62. Unique Paths

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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?

采用动态规划。

对于格点(i,j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的

因此path[i][j] = path[i-1][j]+path[i][j-1]

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