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?

题目大意：给定一个m*n的矩阵，一只机器人想从左上角走到右下角，每次只能向下向右走一格，问有多少种走法。

题目难度：Medium

/**
 * Created by gzdaijie on 16/5/26
 * 动态规划，map[i][j] = map[i - 1][j] + [i][j - 1]
 * 复杂度 O(M * N)
 */
public class Solution {
    public int uniquePaths(int m, int n) {
        if (m < 1 || n < 1) return 0;

        int[][] map = new int[m][n];

        for (int i = 0; i < m; i++) map[i][0] = 1;
        for (int i = 0; i < n; i++) map[0][i] = 1;


        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                map[i][j] = map[i - 1][j] + map[i][j - 1];
            }
        }
        return map[m - 1][n - 1];
    }
}