0062. Unique Paths

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

Notem 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
``````

## 解题思路 #

• 这是一道简单的 DP 题。输出地图上从左上角走到右下角的走法数。
• 由于机器人只能向右走和向下走，所以地图的第一行和第一列的走法数都是 1，地图中任意一点的走法数是 `dp[i][j] = dp[i-1][j] + dp[i][j-1]`

## 代码 #

``````
package leetcode

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

``````