# 64. Minimum Path Sum

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

Note: You can only move either down or right at any point in time.

Example:

```Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.```

grid[i][j] = grid[i][j] + min(grid[i - 1][j], grid[i][j - 1]

Runtime: 4 ms, faster than 97.83% of Java online submissions for Minimum Path Sum.

Memory Usage: 40.8 MB, less than 1.47% of Java online submissions for Minimum Path Sum.

```class Solution {
public int minPathSum(int[][] grid) {
int m = grid.length, n = grid[0].length;
for (int i = 1; i < n; i++) {
grid[0][i] += grid[0][i - 1];
}
for (int i = 1; i < m; i++) {
grid[i][0] += grid[i - 1][0];
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]);
}
}

return grid[m - 1][n - 1];
}
}```

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