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? （Medium）
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
分析：
今天时间比较晚了，先写两道比较熟悉的题目吧。
典型的矩阵型动态规划，dp[i][j]定义为到当前节点的...（视题目而定）。
所以本题dp[i][j]表示到当前节点的不同路径数。则第一行全为1，第一列全为1。
后续的 dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
1 class Solution { 2 public: 3 int uniquePaths(int m, int n) { 4 int dp[m][n] = {0}; 5 dp[0][0] = 1; 6 for (int i = 0; i < n; ++i) { 7 dp[0][i] = 1; 8 } 9 for (int i = 0; i < m; ++i) { 10 dp[i][0] = 1; 11 } 12 for (int i = 1; i < m; ++i) { 13 for (int j = 1; j < n; ++j) { 14 dp[i][j] = dp[i - 1][j] + dp[i][j - 1]; 15 } 16 } 17 return dp[m - 1][n - 1]; 18 } 19 };