Leetcode: Unique Paths

Unique Paths



Similar Problems:


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?

Unique Paths

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

Note: m and n will be at most 100.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.


## Blog link: 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]
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