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maximum-strong-pair-xor-i.py
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maximum-strong-pair-xor-i.py
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# Time: O(nlogn + nlogr) = O(nlogr), r = max(nums)
# Space: O(t)
# bit manipulation, greedy, trie, sort, two pointers
class Solution(object):
def maximumStrongPairXor(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
class Trie(object):
def __init__(self, bit_length):
self.__nodes = []
self.__cnts = []
self.__new_node()
self.__bit_length = bit_length
def __new_node(self):
self.__nodes.append([-1]*2)
self.__cnts.append(0)
return len(self.__nodes)-1
def update(self, num, d):
curr = 0
for i in reversed(xrange(self.__bit_length)):
x = num>>i
if self.__nodes[curr][x&1] == -1:
self.__nodes[curr][x&1] = self.__new_node()
curr = self.__nodes[curr][x&1]
self.__cnts[curr] += d
def query(self, num):
result = curr = 0
for i in reversed(xrange(self.__bit_length)):
result <<= 1
x = num>>i
if self.__nodes[curr][1^(x&1)] != -1 and self.__cnts[self.__nodes[curr][1^(x&1)]]:
curr = self.__nodes[curr][1^(x&1)]
result |= 1
else:
curr = self.__nodes[curr][x&1]
return result
nums.sort()
trie = Trie(nums[-1].bit_length())
result = j = 0
for i, num in enumerate(nums):
trie.update(num, +1)
while not (nums[i] <= 2*nums[j]) :
trie.update(nums[j], -1)
j += 1
result = max(result, trie.query(num))
return result
# Time: O(nlogr), r = max(nums)
# Space: O(t)
# bit manipulation, greedy, trie, dp
class Solution2(object):
def maximumStrongPairXor(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
class Trie(object):
def __init__(self, bit_length):
self.__nodes = []
self.__mins = []
self.__maxs = []
self.__new_node()
self.__bit_length = bit_length
def __new_node(self):
self.__nodes.append([-1]*2)
self.__mins.append(float("inf"))
self.__maxs.append(float("-inf"))
return len(self.__nodes)-1
def insert(self, num):
curr = 0
for i in reversed(xrange(self.__bit_length)):
x = num>>i
if self.__nodes[curr][x&1] == -1:
self.__nodes[curr][x&1] = self.__new_node()
curr = self.__nodes[curr][x&1]
self.__mins[curr] = min(self.__mins[curr], num)
self.__maxs[curr] = max(self.__maxs[curr], num)
def query(self, num):
result = curr = 0
for i in reversed(xrange(self.__bit_length)):
result <<= 1
x = num>>i
y = (result|1)^x
assert(x != y)
if (self.__nodes[curr][y&1] != -1 and
((x > y and num <= 2*self.__maxs[self.__nodes[curr][y&1]]) or
(x < y and self.__mins[self.__nodes[curr][y&1]] <= 2*num))):
result |= 1
curr = self.__nodes[curr][y&1]
else:
curr = self.__nodes[curr][1^(y&1)]
return result
trie = Trie(max(nums).bit_length())
result = 0
for num in nums:
trie.insert(num)
result = max(result, trie.query(num))
return result
# Time: O(nlogr), r = max(nums)
# Space: O(n)
# bit manipulation, greedy, dp
class Solution3(object):
def maximumStrongPairXor(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
result = 0
for i in reversed(xrange(max(nums).bit_length())):
prefix_min, prefix_max = {}, {}
for x in nums:
y = x>>i
if y not in prefix_min:
prefix_min[y] = prefix_max[y] = x
prefix_min[y] = min(prefix_min[y], x)
prefix_max[y] = max(prefix_max[y], x)
result <<= 1
for x in prefix_min.iterkeys():
y = (result|1)^x
assert(x != y)
if y in prefix_max and prefix_min[max(x, y)] <= 2*prefix_max[min(x, y)]:
result |= 1
break
return result
# Time: O(n^2)
# Space: O(1)
# bit manipulation, brute force
class Solution4(object):
def maximumStrongPairXor(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
return max(nums[i]^nums[j] for i in xrange(len(nums)) for j in xrange(i, len(nums)) if abs(nums[i]-nums[j]) <= min(nums[i], nums[j]))