Queue reconstruction by height [Tricky]

Time: O(Nsqrt(N)); Space: O(N); medium*

Suppose you have a random list of people standing in a queue.

Each person is described by a pair of integers (h, k), where h is the height of the person and k is the number of people in front of this person who have a height greater than or equal to h.

Write an algorithm to reconstruct the queue.

Note:

  • The number of people is less than 1,100.

Example 1:

Input: people = [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]

Output: [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]

[4]:

class Solution1(object):
    """
    Time: O(N*sqrt(N))
    Space: O(N)
    """
    def reconstructQueue(self, people):
        """
        :type people: List[List[int]]
        :rtype: List[List[int]]
        """
        people.sort(key = lambda x: (-x[0], x[1]))

        blocks = [[]]
        for p in people:
            index = p[1]

            for i, block in enumerate(blocks):
                if index <= len(block):
                    break
                index -= len(block)

            block.insert(index, p)

            if len(block) * len(block) > len(people):
                blocks.insert(i + 1, block[len(block)//2:])
                del block[len(block)//2:]

        return [p for block in blocks for p in block]

[5]:

s = Solution1()
people = [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]
assert s.reconstructQueue(people) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]

[6]:

class Solution2(object):
    """
    Time: O(N^2)
    Space: O(N)
    """
    def reconstructQueue(self, people):
        """
        :type people: List[List[int]]
        :rtype: List[List[int]]
        """
        people.sort(key = lambda x: (-x[0], x[1]))

        result = []
        for p in people:
            result.insert(p[1], p)

        return result

[7]:

s = Solution2()
people = [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]
assert s.reconstructQueue(people) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]

[8]:

class Solution3(object):
    def reconstructQueue(self, people):
        """
        :type people: List[List[int]]
        :rtype: List[List[int]]
        """
        people = people[:]
        people.sort(key=lambda x: x[1])
        people.sort(key=lambda x: x[0], reverse=True)

        result = []
        for h, k in people:
            result = result[:k] + [[h, k]] + result[k:]

        return result

[9]:

s = Solution3()
people = [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]
assert s.reconstructQueue(people) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]