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maximum-total-beauty-of-the-gardens.py
164 lines (145 loc) · 5.03 KB
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maximum-total-beauty-of-the-gardens.py
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# Time: O(nlogn)
# Space: O(1)
import bisect
# sort, prefix sum, greedy, two pointers, improved from solution3
class Solution(object):
def maximumBeauty(self, flowers, newFlowers, target, full, partial):
"""
:type flowers: List[int]
:type newFlowers: int
:type target: int
:type full: int
:type partial: int
:rtype: int
"""
flowers.sort()
n = bisect.bisect_left(flowers, target)
prefix, suffix = 0, sum(flowers[i] for i in xrange(n))
result = left = 0
for right in xrange(n+1):
if right:
suffix -= flowers[right-1]
total = newFlowers-((n-right)*target-suffix)
if total < 0:
continue
while not (left == right or (left and (total+prefix)//left <= flowers[left])):
prefix += flowers[left]
left += 1
mn = min((total+prefix)//left if left else 0, target-1)
result = max(result, mn*partial+(len(flowers)-right)*full)
return result
# Time: O(nlogn)
# Space: O(1)
import bisect
# sort, prefix sum, greedy, two pointers, improved from solution4
class Solution2(object):
def maximumBeauty(self, flowers, newFlowers, target, full, partial):
"""
:type flowers: List[int]
:type newFlowers: int
:type target: int
:type full: int
:type partial: int
:rtype: int
"""
flowers.sort()
n = bisect.bisect_left(flowers, target)
prefix = [0]*(n+1)
for i in xrange(n):
prefix[i+1] = prefix[i]+flowers[i]
result = suffix = 0
left = n
for right in reversed(xrange(n+1)):
if right != n:
suffix += flowers[right]
total = newFlowers-((n-right)*target-suffix)
if total < 0:
continue
left = min(left, right)
while not (left == 0 or (prefix[left]-prefix[left-1])*left-prefix[left] <= total):
left -= 1
mn = min((total+prefix[left])//left if left else 0, target-1)
result = max(result, mn*partial+(len(flowers)-right)*full)
return result
# Time: O(nlogn)
# Space: O(n)
import bisect
# sort, prefix sum, greedy, binary search
class Solution3(object):
def maximumBeauty(self, flowers, newFlowers, target, full, partial):
"""
:type flowers: List[int]
:type newFlowers: int
:type target: int
:type full: int
:type partial: int
:rtype: int
"""
def check(prefix, total, x):
return x and (total+prefix[x])//x <= prefix[x+1]-prefix[x]
def binary_search(prefix, total, left, right):
while left <= right:
mid = left+(right-left)//2
if check(prefix, total, mid):
right = mid-1
else:
left = mid+1
return left
flowers.sort()
n = bisect.bisect_left(flowers, target)
prefix = [0]*(n+1)
for i in xrange(n):
prefix[i+1] = prefix[i]+flowers[i]
suffix = sum(flowers[i] for i in xrange(n))
result = left = 0
for right in xrange(n+1):
if right:
suffix -= flowers[right-1]
total = newFlowers-((n-right)*target-suffix)
if total < 0:
continue
left = binary_search(prefix, total, 0, right-1)
mn = min((total+prefix[left])//left if left else 0, target-1)
result = max(result, mn*partial+(len(flowers)-right)*full)
return result
# Time: O(nlogn)
# Space: O(n)
import bisect
# sort, prefix sum, greedy, binary search
class Solution4(object):
def maximumBeauty(self, flowers, newFlowers, target, full, partial):
"""
:type flowers: List[int]
:type newFlowers: int
:type target: int
:type full: int
:type partial: int
:rtype: int
"""
def check(prefix, total, x):
return (prefix[x]-prefix[x-1])*x-prefix[x] <= total
def binary_search_right(prefix, total, left, right):
while left <= right:
mid = left+(right-left)//2
if not check(prefix, total, mid):
right = mid-1
else:
left = mid+1
return right
flowers.sort()
n = bisect.bisect_left(flowers, target)
prefix = [0]*(n+1)
for i in xrange(n):
prefix[i+1] = prefix[i]+flowers[i]
result = suffix = 0
left = n
for right in reversed(xrange(n+1)):
if right != n:
suffix += flowers[right]
total = newFlowers-((n-right)*target-suffix)
if total < 0:
break
left = binary_search_right(prefix, total, 1, right)
mn = min((total+prefix[left])//left if left else 0, target-1)
result = max(result, mn*partial+(len(flowers)-right)*full)
return result