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?

dummy pic

Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.

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Fairly easy piece of cake. 最短路径 动态规划

class Solution {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        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];
            }
        }
        /*
        for(int i = 0; i<m;i++){
            for(int j = 0;j<n;j++){
                System.out.print(dp[i][j]+", ");
            }
            System.out.println();
        }
        */
        return dp[m-1][n-1];
    }
}