### Description:

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.

### Solution:

Time Complexity : O(n^2)

Space Complexity: O(n^2)

```
var minPathSum = function(grid) {
// Create table
const dp = new Array(grid.length).fill(0).map(() => Array(grid[0].length).fill(Infinity));
// Add starting value
dp[0][0] = grid[0][0]
// Populate table
for (let i = 0; i < dp.length; i++) {
for(let j = 0; j < dp[0].length; j++) {
// Add current cell total to cells to the right and below if the current cell + grid value of cell right/below is less than that cell's current total
if(i+1 < dp.length) dp[i+1][j] = Math.min(dp[i+1][j], dp[i][j]+grid[i+1][j])
if(j+1 < dp[0].length) dp[i][j+1] = Math.min(dp[i][j+1], dp[i][j]+grid[i][j+1])
}
}
return dp[dp.length-1][dp[0].length-1]
};
```

## Discussion (0)