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.
题意:
求m*n的矩阵从左上角走到右下角有多少种走法。
思路:
按照数学的方法,结果就是C(m+n-2,m-1)。可以使用组合数进行求解。如果用动态规划,那么边缘的点的路线只有一条,对于其它的点,只能从左边和上边进入。
代码:
class Solution {
public:
int uniquePaths(int m, int n) {
int f[101][101];
f[0][0]=1;
for(int i=0;i<101;i++)
f[0][i]=f[i][0]=1;
for(int i=1;i<m;i++)
for(int j=1;j<n;j++)
f[i][j]=f[i-1][j]+f[i][j-1];
return f[m-1][n-1];
}
};