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.
r如果用公式的话 就是 C(X+Y 选X)
1 class Solution { 2 public int uniquePaths(int m, int n) { 3 int[][] dp = new int[m][n]; 4 5 for(int i =0;i<m;i++){ 6 for (int j = 0;j < n;j++){ 7 if(i==0&&j==0) 8 dp[i][j]=1; 9 else if(i==0) 10 dp[i][j] = dp[i][j-1]; 11 else if(j==0) 12 dp[i][j] = dp[i-1][j]; 13 else 14 dp[i][j] = dp[i-1][j] + dp[i][j-1]; 15 } 16 } 17 return dp[m-1][n-1]; 18 } 19 }
1 class Solution { 2 public int uniquePaths(int m, int n) { 3 int[][] dp = new int[m][n]; 4 for(int i = 0;i<m;i++) 5 dp[i][0] = 1; 6 for(int i = 0;i<n;i++) 7 dp[0][i] = 1; 8 for(int i =1;i<m;i++) 9 for (int j = 1;j < n;j++) 10 dp[i][j] = dp[i-1][j] + dp[i][j-1]; 11 return dp[m-1][n-1]; 12 } 13 }