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)
class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m][n];
for(int i =0;i<m;i++){
for (int j = 0;j < n;j++){
if(i==0&&j==0)
dp[i][j]=1;
else if(i==0)
dp[i][j] = dp[i][j-1];
else if(j==0)
dp[i][j] = dp[i-1][j];
else
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}
return dp[m-1][n-1];
}
}
class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m][n];
for(int i = 0;i<m;i++)
dp[i][0] = 1;
for(int i = 0;i<n;i++)
dp[0][i] = 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];
}
}