﻿ Java - Paths from top-left corner to bottom-right of a grid

# Java: Find possible unique paths from top-left corner to bottom-right corner of a specified grid

## Java Basic: Exercise-136 with Solution

Write a Java program to find possible distinct paths from the top-left corner to the bottom-right corner of a given grid (m x n).

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

Sample Solution:

Java Code:

``````import java.util.*
public class Solution {
/**
* @param n, m: positive integer (1 <= n ,m <= 100)
* @return an integer
*/
public static int unique_Paths(int m, int n) {
if (m <= 0 || n <= 0) {
return 0;
}
int[][] grid = new int[m][n]; // Create a grid to store the number of unique paths

// Nested loops to iterate through the grid
for (int i = m - 1; i >= 0; --i) { // Start from the bottom row and move upwards
for (int j = n - 1; j >= 0; --j) { // Start from the rightmost column and move leftwards
grid[i][j] = get_Paths(grid, i, j); // Calculate the unique paths for the current cell
}
}
return grid; // The top-left corner now contains the total unique paths
}

// Helper function to calculate unique paths for a cell
private static int get_Paths(int[][] grid, int i, int j) {
if (i >= grid.length - 1 || j >= grid.length - 1) {
return 1; // If at the rightmost column or bottom row, there is only one path
}
return grid[i][j + 1] + grid[i + 1][j]; // Sum the unique paths from the right and bottom cells
}

// Main method for testing the unique_Paths function
public static void main(String[] args) {
int m = 3;
int n = 2;
System.out.println("Unique paths from top-left corner to bottom-right corner of the said grid: "+unique_Paths(m, n));
}
}
```
```

Sample Output:

```Unique paths from top-left corner to bottom-right corner of the said grid: 3
```

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