[leetcode]Unique Paths
2014-08-08 22:23
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Unique Paths
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.
算法思路:
典型的二维DP,dp[i][j]表示从左上角(0,0)到(i,j)的paths。状态转移方程:dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
代码如下:
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.
算法思路:
典型的二维DP,dp[i][j]表示从左上角(0,0)到(i,j)的paths。状态转移方程:dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
代码如下:
public class Solution { public int uniquePaths(int m, int n) { if(m == 1 || n == 1) return 1; int[][] dp = new int[m] ; for(int i = 0; i < n; dp[0][i++] = 1); for(int i = 0; i < m; dp[i++][0] = 1); for(int i = 1; i < m; i++){ for(int j = 1; j < n; j++){ dp[i][j] = dp[i - 1][j] + dp[i][j - 1]; } } return dp[m - 1][n - 1]; } }
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