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/45191653
public 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];
}
}