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.
Solution1:
public int uniquePaths(int m, int n) { int[][] map = new int[n][m]; Arrays.fill(map[0],1); for(int i = 1;i<n;i++){ map[i][0] = 1; for(int j=1;j<m;j++){ map[i][j] = map[i-1][j] + map[i][j-1]; } } return map[n-1][m-1]; }Solution2:
better
public int uniquePaths(int m, int n) { if(m > n){ return uniquePaths(n,m); } int[] a = new int[m]; Arrays.fill(a,1); for(int i = 1;i<n;i++){ for(int j=1;j<m;j++){ a[j] += a[j-1]; } } return a[m-1]; }