Expert · Dynamic programming · 217 of 264
Best stretch
Find the largest sum of a non-empty run of neighbouring numbers (Kadane's algorithm works in one pass).
Input: n, then n whole numbers on one line. Output: the largest sum.
Examples
Input
9 -2 1 -3 4 -1 2 1 -5 4
Output
6
Input
3 -3 -1 -2
Output
-1
Input
1 5
Output
5
One more test checks other inputs when you press Check.
Stuck? The idea behind 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 timeWatch for: Fill the table in an order where every cell it needs is already filled.