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

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2

Output: 3

Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3

Output: 28

解法：

此题同样用动态规划法，思路同 Leetcode(63) Unique Paths II。代码如下：

class  {
    public int uniquePaths(int m, int n) {
        int[][] tmp = new int[m][n];
        if(m == 1 || n == 1){
            return 1;
        }
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if(i == 0 && j == 0){
                    tmp[i][j] = 1;
                }
                else if (i == 0 && j > 0) {
                    tmp[i][j] = tmp[i][j - 1];
                }
                else if (j == 0 && i > 0) {
                    tmp[i][j] = tmp[i - 1][j];
                }
                else {
                    tmp[i][j] = tmp[i - 1][j] + tmp[i][j - 1];
                }
            }
        }
        return tmp[m-1][n-1];
    }
}

leetcode(62) unique paths 解法：

解法：

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