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.
这道题属于非常简单的一类dp问题，就不多说了。
class Solution {
public int uniquePaths(int m, int n) {
//state: f[i][j]:the number of unique paths to get to the position matrix[i][j]
int[][] f = new int[m][n];
//initialization:
for (int i = 0; i < m; i++){
f[i][0] = 1;
}
for (int i = 0; i < n; i++){
f[0][i] = 1;
}
//function:
for (int i = 1; i < m; i++){
for (int j = 1; j < n; j++){
f[i][j] = f[i - 1][j] + f[i][j - 1];
}
}
//answer
return f[m - 1][n - 1];
}
}
