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

/**
 * @Desc
 * @Author liuyazhou
 * @CreateTime 2018/11/18 17:19
 **/
public class LeetCode_62_UniquePaths {

    public static void main(String[] args) {
        System.out.println(new LeetCode_62_UniquePaths().uniquePaths(7,3));
    }

    /**
     * @param m 列數
     * @param n 行數
     * @return
     */
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[n][m];

        for (int i = 0; i < m; i++) {
            dp[0][i] = 1;
        }

        for (int i = 0; i < n; i++) {
            dp[i][0] = 1;
        }

        for (int i = 1; i < n; i++) {
            for (int j = 1; j < m; j++) {
                dp[i][j] = dp[i][j - 1] + dp[i - 1][j];//該元素值等於上邊與左邊的元素值之和
            }
        }
        return dp[n - 1][m - 1];
    }
}
 

Runtime: 0 ms, faster than 100.00% of Java online submissions for Unique Paths.