Leetcode题集——unique-path

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.

动态规划法： 定义一个二维数组 A[m][n]，从左上开始依次计算每一行的值，最后返回 A[m-1][n-1]即可，递推方程是：

A[i][j]=A[i-1][j]+A[i][j-1]；

int uniquePaths(int m, int n) 
    {
      vector > v(m,vector(n,1));
       
        for(int i=1;i

还可以继续优化，用一个长度为 n 的一维数组即可，数组元素初始值都设为1，递推方程为：A[j] += A[j-1]；

也就是从第二行开始更新数组值，每次都存储当前行的值，到最后一行计算完成后，返回 A[n-1]即可。

class Solution {
public:
    int uniquePaths(int m, int n) 
    {
      vector v(n,1);
       
        for(int i=1;i