62. Unique Paths

62. Unique Paths

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?



Note: m and n will be at most 100.

题目大意

给定一个迷宫的长宽，起点在左上角，终点在右上角，只能向右、向下移动。求从起点到终点的所有可能的路径总数。

解题思路

使用动态规划的思路，每个位置的等于其上方位置和左方位置的路径总数之和。

PS: 需要考虑上边界和所左边界问题。

算法复杂度

O(n2)

代码实现

class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int> > maze(m, vector<int>(n, 1));
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0 && j == 0) { con
4000
tinue; }
if (i > 0 && j > 0) {
maze[i][j] = maze[i-1][j] + maze[i][j-1];
} else if (i > 0) {
maze[i][j] = maze[i-1][j];
} else if (j > 0) {
maze[i][j] = maze[i][j-1];
}
}
}
return maze[m-1][n-1];
}
};