作者推荐
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。
{ 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 \begin{cases} 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{cases}{如果人可以左移,人左移,加到队首如果人和箱子都可以左移,人箱子左移,加到队尾箱子不在左边箱子在人左边
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:
{ 如果没箱子,人无法到达 无法到达。 e l s e 箱子不是割点 能到达 e l s e 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。 o t h e r 不能到达。 \begin{cases} 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{cases}⎩⎨⎧如果没箱子,人无法到达else箱子不是割点else是割点,源点和目标点到时间戳都大于(小于)割点时间戳other无法到达。能到达能到达。不能到达。
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2 template<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;
};