# 1219. Path with Maximum Gold

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.

Return the maximum amount of gold you can collect under the conditions:

• Every time you are located in a cell you will collect all the gold in that cell.
• From your position, you can walk one step to the left, right, up, or down.
• You can’t visit the same cell more than once.
• Never visit a cell with `0` gold.
• You can start and stop collecting gold from any position in the grid that has some gold.

Example 1:

``````Input: grid = [[0,6,0],[5,8,7],[0,9,0]]
Output: 24
Explanation:
[[0,6,0],
[5,8,7],
[0,9,0]]
Path to get the maximum gold, 9 -> 8 -> 7.
``````

Example 2:

``````Input: grid = [[1,0,7],[2,0,6],[3,4,5],[0,3,0],[9,0,20]]
Output: 28
Explanation:
[[1,0,7],
[2,0,6],
[3,4,5],
[0,3,0],
[9,0,20]]
Path to get the maximum gold, 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7.
``````

Constraints:

• `m == grid.length`
• `n == grid[i].length`
• `1 <= m, n <= 15`
• `0 <= grid[i][j] <= 100`
• There are at most 25 cells containing gold.

``````class Solution {
public:
int getMaximumGold(vector<vector<int>>& grid) {
int res = 0, m = grid.size(), n = grid[0].size();
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (grid[i][j] == 0) continue;
res = max(res, helper(grid, i, j));
}
}
return res;
}
int helper(vector<vector<int>>& grid, int i, int j) {
int m = grid.size(), n = grid[0].size();
if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == 0) return 0;
int val = grid[i][j], mx = 0;
grid[i][j] = 0;
mx = max({helper(grid, i + 1, j), helper(grid, i - 1, j), helper(grid, i, j + 1), helper(grid, i, j - 1)});
grid[i][j] = val;
return mx + val;
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1219

https://leetcode.com/problems/path-with-maximum-gold/

https://leetcode.com/problems/path-with-maximum-gold/discuss/398388/C%2B%2BJavaPython-DFS-Backtracking-Clean-code-O(3k)

https://leetcode.com/problems/path-with-maximum-gold/discuss/398282/JavaPython-3-DFS-and-BFS-w-comment-brief-explanation-and-analysis.

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