Question

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

Solution

class Solution(object):
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        if len(triangle) == 0 or len(triangle[0]) == 0:
            return 0

        numRows = len(triangle)

        prev_row = triangle[0]
        for i in range(1, numRows):
            row = triangle[i]
            for j in range(0, len(row)):
                if j == 0:
                    row[j] += prev_row[j]
                elif j == len(row) - 1:
                    row[j] += prev_row[j - 1]
                else:
                    row[j] += min(prev_row[j], prev_row[j - 1])
            prev_row = row

        return min(prev_row)