算法分析與設計——LeetCode Problem.62 Unique Paths

題目鏈接

問題描述

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.

解題思路

顯然這題採用動態規劃方法可以簡單解決，在點[i,j]有遞推式path[i][j] = path[i-1][j] + path[i][j-1]

代碼如下

class Solution {
public:
	int uniquePaths(int m, int n) {
		vector <vector<int>> vec(m, vector<int>(n, 1));
		for (int i = 1; i < m; i++) {
			for (int j = 1; j < n; j++) {
				vec[i][j] = vec[i - 1][j] + vec[i][j - 1];
			}
		}
		return vec[m - 1][n - 1];
	}
};