【广度优先搜索】【网格】【割点】【 推荐】1263. 推箱子

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视频算法专题

涉及知识点

广度优先搜索 网格 割点 并集查找

LeetCode:1263. 推箱子

「推箱子」是一款风靡全球的益智小游戏，玩家需要将箱子推到仓库中的目标位置。
游戏地图用大小为 m x n 的网格 grid 表示，其中每个元素可以是墙、地板或者是箱子。
现在你将作为玩家参与游戏，按规则将箱子 ‘B’ 移动到目标位置 ‘T’ ：
玩家用字符 ‘S’ 表示，只要他在地板上，就可以在网格中向上、下、左、右四个方向移动。
地板用字符 ‘.’ 表示，意味着可以自由行走。
墙用字符 ‘#’ 表示，意味着障碍物，不能通行。
箱子仅有一个，用字符 ‘B’ 表示。相应地，网格上有一个目标位置 ‘T’。
玩家需要站在箱子旁边，然后沿着箱子的方向进行移动，此时箱子会被移动到相邻的地板单元格。记作一次「推动」。
玩家无法越过箱子。
返回将箱子推到目标位置的最小 推动 次数，如果无法做到，请返回 -1。
示例 1：
输入：grid = [[“#”,“#”,“#”,“#”,“#”,“#”],
[“#”,“T”,“#”,“#”,“#”,“#”],
[“#”,“.”,“.”,“B”,“.”,“#”],
[“#”,“.”,“#”,“#”,“.”,“#”],
[“#”,“.”,“.”,“.”,“S”,“#”],
[“#”,“#”,“#”,“#”,“#”,“#”]]

输出：3
解释：我们只需要返回推箱子的次数。
示例 2：
输入：grid = [[“#”,“#”,“#”,“#”,“#”,“#”],
[“#”,“T”,“#”,“#”,“#”,“#”],
[“#”,“.”,“.”,“B”,“.”,“#”],
[“#”,“#”,“#”,“#”,“.”,“#”],
[“#”,“.”,“.”,“.”,“S”,“#”],
[“#”,“#”,“#”,“#”,“#”,“#”]]
输出：-1
示例 3：
输入：grid = [[“#”,“#”,“#”,“#”,“#”,“#”],
[“#”,“T”,“.”,“.”,“#”,“#”],
[“#”,“.”,“#”,“B”,“.”,“#”],
[“#”,“.”,“.”,“.”,“.”,“#”],
[“#”,“.”,“.”,“.”,“S”,“#”],
[“#”,“#”,“#”,“#”,“#”,“#”]]
输出：5
解释：向下、向左、向左、向上再向上。

提示：

m == grid.length
n == grid[i].length
1 <= m, n <= 20
grid 仅包含字符 ‘.’, ‘#’, ‘S’ , ‘T’, 以及 ‘B’。
grid 中 ‘S’, ‘B’ 和 ‘T’ 各只能出现一个。

01广度优先搜索

状态：箱子所在行列，人所在行列
人试图向上下左右移动。以左移为例。
$$\{\begin{array}{ll}如果人可以左移，人左移，加到队首& 箱子不在左边\\ 如果人和箱子都可以左移，人箱子左移，加到队尾& 箱子在人左边\end{array}$$
妙在无需考虑： 箱子对人的影响。

