unique-paths.py

# Time:  O(m * n)
# Space: O(m + n)
#
# 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?
# 
# Note: m and n will be at most 100.
#

class Solution:
    # @return an integer
    def uniquePaths(self, m, n):
        if m < n:
            return self.uniquePaths(n, m)
        ways = [1] * n
        
        for i in xrange(1, m):
            for j in xrange(1, n):
                ways[j] += ways[j - 1]
        
        return ways[n - 1]

if __name__ == "__main__":
    print Solution().uniquePaths(1, 2)