# [64\. Minimum Path Sum](https://leetcode.com/problems/minimum-path-sum/)

:::spoiler Hint

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid)
    {
        // Update the first column by accumulating values from top to bottom

        // Update the first row by accumulating values from left to right
        
        // Update the rest of the grid by choosing the minimum path sum at each cell
        for ()
        {
            for ()
            {
                // Add the minimum value from the cell above or to the left
            }
        }

        // The bottom-right cell contains the minimum path sum
    }
};

:::

:::spoiler

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid)
    {
        int m = grid.size(), n = grid[0].size();

        for (int i = 1; i < m; ++i)
        {
            grid[i][0] += grid[i - 1][0];
        }

        for (int j = 1; j < n; ++j)
        {
            grid[0][j] += grid[0][j - 1];
        }
        
        for (int i = 1; i < m; ++i)
        {
            for (int j = 1; j < n; ++j)
            {
                grid[i][j] += min(grid[i - 1][j], grid[i][j - 1]);
            }
        }
        return grid[m - 1][n - 1];
    }
};

- T: $O(M \cdot N)$
- S: $O(1)$
:::