Solved! Leetcode 1219. Path with Maximum Gold


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.

Example 1

Example 2


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


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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