leetcode: Unique Paths

最新推荐文章于 2019-04-14 18:52:56 发布

martin_liang

最新推荐文章于 2019-04-14 18:52:56 发布

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分类专栏：算法 C++/C leetcode

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本文介绍了一种使用动态规划方法计算机器人从网格左上角到右下角的不同路径数量的算法。该算法通过填充一个表格来实现，表格中的每个单元格记录了到达该位置的不同路径数目。

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

Note: m and n will be at most 100.

class Solution {
    
    int table[100][100];
    void resetTable()
    {
        for (int i=0; i<100; i++)
        {
            for (int j=0; j<100; j++)
                table[i][j] = 0;            
        }
    }
    
public:
    int uniquePaths(int m, int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        resetTable();
        
        for (int j=0; j<n; j++)
            table[0][j] = 1;
            
        for (int i=0; i<m; i++)
            table[i][0] = 1;
            
        for (int i=1; i<m; i++)
        {
            for (int j=1; j<n; j++)
            {
                table[i][j] = table[i-1][j] + table[i][j-1];
            }
        }
        
        return table[m-1][n-1];
    }
};