##### Short Problem Definition:

Count the minimum number of nails that allow a series of planks to be nailed..

##### Link

NailingPlanks

##### Complexity:

expected worst-case time complexity is O((N+M)*log(M));

expected worst-case space complexity is O(M)

##### Execution:

The solution gets 100/100, but I am skeptical. The runtime is rather O(N * (log(M)+M)) than O((N+M)*log(M)). Maybe it can be proven that the execution of the linear scan will never have to scan all possible positions. I also violate the space complexity by creating a copy of A+B.

##### Solution:

PLANK_START = 0
PLANK_END = 1
NAIL_ARR_IDX = 0
NAIL_HIT_LOCATION = 1
class NoNailFoundException(Exception):
def __init__(self):
pass
def findPosOfNail(nails, plank, previous_max):
nail_idx = -1
result = -1
# logarithmic scan O(log(M))
lower_idx = 0
upper_idx = len(nails) - 1
while lower_idx <= upper_idx:
mid_idx = (lower_idx + upper_idx) // 2
if nails[mid_idx][NAIL_HIT_LOCATION] < plank[PLANK_START]:
lower_idx = mid_idx + 1
elif nails[mid_idx][NAIL_HIT_LOCATION] > plank[PLANK_END]:
upper_idx = mid_idx - 1
else:
upper_idx = mid_idx - 1
result = nails[mid_idx][PLANK_START]
nail_idx = mid_idx
if result == -1:
raise NoNailFoundException
# linear scan O(M)
nail_idx += 1
while nail_idx < len(nails):
if nails[nail_idx][NAIL_HIT_LOCATION] > plank[PLANK_END]:
break
result = min(result, nails[nail_idx][NAIL_ARR_IDX])
if result <= previous_max:
return result
nail_idx += 1
if result == -1:
raise NoNailFoundException
return result
def getNrNailsRequired(planks, nails):
result = 0
for plank in planks:
result = max(result, findPosOfNail(nails, plank, result))
return result+1
def solution(A, B ,C):
planks = zip(A,B)
nails = sorted(enumerate(C), key=lambda var: var[1])
try:
return getNrNailsRequired(planks, nails)
except NoNailFoundException:
return -1

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