062 Unique Paths.py

'''
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(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        dp = [[1 for __ in range(n)] for __ in range(m)]
        for i in range(1, n):
            for j in range(1, m):
                dp[j][i] = dp[j - 1][i] + dp[j][i - 1]
        return dp[m - 1][n - 1]


if __name__ == "__main__":
    assert Solution().uniquePaths(3, 7) == 28