LeetCode62 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? （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];

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