Unique Paths
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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.
方法一:相当于求C(m+n,m),可以用递推公式C(x,y) = C(x-1,y-1) + C(x-1,y)
方法二:用动态规划,每次只能向右向下,所以(n,m)处的方法是走到(n-1,m)向右一步或者C(n,m-1)向下一步。
所以F(n,m) = F(n-1,m) + F(n,m-1)。代码如下:
class Solution {public: int uniquePaths(int m, int n) { // Start typing your C/C++ solution below // DO NOT write int main() function int a[100][100]; for(int i = 0;i < n;i++) a[i][0] = 1; for(int j = 0;j < m;j++) a[0][j] = 1; for(int i = 1;i < n;i++) { for(int j = 1;j < m;j++) { a[i][j] = a[i-1][j] + a[i][j-1]; } } return a[n-1][m-1]; }};
8 milli secs
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