代码

核心代码

class CBFS
{
public:CBFS(int iStatuCount, int iInit = -1):m_iStatuCount(iStatuCount),m_iInit(iInit){m_res.assign(iStatuCount, iInit);}bool Peek(int& statu){if (m_que.empty()){return false;}statu = m_que.front();m_que.pop_front();return true;}void PushBack(int statu, int value){if (m_iInit != m_res[statu]){return;}m_res[statu] = value;m_que.push_back(statu);}void PushFront(int statu, int value){if (m_iInit != m_res[statu]){return;}m_res[statu] = value;m_que.push_front(statu);}int Get(int statu){return m_res[statu];}
private:const int m_iStatuCount;const int m_iInit;deque<int> m_que;vector<int> m_res;
};class CBFS2 : protected CBFS
{
public:CBFS2(int iStatuCount1,int iStatuCount2, int iInit = -1) :CBFS(iStatuCount1* iStatuCount2, iInit ), m_iStatuCount2(iStatuCount2){}bool Peek(int& statu1,int& statu2 ){int statu;if (!CBFS::Peek(statu)){return false;}statu1 = statu / m_iStatuCount2;statu2 = statu % m_iStatuCount2;return true;}void PushBack(int statu1,int statu2, int value){CBFS::PushBack(statu1 * m_iStatuCount2 + statu2, value);}void PushFront(int statu1, int statu2, int value){CBFS::PushFront(statu1 * m_iStatuCount2 + statu2, value);}int Get(int statu1, int statu2){return CBFS::Get(statu1 * m_iStatuCount2 + statu2);}
private:const int m_iStatuCount2;
};class CBFS3 : protected CBFS2
{
public:CBFS3(int iStatuCount1, int iStatuCount2, int iStatuCount3,int iInit = -1) :CBFS2(iStatuCount1, iStatuCount2* iStatuCount3, iInit), m_iStatuCount3(iStatuCount3){}bool Peek(int& statu1, int& statu2,int& statu3 ){int statu23;if (!CBFS2::Peek(statu1,statu23)){return false;}statu2 = statu23 / m_iStatuCount3;statu3 = statu23 % m_iStatuCount3;return true;}void PushBack(int statu1, int statu2,int statu3, int value){CBFS2::PushBack(statu1 , statu2*m_iStatuCount3+statu3, value);}void PushFront(int statu1, int statu2, int statu3, int value){CBFS2::PushFront(statu1, statu2 * m_iStatuCount3 + statu3, value);}int Get(int statu1, int statu2, int statu3){return CBFS2::Get(statu1, statu2 * m_iStatuCount3 + statu3);}const int m_iStatuCount3;
};class CBFS4 : protected CBFS3
{
public:CBFS4(int iStatuCount1, int iStatuCount2, int iStatuCount3,int iStatuCount4, int iInit = -1) :CBFS3(iStatuCount1, iStatuCount2, iStatuCount3* iStatuCount4, iInit), m_iStatuCount4(iStatuCount4){}bool Peek(int& statu1, int& statu2, int& statu3,int& statu4){int statu34;if (!CBFS3::Peek(statu1, statu2,statu34)){return false;}statu3 = statu34 / m_iStatuCount4;statu4 = statu34 % m_iStatuCount4;return true;}void PushBack(int statu1, int statu2, int statu3,int statu4, int value){CBFS3::PushBack(statu1, statu2 , statu3* m_iStatuCount4+ statu4, value);}void PushFront(int statu1, int statu2, int statu3, int statu4, int value){CBFS3::PushFront(statu1, statu2, statu3 * m_iStatuCount4 + statu4, value);}int Get(int statu1, int statu2, int statu3, int statu4){return CBFS3::Get(statu1, statu2, statu3 * m_iStatuCount4 + statu4);}const int m_iStatuCount4;
};template<class T>
class CEnumGrid
{
public:static  void EnumGrid(const vector<vector<T>>& grid,std::function<void(int,int,T)> call ){for (int r = 0; r < grid.size(); r++){for (int c = 0; c < grid.front().size(); c++){call(r, c, grid[r][c]);}}}
};
class Solution {
public:int minPushBox(vector<vector<char>>& grid) {m_r = grid.size();m_c = grid[0].size();int move[4][2] = { {1,0},{-1,0},{0,1},{0,-1} };auto CanMove = [&grid](int r, int c){if ((r < 0) || (r >= grid.size())){return false;}if ((c < 0) || (c >= grid[0].size())){return false;}return '#' != grid[r][c];};int sr, sc, br, bc,tr,tc;CEnumGrid<char>::EnumGrid(grid, [&](int r, int c, char ch){if ('B' == ch){br = r;bc = c;}if ('S' == ch){sr = r;sc = c;}if ('T' == ch){tr = r;tc = c;}});CBFS4 bfs(m_r, m_c, m_r, m_c);bfs.PushBack(sr, sc, br, bc, 0);int r1, c1, r2, c2;while (bfs.Peek(r1, c1, r2, c2)){const int dis = bfs.Get(r1, c1, r2, c2);if ((r2 == tr) && (c2 == tc)){return dis;}for (const auto& [mr,mc] : move){auto r3 = r1 + mr;auto c3 = c1 + mc;if (!CanMove(r3, c3)){continue;}if ((r3 == r2) && (c3 == c2)){//必须移动箱子auto r4 = r3 + mr;auto c4 = c3 + mc;if (!CanMove(r4, c4)){continue;}bfs.PushBack(r3, c3, r4, c4, dis + 1);}else{bfs.PushFront(r3, c3, r2, c2, dis );}}}return -1;}int m_r, m_c;
};

测试用例

template<class T,class T2>
void Assert(const T& t1, const T2& 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<vector<char>> grid;{Solution sln;grid = { {'#','#','#','#','#','#'},{'#','T','#','#','#','#'},{'#','.','.','B','.','#'},{'#','.','#','#','.','#'},{'#','.','.','.','S','#'},{'#','#','#','#','#','#'} };auto res = sln.minPushBox(grid);Assert(3, res);}{Solution sln;grid = { {'#','#','#','#','#','#'},{'#','T','.','.','#','#'},{'#','.','#','B','.','#'},{'#','.','.','.','.','#'},{'#','.','.','.','S','#'},{'#','#','#','#','#','#'} };auto res = sln.minPushBox(grid);Assert(5, res);}
}

想法而已，过于复杂：割点、并集查找

状态：箱子所在行列，人所在方位（上右下左） 。
箱子右移的条件：
人能移到箱子左边，箱子能右移（右边没出界，不是墙）
人可能被箱子阻拦：
$$\{\begin{array}{ll}如果没箱子，人无法到达& 无法到达。\\ else箱子不是割点& 能到达\\ else是割点，源点和目标点到时间戳都大于（小于）割点时间戳& 能到达。\\ other& 不能到达。\end{array}$$

写了下代码，太复杂了。
错误原因：源点和目标点到时间戳都大于（小于）割点时间戳则能到达是错误的。因为：割点可能被多次访问，所以需要记录割点所有的时间戳，在同一个时间段的可以访问。但这要修改割点函数。抱着一根筋精神，改进了割点函数。

