1219. Path with Maximum Gold

Description

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.

 

Solutions

Solution: Depth-First Search

• Time complexity: O(4^mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {number[][]} grid
 * @return {number}
 */
const getMaximumGold = function (grid) {
  const m = grid.length;
  const n = grid[0].length;
  const collectGold = (row, col) => {
    if (row < 0 || col < 0 || row >= m || col >= n) return 0;
    const gold = grid[row][col];

    if (!gold) return 0;
    grid[row][col] = 0;
    const left = collectGold(row, col - 1);
    const right = collectGold(row, col + 1);
    const up = collectGold(row - 1, col);
    const down = collectGold(row + 1, col);

    grid[row][col] = gold;
    return gold + Math.max(left, right, up, down);
  };
  let result = 0;

  for (let row = 0; row < m; row++) {
    for (let col = 0; col < n; col++) {
      const gold = grid[row][col];

      if (!gold) continue;
      const total = collectGold(row, col);

      result = Math.max(total, result);
    }
  }
  return result;
};