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‎Problemset/1219-Path with Maximum Gold/README.md

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# 1219. Path with Maximum Gold
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In a gold mine `grid` of size `m x n`, each cell in this mine has an integer representing the amount of gold in that cell, `0` if it is empty.
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Return the maximum amount of gold you can collect under the conditions:
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* Every time you are located in a cell you will collect all the gold in that cell.
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* From your position, you can walk one step to the left, right, up, or down.
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* You can't visit the same cell more than once.
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* Never visit a cell with `0` gold.
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* You can start and stop collecting gold from **any** position in the grid that has some gold.
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#### Example 1:
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<pre>
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<strong>Input:</strong> grid = [[0,6,0],[5,8,7],[0,9,0]]
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<strong>Output:</strong> 24
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<strong>Explanation:</strong>
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[[0,6,0],
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[5,8,7],
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[0,9,0]]
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Path to get the maximum gold, 9 -> 8 -> 7.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> grid = [[1,0,7],[2,0,6],[3,4,5],[0,3,0],[9,0,20]]
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<strong>Output:</strong> 28
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<strong>Explanation:</strong>
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[[1,0,7],
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[2,0,6],
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[3,4,5],
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[0,3,0],
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[9,0,20]]
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Path to get the maximum gold, 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7.
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</pre>
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#### Constraints:
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* `m == grid.length`
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* `n == grid[i].length`
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* `1 <= m, n <= 15`
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* `0 <= grid[i][j] <= 100`
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* There are at most **25** cells containing gold.
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## Solutions (Python)
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### 1. Solution
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```Python
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class Solution:
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def getMaximumGold(self, grid: List[List[int]]) -> int:
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m, n = len(grid), len(grid[0])
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gold = 0
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ret = 0
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def dfs(i: int, j: int) -> None:
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nonlocal gold, ret
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ret = max(ret, gold)
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if i > 0 and grid[i - 1][j] > 0:
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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dfs(i - 1, j)
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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if i + 1 < m and grid[i + 1][j] > 0:
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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dfs(i + 1, j)
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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if j > 0 and grid[i][j - 1] > 0:
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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dfs(i, j - 1)
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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if j + 1 < n and grid[i][j + 1] > 0:
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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dfs(i, j + 1)
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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for i in range(m):
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for j in range(n):
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if grid[i][j] > 0:
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gold = grid[i][j]
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grid[i][j] = -grid[i][j]
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dfs(i, j)
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grid[i][j] = -grid[i][j]
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return ret
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```

‎Problemset/1219-Path with Maximum Gold/README_CN.md

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# 1219. 黄金矿工
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你要开发一座金矿，地质勘测学家已经探明了这座金矿中的资源分布，并用大小为 `m * n` 的网格 `grid` 进行了标注。每个单元格中的整数就表示这一单元格中的黄金数量；如果该单元格是空的，那么就是 `0`。
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为了使收益最大化，矿工需要按以下规则来开采黄金：
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* 每当矿工进入一个单元，就会收集该单元格中的所有黄金。
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* 矿工每次可以从当前位置向上下左右四个方向走。
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* 每个单元格只能被开采（进入）一次。
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* 不得开采（进入）黄金数目为 `0` 的单元格。
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* 矿工可以从网格中 **任意一个** 有黄金的单元格出发或者是停止。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> grid = [[0,6,0],[5,8,7],[0,9,0]]
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<strong>输出:</strong> 24
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<strong>解释:</strong>
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[[0,6,0],
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[5,8,7],
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[0,9,0]]
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一种收集最多黄金的路线是：9 -> 8 -> 7。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> grid = [[1,0,7],[2,0,6],[3,4,5],[0,3,0],[9,0,20]]
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<strong>输出:</strong> 28
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<strong>解释:</strong>
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[[1,0,7],
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[2,0,6],
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[3,4,5],
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[0,3,0],
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[9,0,20]]
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一种收集最多黄金的路线是：1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7。
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</pre>
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#### 提示:
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* `1 <= grid.length, grid[i].length <= 15`
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* `0 <= grid[i][j] <= 100`
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* 最多 **25** 个单元格中有黄金。
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## 题解 (Python)
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### 1. 题解
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```Python
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class Solution:
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def getMaximumGold(self, grid: List[List[int]]) -> int:
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m, n = len(grid), len(grid[0])
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gold = 0
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ret = 0
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def dfs(i: int, j: int) -> None:
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nonlocal gold, ret
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ret = max(ret, gold)
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if i > 0 and grid[i - 1][j] > 0:
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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dfs(i - 1, j)
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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if i + 1 < m and grid[i + 1][j] > 0:
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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dfs(i + 1, j)
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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if j > 0 and grid[i][j - 1] > 0:
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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dfs(i, j - 1)
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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if j + 1 < n and grid[i][j + 1] > 0:
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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dfs(i, j + 1)
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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for i in range(m):
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for j in range(n):
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if grid[i][j] > 0:
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gold = grid[i][j]
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grid[i][j] = -grid[i][j]
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dfs(i, j)
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grid[i][j] = -grid[i][j]
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return ret
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```

