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69 lines
1.8 KiB
Markdown
Executable File
69 lines
1.8 KiB
Markdown
Executable File
# [62. Unique Paths](https://leetcode.com/problems/unique-paths/)
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## 题目
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A robot is located at the top-left corner of a *m* x *n* grid (marked 'Start' in the diagram below).
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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).
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How many possible unique paths are there?
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Above is a 7 x 3 grid. How many possible unique paths are there?
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**Note**: *m* and *n* will be at most 100.
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**Example 1**:
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Input: m = 3, n = 2
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Output: 3
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Explanation:
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From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
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1. Right -> Right -> Down
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2. Right -> Down -> Right
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3. Down -> Right -> Right
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**Example 2**:
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Input: m = 7, n = 3
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Output: 28
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## 题目大意
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一个机器人位于一个 m x n 网格的左上角 （起始点在下图中标记为“Start” ）。机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角（在下图中标记为“Finish”）。问总共有多少条不同的路径？
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## 解题思路
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- 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。
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- 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]`
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## 代码
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```go
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package leetcode
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func uniquePaths(m int, n int) int {
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dp := make([][]int, n)
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for i := 0; i < n; i++ {
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dp[i] = make([]int, m)
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}
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for i := 0; i < m; i++ {
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dp[0][i] = 1
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}
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for i := 0; i < n; i++ {
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dp[i][0] = 1
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}
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for i := 1; i < n; i++ {
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for j := 1; j < m; j++ {
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dp[i][j] = dp[i-1][j] + dp[i][j-1]
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}
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}
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return dp[n-1][m-1]
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}
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``` |