```
public int minPathSum(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
int[][] sum = new int[m][n];
for (int[] row : sum)
Arrays.fill(row, grid[0][0]);
for (int i = 1; i < m; i++)
sum[i][0] = sum[i - 1][0] + grid[i][0];
for (int j = 1; j < n; j++)
sum[0][j] = sum[0][j - 1] + grid[0][j];
for (int i = 1; i < m; i++)
for (int j = 1; j < n; j++)
sum[i][j] = Math.min(sum[i][j - 1], sum[i - 1][j]) + grid[i][j];
return sum[m - 1][n - 1];
}
```

## space O(n)

## time O(n)

- 2 pass.
- 1 pass to initialize,
- 1 pass to solve sum.

original post is herehttps://leetcode.com/discuss/38360/10-lines-28ms-o-n-space-dp-solution-in-c-with-explanations