Python dynamic programming

Break the problem into smaller ones that repeat, and keep each answer in a table so it is worked out only once.

Decide what one cell of the table means ("the best total using the first i items"), how it follows from earlier cells, and where it starts.

n = 10
ways = [0] * (n + 1)
ways[0] = 1
for i in range(1, n + 1):
    ways[i] = ways[i - 1] + (ways[i - 2] if i >= 2 else 0)
print(ways[n])  # climbing 10 stairs, 1 or 2 at a time

Watch for: Fill the table in an order where every cell it needs is already filled.