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

Input:
[[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]]

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: Sorting

Range queries

Greedy algorithms

Segment trees revisited

Data structures

Starter code: class Solution:
    def reconstructQueue(self, people: List[List[int]]) -> List[List[int]]:
        

Solutions:
class Solution:

	def reconstructQueue(self, people):
		people.sort(key=lambda x: (-x[0], x[1]))
		queue = []
		for p in people:
			queue.insert(p[1], p)
		return queue


class Solution:

	def reconstructQueue(self, people):
		people.sort(key=lambda x: (-x[0], x[1]))
		result = []
		for person in people:
			result.insert(person[1], person)
		return result


class Solution:

	def reconstructQueue(self, people):
		if not people:
			return []
		ordered_line = []
		people = sorted(people, key=lambda x: x[1])
		people = sorted(people, key=lambda x: -x[0])
		for person in people:
			ordered_line.insert(person[1], person)
		return ordered_line