<p>Given a <code>m x n</code> <code>grid</code> filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.</p>

<p><strong>Note:</strong> You can only move either down or right at any point in time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,1],[1,5,1],[4,2,1]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Because the path 1 &rarr; 3 &rarr; 1 &rarr; 1 &rarr; 1 minimizes the sum.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6]]
<strong>Output:</strong> 12
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 200</code></li>
</ul>

class Solution {
public:
    int solve(int row, int col, int sum, int rows, int cols,
              vector<vector<int>>& grid, vector<vector<int>>& visited, vector<vector<int>>& dp) {
        if (row < 0 || row >= rows || col < 0 || col >= cols ||
            visited[row][col] == 1) {
            return 1e9;
        }

        if (row == rows - 1 && col == cols - 1) {
            return grid[row][col];
        }

        if(dp[row][col] != -1) return dp[row][col];


        visited[row][col] = 1;

        int down =
            solve(row + 1, col, sum + grid[row][col], rows, cols, grid, visited, dp);
        int right =
            solve(row, col + 1, sum + grid[row][col], rows, cols, grid, visited, dp);

        visited[row][col] = 0;
        return dp[row][col] = grid[row][col] + min(down, right);
    }
    int minPathSum(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();
        vector<vector<int>> visited(rows + 1, vector<int>(cols + 1, 0));
        vector<vector<int>> dp(rows + 1, vector<int>(cols + 1, -1));
        return solve(0, 0, 0, rows, cols, grid, visited, dp);
    }
};
13500