代码

class CUnionFind
{
public:CUnionFind(int iSize) :m_vNodeToRegion(iSize){for (int i = 0; i < iSize; i++){m_vNodeToRegion[i] = i;}m_iConnetRegionCount = iSize;}	CUnionFind(vector<vector<int>>& vNeiBo):CUnionFind(vNeiBo.size()){for (int i = 0; i < vNeiBo.size(); i++) {for (const auto& n : vNeiBo[i]) {Union(i, n);}}}int GetConnectRegionIndex(int iNode){int& iConnectNO = m_vNodeToRegion[iNode];if (iNode == iConnectNO){return iNode;}return iConnectNO = GetConnectRegionIndex(iConnectNO);}void Union(int iNode1, int iNode2){const int iConnectNO1 = GetConnectRegionIndex(iNode1);const int iConnectNO2 = GetConnectRegionIndex(iNode2);if (iConnectNO1 == iConnectNO2){return;}m_iConnetRegionCount--;if (iConnectNO1 > iConnectNO2){UnionConnect(iConnectNO1, iConnectNO2);}else{UnionConnect(iConnectNO2, iConnectNO1);}}bool IsConnect(int iNode1, int iNode2){return GetConnectRegionIndex(iNode1) == GetConnectRegionIndex(iNode2);}int GetConnetRegionCount()const{return m_iConnetRegionCount;}vector<int> GetNodeCountOfRegion()//各联通区域的节点数量{const int iNodeSize = m_vNodeToRegion.size();vector<int> vRet(iNodeSize);for (int i = 0; i < iNodeSize; i++){vRet[GetConnectRegionIndex(i)]++;}return vRet;}std::unordered_map<int, vector<int>> GetNodeOfRegion(){std::unordered_map<int, vector<int>> ret;const int iNodeSize = m_vNodeToRegion.size();for (int i = 0; i < iNodeSize; i++){ret[GetConnectRegionIndex(i)].emplace_back(i);}return ret;}
private:void UnionConnect(int iFrom, int iTo){m_vNodeToRegion[iFrom] = iTo;}vector<int> m_vNodeToRegion;//各点所在联通区域的索引,本联通区域任意一点的索引，为了增加可理解性，用最小索引int m_iConnetRegionCount;
};class CUnionFindMST
{
public:CUnionFindMST(const int iNodeSize) :m_uf(iNodeSize){}void AddEdge(const int iNode1, const int iNode2, int iWeight){if (m_uf.IsConnect(iNode1, iNode2)){return;}m_iMST += iWeight;m_uf.Union(iNode1, iNode2);}void AddEdge(const vector<int>& v){AddEdge(v[0], v[1], v[2]);}int MST(){if (m_uf.GetConnetRegionCount() > 1){return -1;}return m_iMST;}
private:int m_iMST = 0;CUnionFind m_uf;
};class CUnionFindDirect
{
public:CUnionFindDirect(int iSize){m_vRoot.resize(iSize);iota(m_vRoot.begin(), m_vRoot.end(), 0);}void Connect(bool& bConflic, bool& bCyc, int iFrom, int iTo){bConflic = bCyc = false;if (iFrom != m_vRoot[iFrom]){bConflic = true;}Fresh(iTo);if (m_vRoot[iTo] == iFrom){bCyc = true;}if (bConflic || bCyc){return;}m_vRoot[iFrom] = m_vRoot[iTo];}int GetMaxDest(int iFrom){Fresh(iFrom);return m_vRoot[iFrom];}	
private:int Fresh(int iNode){if (m_vRoot[iNode] == iNode){return iNode;}return m_vRoot[iNode] = Fresh(m_vRoot[iNode]);}vector<int> m_vRoot;
};class CNearestMST
{
public:CNearestMST(const int iNodeSize) :m_bDo(iNodeSize), m_vDis(iNodeSize, INT_MAX), m_vNeiTable(iNodeSize){}void Init(const vector<vector<int>>& edges){for (const auto& v : edges){Add(v);}}void Add(const vector<int>& v){m_vNeiTable[v[0]].emplace_back(v[1], v[2]);m_vNeiTable[v[1]].emplace_back(v[0], v[2]);}int MST(int start){int next = start;while ((next = AddNode(next)) >= 0);return m_iMST;}int MST(int iNode1, int iNode2, int iWeight){m_bDo[iNode1] = true;for (const auto& it : m_vNeiTable[iNode1]){if (m_bDo[it.first]){continue;}m_vDis[it.first] = min(m_vDis[it.first], (long long)it.second);}m_iMST = iWeight;int next = iNode2;while ((next = AddNode(next)) >= 0);return m_iMST;}private:int AddNode(int iCur){m_bDo[iCur] = true;for (const auto& it : m_vNeiTable[iCur]){if (m_bDo[it.first]){continue;}m_vDis[it.first] = min(m_vDis[it.first], (long long)it.second);}int iMinIndex = -1;for (int i = 0; i < m_vDis.size(); i++){if (m_bDo[i]){continue;}if ((-1 == iMinIndex) || (m_vDis[i] < m_vDis[iMinIndex])){iMinIndex = i;}}if (-1 != iMinIndex){if (INT_MAX == m_vDis[iMinIndex]){m_iMST = -1;return -1;}m_iMST += m_vDis[iMinIndex];}return iMinIndex;}vector<bool> m_bDo;vector<long long> m_vDis;vector < vector<std::pair<int, int>>> m_vNeiTable;long long m_iMST = 0;
};class CBFSDis
{
