LeetCode: Unique Paths

## https://code.dennyzhang.com/unique-paths
class Solution(object):
    ## Basic Ideas: Dynamic programming
    ##              For the previous step of finish point, it should come from either up or left
    ##              f(i, j) = f(i-1, j) + f(j, j-1)
    ##
    ## Complexity: Time O(m*n), Space O(m)
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if m == 0 or n == 0: return 0
        dp = [1 for i in range(n)]
        for i in range(1, m):
            for j in range(1, n):
                dp[j] = dp[j-1] + dp[j]
        return dp[-1]

    ## Basic Ideas: Dynamic programming
    ##              For the previous step of finish point, it should come from either up or left
    ##              f(i, j) = f(i-1, j) + f(j, j-1)
    ##
    ## Complexity: Time O(m*n), Space O(m*n)
    def uniquePaths_v1(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if m == 0 or n == 0: return 0
        matrix = [None]*m
        for i in range(m): matrix[i] = [1]*n
        for i in range(1, m):
            for j in range(1, n):
                matrix[i][j] = matrix[i-1][j] + matrix[i][j-1]
        return matrix[-1][-1]