【LeetCode】62. Unique Paths

转载于 2014-12-10 13:17:00 发布 · 66 阅读

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#数据结构与算法

本文介绍了一个经典算法问题——机器人如何从网格左上角到达右下角，仅能向下或向右移动，求解所有唯一路径数量的方法。通过动态规划策略，递推地计算每个网格点的路径数，最终得到目标点的路径总数。

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

采用动态规划。

对于格点(i,j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的

因此path[i][j] = path[i-1][j]+path[i][j-1]

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