LeetCode：62. Unique Paths(一个点到另一个点的所有路径)

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

---

方法一:（碰到这种问题，直接解答无法解答，直接利用动态规划）

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

时间复杂度：O(n^2)

空间复杂度：O(n)