[LC] 62. 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?

Solution:

Space: O(M * N)

class Solution {
    public int uniquePaths(int m, int n) {
        int [] paths = new int[m][n];
        for (int i = 0; i < m; i++) {
            paths[i][0] = 1;
        }
        for (int i = 0; i < n; i++) {
            paths[0][i] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
            }
        }
        return paths[m - 1][n - 1];
    }
}

Optimized Space to O(N)

class Solution {
    public int uniquePaths(int m, int n) {
        if (m == 0 || n == 0) {
            return 0;
        }
        if (m == 1 ||n == 1) {
            return 1;
        }
        int [] paths = new int[n];
        Arrays.fill(paths, 1);
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                paths[j] += paths[j - 1];
            }
        }
        return paths[n - 1];
    }
}