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.
public class Solution { /** * This is an implementation of dynamic programming * Using a 2-dimensional array paths to denote the number of paths, we have * paths[i][j] = paths[i-1][j] + paths[i][j-1].<br> * Notice the initial condition paths[i][0] = 1, paths[0][j] = 1.<br> * @param m --integer, the number of rows of a grid * @param n --integer, the number of columns of a grid * @return Integer, the number of paths from top-left corner to bottom-right corner * @author Averill Zheng * @version 2014-06-05 * @since JDK 1.7 */ public int uniquePaths(int m, int n) { int path = 0; if(m > 0 && n > 0){ int[][] paths = new int[m][n]; for(int i = 0; i < m; ++i) paths[i][0] = 1; for(int i = 0; i < n; ++i) paths[0][i] = 1; for(int i = 1; i < m; ++i) for(int j = 1; j < n; ++j) paths[i][j] = paths[i - 1][j] + paths[i][j - 1]; path = paths[m - 1][n - 1]; } return path; } }