LeetCode 62. Unique Paths
Posted 皇家大鹏鹏
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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 7 x 3 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
Example 1:
Input: m = 3, n = 2 Output: 3 Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3 Output: 28
解答:
典型的动态规划问题,用一个矩阵来记录方法数量,每个数字表示从起始位置走到该位置有多少种方法。第一行和第一列均初始化为1,每一格数字更新结果为该格子上方和左方格子求和,表示我nums[i][j] = nums[i-1][j] + nums[i][j-1]。应该还有一些优化的方法,暂时先不讨论。
代码:
1 class Solution { 2 public: 3 int uniquePaths(int m, int n) { 4 vector<vector<int>> num(m, vector<int>(n, 1)); 5 for (int i = 1; i < m; i++) 6 for (int j = 1; j < n; j++) 7 num[i][j] = num[i - 1][j] + num[i][j-1]; 8 return num[m - 1][n - 1]; 9 } 10 };
时间复杂度:O(m*n)
空间复杂度:O(m*n)
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