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LeetCode-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 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

使用dp,时间复杂度O(mn)

public int uniquePaths(int m, int n) {//my dp
        int[][] flag = new int[m][n];      
        for(int i = 0;i<m;i++){
            for(int j = 0;j<n;j++){
                if(i==0||j==0){//第一行第一列设置为1
                    flag[i][j] =1;
                }
                else{
                    flag[i][j] = flag[i-1][j]+flag[i][j-1];
                }
                
            }
        }
        return flag[m-1][n-1];
    }