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?

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]
;
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];
}