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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;
};
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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