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?

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

Note: m and n will be at most 100.

java

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

python

class Solution:    """    @param: m: positive integer (1 <= m <= 100)    @param: n: positive integer (1 <= n <= 100)    @return: An integer    """    def uniquePaths(self, m, n):        # write your code here        res = [[1] * n] * m        for i in range(1, m):            for j in range(1, n):                res[i][j] = res[i - 1][j] + res[i][j - 1]        return res[m - 1][n - 1]