Description
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.
Solution
DP
灰常基础的动态规划题。
class Solution {
public int uniquePaths(int m, int n) {
if (m < 0 || n < 0) return 0;
int[][] path = new int[m][n];
path[0][0] = 1;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (i > 0) path[i][j] += path[i - 1][j];
if (j > 0) path[i][j] += path[i][j - 1];
}
}
return path[m - 1][n - 1];
}
}
