Min Sum Path in Triangle

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


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

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.

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