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 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

题意：如图地图为m*n，机器人在左上角，星星在右下角。机器人每次只能向下或者向右移动，求机器人移动到星星一共有多少种不同的走法。

分类：数组，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]

主要是边界处理： p[i][0]=1; p[0][j]=0; 因为只有一行或者l一列只有一种走法：

public class Solution {
public int uniquePaths(int m, int n) {
// DP with 2 dimensions array
int[][] a = new int[m]
;
for (int i = 0; i < m; i++) {
a[i][0] = 1;
}
for (int i = 0; i < n; i++) {
a[0][i] = 1;
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
a[i][j] = a[i-1][j] + a[i][j-1];
}
}
return a[m-1][n-1];
}
}