public:CBFSDis(vector<vector<int>>& vNeiB, vector<int> start){m_vDis.assign(vNeiB.size(), m_iNotMayDis);queue<int> que;for (const auto& n : start){m_vDis[n] = 0;que.emplace(n);}while (que.size()){const int cur = que.front();que.pop();for (const auto next : vNeiB[cur]){if (m_iNotMayDis != m_vDis[next]){continue;}m_vDis[next] = m_vDis[cur] + 1;que.emplace(next);}}}
public:const int m_iNotMayDis = 1e9;vector<int> m_vDis;
};class C01BFSDis
{
public:C01BFSDis(vector<vector<int>>& vNeiB0, vector<vector<int>>& vNeiB1, int s){m_vDis.assign(vNeiB0.size(), -1);std::deque<std::pair<int, int>> que;que.emplace_back(s, 0);while (que.size()){auto it = que.front();const int cur = it.first;const int dis = it.second;que.pop_front();if (-1 != m_vDis[cur]){continue;}m_vDis[cur] = it.second;for (const auto next : vNeiB0[cur]){if (-1 != m_vDis[next]){continue;}que.emplace_front(next, dis);}for (const auto next : vNeiB1[cur]){if (-1 != m_vDis[next]){continue;}que.emplace_back(next, dis + 1);}}}
public:vector<int> m_vDis;
};
//堆（优先队列)优化迪杰斯特拉算法 狄克斯特拉(Dijkstra)算法详解
typedef pair<long long, int> PAIRLLI;
class  CHeapDis
{
public:CHeapDis(int n){m_vDis.assign(n, -1);}void Cal(int start, const vector<vector<pair<int, int>>>& vNeiB){std::priority_queue<PAIRLLI, vector<PAIRLLI>, greater<PAIRLLI>> minHeap;minHeap.emplace(0, start);while (minHeap.size()){const long long llDist = minHeap.top().first;const int iCur = minHeap.top().second;minHeap.pop();if (-1 != m_vDis[iCur]){continue;}m_vDis[iCur] = llDist;for (const auto& it : vNeiB[iCur]){minHeap.emplace(llDist + it.second, it.first);}}}vector<long long> m_vDis;
};//朴素迪杰斯特拉算法
class CN2Dis
{
public:CN2Dis(int iSize) :m_iSize(iSize), DIS(m_vDis), PRE(m_vPre){}void Cal(int start, const vector<vector<pair<int, int>>>& vNeiB){m_vDis.assign(m_iSize, -1);m_vPre.assign(m_iSize, -1);vector<bool> vDo(m_iSize);//点是否已处理auto AddNode = [&](int iNode){//const int iPreNode = m_vPre[iNode];long long llPreDis = m_vDis[iNode];vDo[iNode] = true;for (const auto& it : vNeiB[iNode]){if (vDo[it.first]){continue;}if ((-1 == m_vDis[it.first]) || (it.second + llPreDis < m_vDis[it.first])){m_vDis[it.first] = it.second + llPreDis;m_vPre[it.first] = iNode;}}long long llMinDis = LLONG_MAX;int iMinIndex = -1;for (int i = 0; i < m_vDis.size(); i++){if (vDo[i]){continue;}if (-1 == m_vDis[i]){continue;}if (m_vDis[i] < llMinDis){iMinIndex = i;llMinDis = m_vDis[i];}}return (LLONG_MAX == llMinDis) ? -1 : iMinIndex;};int next = start;m_vDis[start] = 0;while (-1 != (next = AddNode(next)));}void Cal(int start, const vector<vector<int>>& mat){m_vDis.assign(m_iSize, LLONG_MAX);m_vPre.assign(m_iSize, -1);vector<bool> vDo(m_iSize);//点是否已处理auto AddNode = [&](int iNode){long long llPreDis = m_vDis[iNode];vDo[iNode] = true;for (int i = 0; i < m_iSize; i++){if (vDo[i]){continue;}const long long llCurDis = mat[iNode][i];if (llCurDis <= 0){continue;}m_vDis[i] = min(m_vDis[i], m_vDis[iNode] + llCurDis);}long long llMinDis = LLONG_MAX;int iMinIndex = -1;for (int i = 0; i < m_iSize; i++){if (vDo[i]){continue;}if (m_vDis[i] < llMinDis){iMinIndex = i;llMinDis = m_vDis[i];}}if (LLONG_MAX == llMinDis){return -1;}m_vPre[iMinIndex] = iNode;return iMinIndex;};int next = start;m_vDis[start] = 0;while (-1 != (next = AddNode(next)));}const vector<long long>& DIS;const vector<int>& PRE;
private:const int m_iSize;vector<long long> m_vDis;//各点到起点的最短距离vector<int>  m_vPre;//最短路径的前一点
};//多源码路径
template<class T, T INF = 1000 * 1000 * 1000>
class CFloyd
{
public:CFloyd(const  vector<vector<T>>& mat){m_vMat = mat;const int n = mat.size();for (int i = 0; i < n; i++){//通过i中转for (int i1 = 0; i1 < n; i1++){for (int i2 = 0; i2 < n; i2++){//此时：m_vMat[i1][i2] 表示通过[0,i)中转的最短距离m_vMat[i1][i2] = min(m_vMat[i1][i2], m_vMat[i1][i] + m_vMat[i][i2]);//m_vMat[i1][i2] 表示通过[0,i]中转的最短距离}}}};vector<vector<T>> m_vMat;
};class CParentToNeiBo
{
public:CParentToNeiBo(const vector<int>& parents){m_vNeiBo.resize(parents.size());for (int i = 0; i < parents.size(); i++){if (-1 == parents[i]){m_root = i;}else{m_vNeiBo[parents[i]].emplace_back(i);}}}vector<vector<int>> m_vNeiBo;int m_root = -1;
};class CNeiBo2
{
