LeetCode——Unique Paths，leetcodeunique

LeetCode——Unique Paths，leetcodeunique

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

Note: m and n will be at most 100.

原題連結：https://oj.leetcode.com/problems/unique-paths/

求m*n矩陣的(0,0)到(m,n)有多少種唯一走法，其中每次只能向右或向下走一步。

動態規劃狀態轉移方程：dp[m][n] = dp[m][n-1] + dp[m-1][n]，其中dp[m][n]表示到達座標[m][n]時有多少條唯一的路徑

public class UniquePaths {public int uniquePaths(int m, int n) {if (m == 0 || n == 0)return 1;int dp[][] = new int[m][n];for (int r = 0; r < m; r++)dp[r][0] = 1;for (int c = 0; c < n; c++)dp[0][c] = 1;for (int r = 1; r < m; r++) {for (int c = 1; c < n; c++)dp[r][c] = dp[r - 1][c] + dp[r][c - 1];}return dp[m - 1][n - 1];}}