# Java: Find a path from top left to bottom in right direction

## Java Basic: Exercise-133 with Solution

Write a Java program to find a path from top left to bottom in the right direction which minimizes the sum of all numbers along its path.

Note: Move either down or right at any point in time.

**Pictorial Presentation:**

**Sample Solution:**

**Java Code:**

```
import java.util.*
public class Solution {
// Static method to find the minimum path sum in a 2D grid
public static int minPathSum(int[][] grid) {
// Check for invalid or empty input grid
if (grid == null || grid.length == 0 || grid[0] == null || grid[0].length == 0) {
return 0;
}
int m = grid.length; // Number of rows in the grid
int n = grid[0].length; // Number of columns in the grid
int[][] temp = new int[m][n]; // Temporary array to store minimum path sum
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0 && j == 0) {
temp[i][j] = grid[i][j]; // Initialize the starting point
continue;
}
// Calculate the minimum path sum from either the cell above or the cell on the left
int from_up = i == 0 ? Integer.MAX_VALUE : temp[i - 1][j];
int from_left = j == 0 ? Integer.MAX_VALUE : temp[i][j - 1];
temp[i][j] = Math.min(from_up, from_left) + grid[i][j]; // Update the temporary array
}
}
// Return the minimum path sum for the last cell
return temp[m - 1][n - 1];
}
public static void main(String[] args) {
// Example grid
int[][] grid = new int[][] {{7, 4, 2},
{0, 5, 6},
{3, 1, 2}};
System.out.println("Sum of all numbers along its path: " + minPathSum(grid));
}
}
```

Sample Output:

Sum of all numbers along its path: 13

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