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.
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
题目
给定MxN棋盘，只允许从左上往右下走，每次走一格。共有多少种走法？
思路
Matrix DP（二维DP） 问题
1. 初始化
预处理第一个row： dp[0][j] = 1 因为从左上起点出发，往右走的每一个unique path都是1
预处理第一个col： dp[i][0]= 1 因为从左上起点出发，往下走的每一个unique path 都是1
2. 转移方程
因为要求所有possible unique paths之和
dp[i][j] 要么来自dp[i-1][j] 要么来自dp[i][j-1]
代码
1 class Solution { 2 public int uniquePaths(int m, int n) { 3 int[][]dp = new int[n][m]; // [row][col] 4 5 // 预处理第一个col 6 for(int i= 0; i < n; i++){ 7 dp[i][0] = 1; 8 } 9 //预处理第一个row 10 for(int j=0; i < m; i++){ 11 dp[0][j] = 1; 12 } 13 for(int i= 1; i < n; i++){ 14 for(int j= 1; j < m; j++){ 15 dp[i][j] = dp[i-1][j] + dp[i][j-1]; 16 } 17 } 18 return dp[n-1][m-1]; 19 } 20 }
转载于:https://www.cnblogs.com/liuliu5151/p/10477669.html
