[LeetCode]Unique Paths
2016-03-18 15:40
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题目描述:
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.
解题思路:
组合数学中的例子,向下m - 1步,向右n - 1步,也就是m + n - 2个数中选择m - 1个数的组合数。
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.
解题思路:
组合数学中的例子,向下m - 1步,向右n - 1步,也就是m + n - 2个数中选择m - 1个数的组合数。
class Solution { public: int uniquePaths(int m, int n) { // 递归超时 // if (n == 1 || m == 1) { // return 1; // } else { // return uniquePaths(m - 1, n) + uniquePaths(m, n - 1); // } // DP vector<vector<int>> matrix(m, vector<int>(n, 1)); for (int i = 1; i< m; ++i) { for (int j = 1; j < n; ++j) { matrix[i][j] = matrix[i - 1][j] + matrix[i][j - 1]; } } return matrix[m - 1][n - 1]; } };
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