62. Unique Paths

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];
    }
}