# ---
# title: 1219. Path with Maximum Gold
# id: problem1219
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Backtracking
# link: <https://leetcode.com/problems/path-with-maximum-gold/description/>
# hidden: true
# ---
# 
# In a gold mine `grid` of size `m * 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:**
# 
#   * `1 <= grid.length, grid[i].length <= 15`
#   * `0 <= grid[i][j] <= 100`
#   * There are at most **25  **cells containing gold.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
