Unique Paths

Problem:

A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

How many possible unique paths are there?

Thinking:

This problem is actually an example when we are having the Algorithm course, when introducing DP (Well of course the not the first example because the first example is always Fibonacci Numbers.)

 

 


public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] table= new int[m+1][n+1];
        for (int i = 1; i <= m; i++) {
            table[i][1] = 1;
        }
        
        for (int i = 1; i <= n; i++) {
            table[1][i] = 1;
        }
        
        for (int i = 2; i <= m; i++) {
            for (int j = 2; j <= n; j++) {
                table[i][j] = table[i-1][j] + table[i][j-1];
            }
        }
        
        return table[m][n];
    }
}
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