public:CNeiBo2(int n, bool bDirect, int iBase = 0) :m_iN(n), m_bDirect(bDirect), m_iBase(iBase){m_vNeiB.resize(n);}CNeiBo2(int n, vector<vector<int>>& edges, bool bDirect, int iBase = 0) :m_iN(n), m_bDirect(bDirect), m_iBase(iBase){m_vNeiB.resize(n);for (const auto& v : edges){m_vNeiB[v[0] - iBase].emplace_back(v[1] - iBase);if (!bDirect){m_vNeiB[v[1] - iBase].emplace_back(v[0] - iBase);}}}inline void Add(int iNode1, int iNode2){iNode1 -= m_iBase;iNode2 -= m_iBase;m_vNeiB[iNode1].emplace_back(iNode2);if (!m_bDirect){m_vNeiB[iNode2].emplace_back(iNode1);}}const int m_iN;const bool m_bDirect;const int m_iBase;vector<vector<int>> m_vNeiB;
};class CNeiBo3
{
public:CNeiBo3(int n, vector<vector<int>>& edges, bool bDirect, int iBase = 0){m_vNeiB.resize(n);AddEdges(edges, bDirect, iBase);}CNeiBo3(int n){m_vNeiB.resize(n);}void AddEdges(vector<vector<int>>& edges, bool bDirect, int iBase = 0){for (const auto& v : edges){m_vNeiB[v[0] - iBase].emplace_back(v[1] - iBase, v[2]);if (!bDirect){m_vNeiB[v[1] - iBase].emplace_back(v[0] - iBase, v[2]);}}}vector<vector<std::pair<int, int>>> m_vNeiB;
};template<class T, T INF = 1000 * 1000 * 1000>
class CNeiBoToMat
{
public:CNeiBoToMat(int n, const vector<vector<int>>& edges, bool bDirect = false, bool b1Base = false){m_vMat.assign(n, vector<int>(n, INF));for (int i = 0; i < n; i++){m_vMat[i][i] = 0;}for (const auto& v : edges){m_vMat[v[0] - b1Base][v[1] - b1Base] = v[2];if (!bDirect){m_vMat[v[1] - b1Base][v[0] - b1Base] = v[2];}}}vector<vector<int>> m_vMat;
};
class CCutEdge
{
public:CCutEdge(const vector<vector<int>>& vNeiB) : m_iSize(vNeiB.size()){m_vTime.assign(m_iSize, -1);m_vCutEdges.resize(m_iSize);for (int i = 0; i < m_iSize; i++){if (-1 != m_vTime[i]){continue;}m_iRegionCount++;dfs(i, -1, vNeiB);}}bool IsCut(int node1, int node2){return m_vCutEdges[node1].count(node2);}bool IsCut(int node){return m_vCutEdges[node].size();}int RegionCount()const{return m_iRegionCount;}
protected:int dfs(int cur, int parent, const vector<vector<int>>& vNeiB){auto& curTime = m_vTime[cur];curTime = m_iTime++;int iRet = curTime;for (const auto& next : vNeiB[cur]){if (next == parent){continue;}if (-1 != m_vTime[next]){iRet = min(iRet, m_vTime[next]);continue;}int iNextTime = dfs(next, cur, vNeiB);if (iNextTime > curTime){m_vCutEdges[cur].emplace(next);}iRet = min(iRet, iNextTime);}return iRet;}vector<int> m_vTime;int m_iTime = 0;int m_iRegionCount = 0;vector<std::unordered_set<int>> m_vCutEdges;const int m_iSize;
};//割点
class CCutPoint
{
public:CCutPoint(const vector<vector<int>>& vNeiB) : m_iSize(vNeiB.size()){m_vTime.assign(m_iSize, -1);m_vVisitMin.assign(m_iSize, -1);for (int i = 0; i < m_iSize; i++){if (-1 != m_vTime[i]){continue;}m_iRegionCount++;dfs(i, -1, vNeiB);}}int RegionCount()const{return m_iRegionCount;}const vector<int>& CutPoints()const{return m_vCutPoints;}const vector<int>& Tinme()const { return m_vTime; }
protected:void dfs(int cur, int parent, const vector<vector<int>>& vNeiB){auto& curTime = m_vTime[cur];auto& visitMin = m_vVisitMin[cur];curTime = m_iTime++;visitMin = curTime;int iMax = -1;int iChildNum = 0;for (const auto& next : vNeiB[cur]){if (next == parent){continue;}if (-1 != m_vTime[next]){visitMin = min(visitMin, m_vTime[next]);continue;}iChildNum++;dfs(next, cur, vNeiB);visitMin = min(visitMin, m_vVisitMin[next]);iMax = max(iMax, m_vVisitMin[next]);}if (-1 == parent){if (iChildNum >= 2){m_vCutPoints.emplace_back(cur);}}else{if (iMax >= curTime){m_vCutPoints.emplace_back(cur);}}}vector<int> m_vTime;//各节点到达时间，从0开始。 -1表示未处理vector<int> m_vVisitMin;// int m_iTime = 0;int m_iRegionCount = 0;vector<int> m_vCutPoints;const int m_iSize;
};class CTopSort
{
public://vBackNeiBo[1] = {2} 表示 1完成后，才能完成2template<class T >void Init(vector<T>& vPreToNext){m_c = vPreToNext.size();vector<int> vInDeg(m_c);for (int cur = 0; cur < m_c; cur++){for (const auto& next : vPreToNext[cur]){vInDeg[next]++;}}queue<int> que;for (int i = 0; i < m_c; i++){if (0 == vInDeg[i]){que.emplace(i);m_vLeaf.emplace_back(i);OnDo(-1, i);}}while (que.size()){const int cur = que.front();que.pop();for (const auto& next : vPreToNext[cur]){vInDeg[next]--;if (0 == vInDeg[next]){que.emplace(next);OnDo(cur, next);}}};}virtual void OnDo(int pre, int cur) = 0;int m_c;vector<int> m_vLeaf;
