Usually if you can write a solution using memoization, you can write it in DP since you know the recursive formula. DP usually runs faster than memoization.
In memoization, you just simply store solutions to subproblems in cache, and once you encounter a bigger problem, you check the cahce first.
I guess the only advantage of doing memoization is that it is easier to write. :p
def minimumTotal(self, triangle): d = dict() return min([self.helper(triangle, len(triangle)-1, k, d) for k in range(len(triangle))]) def helper(self, triangle, i, j, d): if (i,j) in d: return d[(i, j)] if i == j == 0: d[(0,0)] = triangle return triangle left = self.helper(triangle, i-1, j-1, d) if i >= 1 and j >= 1 else float('inf') right = self.helper(triangle, i-1, j, d) if i >= 1 and j < len(triangle[i-1]) else float('inf') d[(i,j)] = min(left, right) + triangle[i][j] return d[(i,j)]