LeetCode | Unique Paths
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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).
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?
//二维动态规划问题,参考http://blog.csdn.net/do_smile/article/details/45191653public class Solution { public int uniquePaths(int m, int n) { if(m<=1 || n<=1) return 1; //状态变量,dp[i][j]表示达到点(i,j)的路径数目 int[][] dp = new int[m+1][n+1]; //下标从0开始,m*n维数组 for(int i=0; i<=n; i++) dp[0][i] = 1; for(int i=0; i<=n; i++) //为多维数组的第0、1行,第0、1列均赋值为1 dp[1][i] = 1; for(int i=0; i<=m; i++) dp[i][0] = 1; for(int i=0; i<=m; i++) dp[i][1] = 1; //状态转移方程:要达到某个点,只有两种到达方式,从左侧到达或从上侧到达 //dp[i][j] = dp[i-1][j] + dp[i][j-1] , ( i>=2 && j>=2 ) for(int i=2; i<=m; i++){ for(int j=2; j<=n; j++) dp[i][j] = dp[i-1][j] + dp[i][j-1]; } return dp[m][n]; }}
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