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?

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

题目大意

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？

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 < n; i++ {
		for j := 0; j < m; j++ {
			if i == 0 || j == 0 {
				dp[i][j] = 1
				continue
			}
			dp[i][j] = dp[i-1][j] + dp[i][j-1]
		}
	}
	return dp[n-1][m-1]
}

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