};struct CVec
{int r;int c;
};
struct CPos
{	int r = 0, c = 0;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;
};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;
};
class  CGridToNeiBo
{
public:static vector<vector<int>> ToNeiBo(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;}
};template<class T = int>
class CEnumGrid
{
public:	static  void EnumGrid(vector<vector<T>>& grid, std::function<void(int, int, T&)> call){for (int r = 0; r < grid.size(); r++){for (int c = 0; c < grid.front().size(); c++){call(r, c, grid[r][c]);}}}static  void EnumPos(vector<vector<T>>& grid, vector<tuple<T, CPos&>> vRes){EnumGrid(grid, [&vRes](int curR, int curC, T& curV){for (auto& [value, pos] : vRes){if (curV == value){pos = { curR,curC };}}});}inline static const CVec s_Move4[4] = { {1,0},{0,1},{-1,0},{0,-1} };//上右下左enum {UP=0,RIGHT,DOWN,LEFT};
};class CEnumGridEdge
{
public:CEnumGridEdge(int r, int c, std::function<bool(int, int)> funVilidCur, std::function<bool(int, int)> funVilidNext) :m_r(r), m_c(c){m_funVilidCur = funVilidCur;m_funVilidNext = funVilidNext;m_vNext.assign(m_r, vector < vector<pair<int, int>>>(m_c));Init();}vector<vector<int>> BFS(vector<pair<int, int>> start, const int endr = -1, const int endc = -1){vector<vector<int>> vDis(m_r, vector<int>(m_c, -1));queue<pair<int, int>> que;for (const auto& [r, c] : start){vDis[r][c] = 0;que.emplace(make_pair(r, c));}while (que.size()){const auto [r, c] = que.front();que.pop();for (const auto [nr, nc] : m_vNext[r][c]){if (-1 != vDis[nr][nc]){continue;}vDis[nr][nc] = vDis[r][c] + 1;if ((endr == nr) && (endc == nc)){break;}que.emplace(make_pair(nr, nc));}}return vDis;}const int m_r, m_c;vector < vector < vector<pair<int, int>>>> m_vNext;
protected:void Init(){for (int r = 0; r < m_r; r++){for (int c = 0; c < m_c; 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);}}}void Move(int preR, int preC, int r, int c){if ((r < 0) || (r >= m_r)){return;}if ((c < 0) || (c >= m_c)){return;}if (m_funVilidCur(preR, preC) && m_funVilidNext(r, c)){m_vNext[preR][preC].emplace_back(r, c);}};std::function<bool(int, int)> m_funVilidCur, m_funVilidNext;
};class CBFS
{
public:CBFS(int iStatuCount, int iInit = -1) :m_iStatuCount(iStatuCount), m_iInit(iInit){m_res.assign(iStatuCount, iInit);}bool Peek(int& statu){if (m_que.empty()){return false;}statu = m_que.front();m_que.pop_front();return true;}void PushBack(int statu, int value){if (m_iInit != m_res[statu]){return;}m_res[statu] = value;m_que.push_back(statu);}void PushFront(int statu, int value){if (m_iInit != m_res[statu]){return;}m_res[statu] = value;m_que.push_front(statu);}int Get(int statu){return m_res[statu];}
private:const int m_iStatuCount;const int m_iInit;deque<int> m_que;vector<int> m_res;
};class CBFS2 : protected CBFS
{
public:CBFS2(int iStatuCount1, int iStatuCount2, int iInit = -1) :CBFS(iStatuCount1* iStatuCount2, iInit), m_iStatuCount2(iStatuCount2){}bool Peek(int& statu1, int& statu2){int statu;if (!CBFS::Peek(statu)){return false;}statu1 = statu / m_iStatuCount2;statu2 = statu % m_iStatuCount2;return true;}void PushBack(int statu1, int statu2, int value){CBFS::PushBack(statu1 * m_iStatuCount2 + statu2, value);}void PushFront(int statu1, int statu2, int value){CBFS::PushFront(statu1 * m_iStatuCount2 + statu2, value);}int Get(int statu1, int statu2){return CBFS::Get(statu1 * m_iStatuCount2 + statu2);}
private:const int m_iStatuCount2;
};class CBFS3 : protected CBFS2
{
public:CBFS3(int iStatuCount1, int iStatuCount2, int iStatuCount3, int iInit = -1) :CBFS2(iStatuCount1, iStatuCount2* iStatuCount3, iInit), m_iStatuCount3(iStatuCount3){}bool Peek(int& statu1, int& statu2, int& statu3){int statu23;if (!CBFS2::Peek(statu1, statu23)){return false;}statu2 = statu23 / m_iStatuCount3;statu3 = statu23 % m_iStatuCount3;return true;}void PushBack(int statu1, int statu2, int statu3, int value){CBFS2::PushBack(statu1, statu2 * m_iStatuCount3 + statu3, value);}void PushFront(int statu1, int statu2, int statu3, int value){CBFS2::PushFront(statu1, statu2 * m_iStatuCount3 + statu3, value);}int Get(int statu1, int statu2, int statu3){return CBFS2::Get(statu1, statu2 * m_iStatuCount3 + statu3);}const int m_iStatuCount3;
