LeetCoce407. 接雨水 II
给你一个 m x n 的矩阵，其中的值均为非负整数，代表二维高度图每个单元的高度，请计算图中形状最多能接多少体积的雨水。
示例 1:
输入: heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
输出: 4
解释: 下雨后，雨水将会被上图蓝色的方块中。总的接雨水量为1+2+1=4。
示例 2:
输入: heightMap = [[3,3,3,3,3],[3,2,2,2,3],[3,2,1,2,3],[3,2,2,2,3],[3,3,3,3,3]]
输出: 10
提示:
m == heightMap.length
n == heightMap[i].length
1 <= m, n <= 200
0 <= heightMap[i][j] <= 2 * 104
广度优先搜索
vHeight记录各单格包括水的高度，初始为-1，表示未处理。四周边界显然无法留住水，所以四周边界的vHeight等于heightMap。
不断处理vHeight最小单格(r,c)的邻接单格(nr,nc) vHeight[nr][nc] = max(vHeight[r][c],heightMap[nr][nc]。
边界全部在已处理格子中。
{ 不会做什么 已处理格子的邻居都已经处理 不是边界 处理邻居 已处理格子有邻居未处理 边界 \begin{cases} 不会做什么 & 已处理格子的邻居都已经处理 & 不是边界 \\ 处理邻居 & 已处理格子有邻居未处理 & 边界\\ \end{cases} {不会做什么处理邻居已处理格子的邻居都已经处理已处理格子有邻居未处理不是边界边界
假定h1是边界最低vHeight，则任意未处理单格的水达到h1时，都不会流出。
h1所在单格的邻居水不会超过h1，否则会流到h1所在单格。
代码
核心代码
class CEnumGridEdge
{
public:
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);
}
}
}
const int m_r, m_c;
protected:
CEnumGridEdge(int r, int c) :m_r(r), m_c(c)
{
}
void Move(int preR, int preC, int r, int c)
{
if ((r < 0) || (r >= m_r))
{
return;
}
if ((c < 0) || (c >= m_c))
{
return;
}
OnEnumEdge(preR, preC, r, c);
};
virtual void OnEnumEdge(int preR, int preC, int r, int c) = 0;
};
class TNeiBoForGrid : public CEnumGridEdge
{
public:
TNeiBoForGrid(const vector<vector<int>>& grid) :m_grid(grid),
CEnumGridEdge(grid.size(), grid.front().size())
{
m_vNext.assign(m_r, vector < vector<pair<int, int>>>(m_c));
Init();
}
virtual void OnEnumEdge(int preR, int preC, int r, int c)
{
m_vNext[preR][preC].emplace_back(r, c);
}
const vector<vector<int>>& m_grid;
vector < vector < vector<pair<int, int>>>> m_vNext;
};
class Solution {
public:
int trapRainWater(vector<vector<int>>& heightMap) {
TNeiBoForGrid neiBo(heightMap);
vector<vector<int>> vHeight(neiBo.m_r, vector<int>(neiBo.m_c, -1));
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<>> minHeap;
auto Add = [&](int r, int c, int iHeight)
{
if (vHeight[r][c] >= 0)
{
return;
}
vHeight[r][c] = iHeight;
minHeap.emplace(iHeight, r, c);
};
for (int r = 0; r < neiBo.m_r; r++)
{
for (int c = 0; c < neiBo.m_c; c++)
{
if ((0 == r) || (neiBo.m_r == r + 1) || (0 == c) || (neiBo.m_c == c + 1))
{
Add(r, c, heightMap[r][c]);
}
}
}
while (minHeap.size())
{
auto [height, r, c] = minHeap.top();
minHeap.pop();
for (const auto& [nr, nc] : neiBo.m_vNext[r][c])
{
Add(nr, nc, max(height, heightMap[nr][nc]));
}
}
int iRet = 0;
for (int r = 0; r < neiBo.m_r; r++)
{
iRet += std::accumulate(vHeight[r].begin(), vHeight[r].end(), 0) - std::accumulate(heightMap[r].begin(), heightMap[r].end(), 0);
}
return iRet;
}
};
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<int>> heightMap;
{
Solution sln;
heightMap = { {1,4,3,1,3,2},{3,2,1,3,2,4},{2,3,3,2,3,1} };
auto res = sln.trapRainWater(heightMap);
Assert(4, res);
}
{
Solution sln;
heightMap = { {3,3,3,3,3},{3,2,2,2,3},{3,2,1,2,3},{3,2,2,2,3},{3,3,3,3,3} };
auto res = sln.trapRainWater(heightMap);
Assert(10, res);
}
}
2023年3月
class Solution {
public:
int trapRainWater(vector<vector>& heightMap) {
m_r = heightMap.size();
m_c = heightMap[0].size();
//memset(m_arrNeiNum, 4, sizeof(m_arrNeiNum));
for (int c = 0; c < m_c; c++)
{
//m_arrNeiNum[0][c] = 1;
//m_arrNeiNum[m_r - 1][c] = 1;
AddRowColToRange(0, c, heightMap);
AddRowColToRange(m_r-1, c, heightMap);
}
for (int r = 1; r + 1 < m_r; r++)
{
AddRowColToRange(r,0, heightMap);
AddRowColToRange(r,m_c-1, heightMap);
//m_arrNeiNum[r][0] = 1;
//m_arrNeiNum[r][m_c - 1] = 1;
}
while (m_mHeightRowCol.size())
{
const int iHeight = m_mHeightRowCol.begin()->first;
const int r = m_mHeightRowCol.begin()->second / 1000;
const int c = m_mHeightRowCol.begin()->second % 1000;
Add(r + 1, c, iHeight,heightMap);
Add(r - 1, c, iHeight, heightMap);
Add(r, c + 1, iHeight, heightMap);
Add(r, c - 1, iHeight, heightMap);
m_mHeightRowCol.erase(m_mHeightRowCol.begin());
}
return m_iRet;
}
void Add(int r, int c, int iPreHeight, const vector<vector>& heightMap)
{
if ((r < 0) || (r >= m_r))
{
return;
}
if ((c < 0) || (c >= m_c))
{
return;
}
if (m_setHasDo.count(RowColMask(r,c)))
{
return;
}
const int iCurHeight = heightMap[r][c];
const int iWaterHeight = max(iCurHeight, iPreHeight);
if (iWaterHeight > iCurHeight)
{
m_iRet += iWaterHeight - iCurHeight;
}
AddRowColToRange(r, c, iWaterHeight);
}
void AddRowColToRange(int r, int c, const int iWaterHeight)
{
const int iRowCol = RowColMask(r, c);
m_mHeightRowCol.emplace(iWaterHeight, iRowCol);
m_setHasDo.insert(iRowCol);
}
void AddRowColToRange(int r, int c,const vector<vector>& heightMap)
{
AddRowColToRange(r, c, heightMap[r][c]);
}
inline int RowColMask(int r, int c)
{
return 1000 * r + c;
}
int m_r;
int m_c;
std::multimap<int, int> m_mHeightRowCol;//记录当前边界
std::unordered_set m_setHasDo;//记录已经处理的格子
std::unordered_set m_setNeiHasDo;//记录相邻格子已经处理完毕
//char m_arrNeiNum[200][200];//记录邻居数
int m_iRet = 0;
};
