62. Unique Paths（矩阵的总路径数）

Posted 2021-02-12 shaer

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.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

题目描述：统计从矩阵左上角到右下角的路径总数，每次只能向右或者向下移动
分析：先举例再总结规律，第一列的路径只能有一条，第一行同理。dp[1][1] 就有两条，上面一条，左边一条。所以得到公式 dp[i][j]=dp[i-1][j]+dp[i][j-1]