};class CBFS4 : protected CBFS3
{
public:CBFS4(int iStatuCount1, int iStatuCount2, int iStatuCount3, int iStatuCount4, int iInit = -1) :CBFS3(iStatuCount1, iStatuCount2, iStatuCount3* iStatuCount4, iInit), m_iStatuCount4(iStatuCount4){}bool Peek(int& statu1, int& statu2, int& statu3, int& statu4){int statu34;if (!CBFS3::Peek(statu1, statu2, statu34)){return false;}statu3 = statu34 / m_iStatuCount4;statu4 = statu34 % m_iStatuCount4;return true;}void PushBack(int statu1, int statu2, int statu3, int statu4, int value){CBFS3::PushBack(statu1, statu2, statu3 * m_iStatuCount4 + statu4, value);}void PushFront(int statu1, int statu2, int statu3, int statu4, int value){CBFS3::PushFront(statu1, statu2, statu3 * m_iStatuCount4 + statu4, value);}int Get(int statu1, int statu2, int statu3, int statu4){return CBFS3::Get(statu1, statu2, statu3 * m_iStatuCount4 + statu4);}const int m_iStatuCount4;
};class CCutPointEx
{
public:CCutPointEx(const vector<vector<int>>& vNeiB) : m_iSize(vNeiB.size()){m_vTime.assign(m_iSize, -1);	m_vCutRegion.resize(m_iSize);m_vNodeToRegion.assign(m_iSize,-1);m_vCut.assign(m_iSize, false);for (int i = 0; i < m_iSize; i++){if (-1 != m_vTime[i]){continue;}dfs(i, -1, vNeiB);m_iRegionCount++;}}bool Visit(int src, int dest, int iCut){if (m_vNodeToRegion[src] != m_vNodeToRegion[dest]){return false;//不在一个连通区域}if (!m_vCut[iCut]){return true;}const int r1 = GetCutRegion(iCut,src);const int r2 = GetCutRegion(iCut, dest);return r1 == r2;}
protected:int dfs(int cur, int parent, const vector<vector<int>>& vNeiB){		auto& curTime = m_vTime[cur];			m_vNodeToRegion[cur] = m_iRegionCount;curTime = m_iTime++;		int iCutChild=0;int iMinTime = curTime;for (const auto& next : vNeiB[cur]){if (next == parent){continue;}if (-1 != m_vTime[next]){iMinTime = min(iMinTime, m_vTime[next]);continue;}			int iChildBeginTime = m_iTime;const int iChildMinTime = dfs(next, cur, vNeiB);iMinTime = min(iMinTime, iChildMinTime);if (iChildMinTime >= curTime){iCutChild++;m_vCutRegion[cur].push_back({ iChildBeginTime,m_iTime });};}m_vCut[cur] = (iCutChild + (-1 != parent)) >= 2;return iMinTime;}	int GetCutRegion(int iCut, int iNode)const {const auto& v = m_vCutRegion[iCut];auto it = std::upper_bound(v.begin(), v.end(), m_vTime[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_vTime[iNode]) ? (it - v.begin()) : v.size();}int m_iTime = 0;	const int m_iSize;int m_iRegionCount=0;vector<int> m_vTime;//各节点到达时间，从0开始。 -1表示未处理vector<bool> m_vCut;vector<int> m_vNodeToRegion;vector<vector<pair<int,int>>> m_vCutRegion;
};class Solution {
public:int minPushBox(vector<vector<char>>& grid) {		auto Vilid = [&](int r, int c) {return '#' != grid[r][c]; };CRange range(grid.size(), grid.front().size(), Vilid);	CPos::s_MaxC = range.m_c;		auto neiBo = CGridToNeiBo::ToNeiBo(range.m_r, range.m_c, Vilid, Vilid);		CCutPointEx cutPoint(neiBo);auto Visit = [&](CPos s, CPos d, CPos b){			return range.Vilid(d) && cutPoint.Visit(s.ToMask(),d.ToMask(),b.ToMask());};CBFS3 bfs(range.m_r, range.m_c, 4);CPos sInit,tInit,bInit;CEnumGrid<char>::EnumPos(grid, { { 'B',bInit },{'T',tInit},{'S',sInit} });auto MovePeo = [&](CPos peo, CPos bCur, int iCurDis)		{for (int i = 0; i < 4; i++) {if (Visit(peo, bCur + CEnumGrid<>::s_Move4[i], bCur)) {bfs.PushFront(bCur.r, bCur.c, i, iCurDis);}}};MovePeo(sInit, bInit, 0);int br1, bc1, pd;while (bfs.Peek(br1, bc1, pd))		{CPos bCur = { br1,bc1 };CPos peo = bCur + CEnumGrid<>::s_Move4[pd];const int CurDis = bfs.Get(br1, bc1, pd);if (bCur == tInit )			{return CurDis;	}	MovePeo(peo, bCur, CurDis);auto dest = bCur - CEnumGrid<>::s_Move4[pd];if (range.Vilid(dest)){bfs.PushBack(dest.r, dest.c, pd, CurDis + 1);}}			return -1;}
};

