[Leetcode 62, Medium] Unique Paths

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Problem:

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.

Analysis:

Solutions:

C++:

    int uniquePaths(int m, int n) {        if(m == 0 && n == 0)            return 0;                    if(m == 0 || n == 0)            return 1;                    vector<vector<int> > num_of_paths;        for(int row = 0; row < m; ++row) {            vector<int> new_row;            for(int col = 0; col < n; ++col)                new_row.push_back(1);                            num_of_paths.push_back(new_row);        }                for(int i = 1; i < m; ++i) {            for(int j = 1; j < n; ++j) {                num_of_paths[i][j] = num_of_paths[i - 1][j] + num_of_paths[i][j - 1];            }        }                return num_of_paths[m - 1][n - 1];    }

Java:

Python:

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