61. Unique Paths

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

 

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DP

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public class Solution {
    public int uniquePaths(int m, int n) {
        int x = Math.min(m, n);
        int y = Math.max(m, n);
        int[] ret = new int[x];
    
        for(int i = 0; i < x; i++)
            ret[i] = 1;
    
        for(int i = 1; i < y; i++)
            for(int j = 1; j < x; j++)
            {
                ret[j] += ret[j - 1];
            }
    
        return ret[x - 1];
        
    }
}