Short Problem Definition:
Simulate a cannon shooting and heaps of falling cannonballs
Link
Complexity:
expected worst-case time complexity is O(H+M+N)
expected worst-case space complexity is O(H+M)
Execution:
The obvious brute force solution would be to check the minimum index that is high enough to block the shot. This would result in a N*M runtime. Based on observation we can see that the hit location can be precomputed and it changes only with small steps.
- -1 in the hit_location means, that the ball either ricochets or flies above the highest peak
- anything that hits the 0th index also does nothing
Solution:
def solution(A, B):
highest_ball = max(B)
hit_location = [-1] * (highest_ball+1)
ricochet = A[0]
for idx, a in enumerate(A):
lvl = min(a, highest_ball)
while hit_location[lvl] == -1 and lvl > ricochet:
hit_location[lvl] = idx
lvl -= 1
# print hit_location
for ball in B:
hits_at = hit_location[ball]
# print "ball", ball, "hits at", hits_at
if hits_at <= 0:
continue
A[hits_at-1] += 1
hit_location[A[hits_at-1]] = min(hit_location[A[hits_at-1]], hits_at-1)
return A