, int next) {};
	virtual void OnBeginDFS(int cur) {};
	vector<int> m_vNodeToTime;
	vector<int> m_vRegionFirstTime;
	vector < vector<pair<int, int>>> m_vCutNewRegion; //m_vCutNewRegion[c]如果存在[left,r) 表示割掉c后，时间戳[left,r)的节点会形成新区域
	int m_iTime = 0;
};

class CCutEdge : public CCutPoint
{
public:
	using CCutPoint::CCutPoint;
	vector<vector<int>> m_vCutEdges;
protected:
	virtual void OnVisitNextEnd(int childMinTime, int cur, int next) override {
		if (childMinTime > m_vNodeToTime[cur])
		{
			m_vCutEdges.emplace_back(vector<int>{ cur,next });
		}
	}
};

class CConnectAfterCutPoint 
{
public:
	CConnectAfterCutPoint(const vector<vector<int>>& vNeiB) :m_ct(vNeiB)
	{
		m_ct.Init(vNeiB);
		m_vTimeToNode.resize(m_ct.m_iSize);
		m_vNodeToRegion.resize(m_ct.m_iSize);
		for (int iNode = 0; iNode < m_ct.m_iSize; iNode++)
		{
			m_vTimeToNode[m_ct.Time()[iNode]] = iNode;
		}
		for (int iTime = 0,iRegion= 0; iTime < m_ct.m_iSize; iTime++)
		{
			if ((iRegion < m_ct.RegionFirstTime().size()) && (m_ct.RegionFirstTime()[iRegion] == iTime))
			{
				iRegion++;
			}
			m_vNodeToRegion[m_vTimeToNode[iTime]] = (iRegion - 1);
		}
	}
	bool Connect(int src, int dest, int iCut)const
	{
		if (m_vNodeToRegion[src] != m_vNodeToRegion[dest])
		{
			return false;//不在一个连通区域
		}
		if (0 == m_ct.NewRegion()[iCut].size())
		{//不是割点
			return true;
		}
		const int r1 = GetCutRegion(iCut, src);
		const int r2 = GetCutRegion(iCut, dest);
		return r1 == r2;
	}
	vector<vector<int>> GetSubRegionOfCut(const int iCut)const
	{//删除iCut及和它相连的边后，iCut所在的区域会分成几个区域：父节点一个区域、各子节点		一个区域
			//父节点所在区域可能为空，如果iCut所在的连通区域只有一个节点，则返回一个没有节点的			区域。
		const auto& v = m_ct.NewRegion()[iCut];
		vector<int> vParen;
		const int iRegion = m_vNodeToRegion[iCut];
		const int iEndTime = (iRegion + 1 == m_ct.RegionFirstTime().size()) ? m_ct.m_iSize : m_ct.RegionFirstTime()[iRegion+1];
		vector<vector<int>> vRet;	
		for (int iTime = m_ct.RegionFirstTime()[iRegion],j=-1; iTime < iEndTime; iTime++)
		{
			if (iCut == m_vTimeToNode[iTime])
			{
				continue;
			}
			if ((j + 1 < v.size()) && (v[j + 1].first == iTime))
			{
				j++;
				vRet.emplace_back();
			}
			const int iNode = m_vTimeToNode[iTime];
			if ((-1 != j ) && (iTime >= v[j].first) && (iTime < v[j].second))
			{
				vRet.back().emplace_back(iNode);
			}
			else
			{
				vParen.emplace_back(iNode);
			}			
		}
		vRet.emplace_back();
		vRet.back().swap(vParen);
		return vRet;
	}	
protected:
	int GetCutRegion(int iCut, int iNode)const
	{
		const auto& v = m_ct.NewRegion()[iCut];
		auto it = std::upper_bound(v.begin(), v.end(), m_ct.Time()[iNode], [](int time, const std::pair<int, int>& pr) {return  time < pr.first; });
		if (v.begin() == it)
		{
			return v.size();
		}
		--it;
		return (it->second > m_ct.Time()[iNode]) ? (it - v.begin()) : v.size();
	}
	vector<int> m_vTimeToNode;
	vector<int> m_vNodeToRegion;//各节点所在区域
	CCutPoint m_ct;
};

class CMyCut : public CConnectAfterCutPoint
{
public:
	using CConnectAfterCutPoint::CConnectAfterCutPoint;
	int Do(const unordered_set<int>& setInit)
	{
		vector<int> vM;//各区域感染数量
		vector<int> vInitM;
		for (int iRegion = 0; iRegion < m_ct.RegionFirstTime().size(); iRegion++)
		{
			const auto [iBegin, iEnd] = GetBeginEnd(iRegion);
			const int iInitM = MCount(iBegin, iEnd, setInit);
			vInitM.emplace_back(iInitM);
			vM.emplace_back((iInitM>0) ? (iEnd - iBegin) : 0);
		}
		set<pair<int, int>> setPlusSubIndex;
		for (const auto& iNode : setInit)
		{
			const int iRegion = m_vNodeToRegion[iNode];
			int curSub = vM[iRegion];
			auto subRegion = GetSubRegionOfCut(iNode);
			for (const auto& v : subRegion)
			{
				int iInitM = 0;
				for (const auto& n : v)
				{
					iInitM += setInit.count(n);
				}
				if (iInitM > 0)
				{
					curSub -= v.size();
				}
			}
			setPlusSubIndex.emplace(-curSub, iNode);
		}
		return setPlusSubIndex.begin()->second;
	}
	int MCount(int iBegin,int iEnd, const unordered_set<int>& setInit)
	{
		int iM = 0;
		for (int iTime = iBegin; iTime < iEnd; iTime++)
		{
			const int iNode = m_vTimeToNode[iTime];
			if (setInit.count(iNode))
			{
				iM++;
			}
		}
		return iM;
	}
	pair<int, int> GetBeginEnd(int iRegion)
	{
		const int iEnd = (iRegion + 1 == m_ct.RegionFirstTime().size()) ? m_ct.m_iSize : m_ct.RegionFirstTime()[iRegion + 1];
		return { m_ct.RegionFirstTime()[iRegion] ,iEnd};
	}
};
class Solution {
public:
	int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
		m_c = graph.size();
		unordered_set<int> setInit(initial.begin(), initial.end());
		auto neiBo = CNeiBo::Mat(graph);
		CMyCut cut(neiBo);
		return cut.Do(setInit);
	}
	int m_c;
};