标签:style class blog code tar color
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.
思路:同样可以使用动态规划方法解决,f(m,n) = f(m-1, n) + f(m, n-1)
代码一:
class Solution { public: int uniquePaths(int m, int n) { if(m <= 0 || n <= 0) return 0; int result = 0; vector<vector<int>> counts; vector<int> temp; for(int i = 0; i < n; i++) temp.push_back(1); counts.push_back(temp); for(int i = 1; i < m; i++) { temp.clear(); for(int j = 0; j < n; j++) { if(j == 0) temp.push_back(1); else temp.push_back(temp[j - 1] + counts[i - 1][j]); } counts.push_back(temp); } return counts[m - 1][n - 1]; } };
代码二比较巧妙,利用了本题的特殊性,即第一列的所有值都是1,只使用了一个数组即可。
// 动规,滚动数组 // 时间复杂度O(n^2),空间复杂度O(n) class Solution { public: int uniquePaths(int m, int n) { vector<int> f(n, 0); f[0] = 1; for (int i = 0; i < m; i++) { for (int j = 1; j < n; j++) { // 左边的f[j],表示更新后的f[j],与公式中的f[i][j] 对应 // 右边的f[j],表示老的f[j],与公式中的f[i-1][j] 对应 f[j] = f[j - 1] + f[j]; } } return f[n - 1]; } };
【Leetcode】Unique Paths,布布扣,bubuko.com
标签:style class blog code tar color
原文地址:http://blog.csdn.net/lipantechblog/article/details/30478703