62. 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 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

问题：给定N x M的矩阵，机器人只能从[0][0]开始，并且只能向右或者向下走，求它到达[m-1][n-1]的走法有多少

思路：算是简单的动态规划的应用把，主要是要明白要到达位置[ i ][ j ]，只能从[ i - 1 ][ j ]或[ i ][ j - 1 ]开始走，那么第一行，第一列的格子的走法就只有1种，值为1，第[ i ][ j ]个格子的走法数量，就是[ i - 1 ][ j ]加上[ i ][ j - 1 ]走法的数量，那么加到最后就是[m-1][n-1]走法的数量了。

class Solution {
    public int uniquePaths(int m, int n) {
        int[][] map = new int[m][n];
        for(int i=0; i<m; i++)
        {
        	map[i][0] = 1;
        }
        for(int j=0; j<n; j++)
        {
        	map[0][j] = 1;        	
        }
        for(int i=1; i<m; i++)
        {
        	for(int j=1; j<n; j++)
        	{
        		map[i][j] = map[i][j-1] + map[i-1][j];
        	}
        }
    	return map[m-1][n-1];
    }
}