‎Problemset/1219-Path with Maximum Gold/Solution.py

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class Solution:
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def getMaximumGold(self, grid: List[List[int]]) -> int:
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m, n = len(grid), len(grid[0])
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gold = 0
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ret = 0
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def dfs(i: int, j: int) -> None:
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nonlocal gold, ret
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ret = max(ret, gold)
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if i > 0 and grid[i - 1][j] > 0:
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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dfs(i - 1, j)
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gold += grid[i - 1][j]
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grid[i - 1][j] = -grid[i - 1][j]
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if i + 1 < m and grid[i + 1][j] > 0:
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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dfs(i + 1, j)
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gold += grid[i + 1][j]
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grid[i + 1][j] = -grid[i + 1][j]
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if j > 0 and grid[i][j - 1] > 0:
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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dfs(i, j - 1)
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gold += grid[i][j - 1]
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grid[i][j - 1] = -grid[i][j - 1]
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if j + 1 < n and grid[i][j + 1] > 0:
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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dfs(i, j + 1)
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gold += grid[i][j + 1]
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grid[i][j + 1] = -grid[i][j + 1]
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for i in range(m):
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for j in range(n):
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if grid[i][j] > 0:
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gold = grid[i][j]
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grid[i][j] = -grid[i][j]
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dfs(i, j)
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grid[i][j] = -grid[i][j]
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return ret

‎README.md

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[1210][1210l]|[Minimum Moves to Reach Target with Rotations][1210] |![rs]
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[1217][1217l]|[Play with Chips][1217] |![rs]
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[1218][1218l]|[Longest Arithmetic Subsequence of Given Difference][1218] |![rs]
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[1219][1219l]|[Path with Maximum Gold][1219] |![py]
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[1220][1220l]|[Count Vowels Permutation][1220] |![rs]
838839
[1221][1221l]|[Split a String in Balanced Strings][1221] |![rb]&nbsp;&nbsp;![rs]
839840
[1222][1222l]|[Queens That Can Attack the King][1222] |![rs]
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[1210]:Problemset/1210-Minimum%20Moves%20to%20Reach%20Target%20with%20Rotations/README.md#1210-minimum-moves-to-reach-target-with-rotations
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[1217]:Problemset/1217-Play%20with%20Chips/README.md#1217-play-with-chips
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[1218]:Problemset/1218-Longest%20Arithmetic%20Subsequence%20of%20Given%20Difference/README.md#1218-longest-arithmetic-subsequence-of-given-difference
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[1219]:Problemset/1219-Path%20with%20Maximum%20Gold/README.md#1219-path-with-maximum-gold
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[1220]:Problemset/1220-Count%20Vowels%20Permutation/README.md#1220-count-vowels-permutation
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[1221]:Problemset/1221-Split%20a%20String%20in%20Balanced%20Strings/README.md#1221-split-a-string-in-balanced-strings
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[1222]:Problemset/1222-Queens%20That%20Can%20Attack%20the%20King/README.md#1222-queens-that-can-attack-the-king
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[1210l]:https://leetcode.com/problems/minimum-moves-to-reach-target-with-rotations/
43114313
[1217l]:https://leetcode.com/problems/play-with-chips/
43124314
[1218l]:https://leetcode.com/problems/longest-arithmetic-subsequence-of-given-difference/
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[1219l]:https://leetcode.com/problems/path-with-maximum-gold/
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[1220l]:https://leetcode.com/problems/count-vowels-permutation/
43144317
[1221l]:https://leetcode.com/problems/split-a-string-in-balanced-strings/
43154318
[1222l]:https://leetcode.com/problems/queens-that-can-attack-the-king/

‎README_CN.md

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[1210][1210l]|[穿过迷宫的最少移动次数][1210] |![rs]
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[1217][1217l]|[玩筹码][1217] |![rs]
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[1218][1218l]|[最长定差子序列][1218] |![rs]
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[1219][1219l]|[黄金矿工][1219] |![py]
837838
[1220][1220l]|[统计元音字母序列的数目][1220] |![rs]
838839
[1221][1221l]|[分割平衡字符串][1221] |![rb]&nbsp;&nbsp;![rs]
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[1222][1222l]|[可以攻击国王的皇后][1222] |![rs]
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[1210]:Problemset/1210-Minimum%20Moves%20to%20Reach%20Target%20with%20Rotations/README_CN.md#1210-穿过迷宫的最少移动次数
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[1217]:Problemset/1217-Play%20with%20Chips/README_CN.md#1217-玩筹码
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[1218]:Problemset/1218-Longest%20Arithmetic%20Subsequence%20of%20Given%20Difference/README_CN.md#1218-最长定差子序列
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[1219]:Problemset/1219-Path%20with%20Maximum%20Gold/README_CN.md#1219-黄金矿工
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[1220]:Problemset/1220-Count%20Vowels%20Permutation/README_CN.md#1220-统计元音字母序列的数目
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[1221]:Problemset/1221-Split%20a%20String%20in%20Balanced%20Strings/README_CN.md#1221-分割平衡字符串
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[1222]:Problemset/1222-Queens%20That%20Can%20Attack%20the%20King/README_CN.md#1222-可以攻击国王的皇后
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[1210l]:https://leetcode.cn/problems/minimum-moves-to-reach-target-with-rotations/
43114313
[1217l]:https://leetcode.cn/problems/play-with-chips/
43124314
[1218l]:https://leetcode.cn/problems/longest-arithmetic-subsequence-of-given-difference/
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[1219l]:https://leetcode.cn/problems/path-with-maximum-gold/
43134316
[1220l]:https://leetcode.cn/problems/count-vowels-permutation/
43144317
[1221l]:https://leetcode.cn/problems/split-a-string-in-balanced-strings/
43154318
[1222l]:https://leetcode.cn/problems/queens-that-can-attack-the-king/

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