I designed a dynamic programming algorithm and implemented it with Python to find the smallest sum in a descent from the triangle apex to its base through a sequence of adjacent numbers in an equilateral triangle with n numbers in its base.
In the below example, n is 4 and smallest sum path is shown in circles.
General approach for this kind of problem is to start at the bottom and work your way up. Therefore, i took the bottom row and adding each number to the row.
Sample Execution: For tree : [2] [5, 4] [1, 4, 7] [8, 6, 9, 6]
Smallest sum : 14
or
For tree: [2] [5, 4] [7, 4, 1] [8, 2, 9, 6] [11, 3, 8, 8, 6] Smallest sum : 15
Have fun :)