2023年4月

class CGridCanVisit
{
public:
CGridCanVisit(const vector<vector>& bCanVisit, int r, int c) :m_bCanVisit(bCanVisit), m_r(m_bCanVisit.size()), m_c(m_bCanVisit[0].size())
{
m_vDis.assign(m_r, vector(m_c,INT_MAX/2));
Dist(r, c);
}
bool Vilid(const int r,const int c )
{
if ((r < 0) || (r >= m_r))
{
return false;
}
if ((c < 0) || (c >= m_c))
{
return false;
}
return true;
}
const vector<vector>& Dis()const
{
return m_vDis;
}
const vector<vector>& m_bCanVisit;
private:
//INT_MAX/2 表示无法到达
void Dist(int r, int c)
{
m_vDis.assign(m_r, vector(m_c, INT_MAX / 2));
vector<vector> vHasDo(m_r, vector(m_c));
std::queue<std::pair<int, int>> que;
auto Add = [&](const int& r, const int& c, const int& iDis)
{
if (!Vilid(r, c))
{
return;
}
if (vHasDo[r][c])
{
return;
}
if (!m_bCanVisit[r][c])
{
vHasDo[r][c] = true;
return;
}
if (iDis >= m_vDis[r][c])
{
return;
}
que.emplace(r, c);
m_vDis[r][c] = iDis;
vHasDo[r][c] = true;
};
Add(r, c, 0);
while (que.size())
{
const int r = que.front().first;
const int c = que.front().second;
que.pop();
const int iDis = m_vDis[r][c];
Add(r + 1, c, iDis + 1);
Add(r - 1, c, iDis + 1);
Add(r, c + 1, iDis + 1);
Add(r, c - 1, iDis + 1);
}
}
vector<vector> m_vDis;
const int m_r;
const int m_c;
};
class Solution {
public:
int minPushBox(vector<vector>& grid) {
std::pair<int, int> pB, pS, pT;
m_r = grid.size();
m_c = grid[0].size();
vector<vector> vCanVisit(m_r, vector(m_c));
for (int r = 0; r < m_r; r++)
{
for (int c = 0; c < m_c; c++)
{
const char ch = grid[r][c];
if (‘S’ == ch)
{
pS = std::make_pair(r, c);
}
else if (‘T’ == ch)
{
pT = std::make_pair(r, c);
}
else if (‘B’ == ch)
{
pB = std::make_pair(r, c);
}
vCanVisit[r][c] = ‘#’ != ch;
}
}
std::unordered_set vHasDo;
std::queue<std::tuple<int, int, int, int>> que;
auto Add = [&](int r, int c, int iSR, int iSC)
{
const int iMask = r * 100 * 100 * 100 + c * 100 * 100 + iSR * 100 + iSC;
if (vHasDo.count(iMask))
{
return;
}
vHasDo.insert(iMask);
que.emplace(r, c, iSR, iSC);
};
auto Move = [&]( CGridCanVisit& gc,int r, int c, int iOldR, int iOldC, int iSR, int iSC)
{
if (!gc.Vilid(r, c))
{
return;//非法行列好
}
if (!gc.m_bCanVisit[r][c])
{//rc是墙无法推动
return;
}
auto vDis = gc.Dis();
const int r2 = iOldR * 2 - r;
const int c2 = iOldC * 2 - c;
if (!gc.Vilid(r2, c2))
{
return;
}
if (vDis[r2][c2] >= 1000 * 1000)
{
return;//人没有地方占，无法推
}
Add(r, c, iOldR, iOldC);
};
std::queue<std::tuple<int, int, int, int>> preQue;
preQue.emplace(pB.first, pB.second, pS.first, pS.second);
for (int i = 0; preQue.size(); i++ )
{
while (preQue.size())
{
auto cur = preQue.front();
if ((get<0>(cur) == pT.first) && (get<1>(cur) == pT.second))
{
return i;
}
preQue.pop();
auto tmp = vCanVisit;
tmp[get<0>(cur)][get<1>(cur)] = false;
CGridCanVisit gc(tmp, get<2>(cur), get<3>(cur));
Move(gc, get<0>(cur)+1, get<1>(cur), get<0>(cur), get<1>(cur), get<2>(cur), get<3>(cur));
Move(gc, get<0>(cur)-1, get<1>(cur), get<0>(cur), get<1>(cur), get<2>(cur), get<3>(cur));
Move(gc, get<0>(cur), get<1>(cur)+1, get<0>(cur), get<1>(cur), get<2>(cur), get<3>(cur));
Move(gc, get<0>(cur), get<1>(cur)-1, get<0>(cur), get<1>(cur), get<2>(cur), get<3>(cur));
}
preQue.swap(que);
}
return -1;
}
int m_r;
int m_c;
};

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。