【Leetcode】Unique Paths

题目链接：https://leetcode.com/problems/unique-paths/

题目：

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:

思路：

c[i][j]表示从map[0][0] 不同的路径数，状态转移方程：c[i][j] = c[i-1][j]+c[i][j-1]

算法：

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