# Solved! Leetcode 1219. Path with Maximum Gold

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

## Description: 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.

## 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.

## Solution

### Time Complexity

M*N*3^G, We are only running recursion in 3 direction (except for the starting call), as previous cell is already visited and cannot be visited again, where G indicate gold cells

### Space Complexity

O(G), G – Total golden cells in the grid.

As the DFS call can only go so far as to visit all connected Golden cells, it has O(G)O(G)O(G) space complexity.

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