# 406 Queue Reconstruction by Height

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]]
```

**The Idea:** Sort by h descending and then by k ascending. Then iterate through this new array, and insert by position k. Sorted by height ensures that when we insert by position k, that every iteration is correct all the way through.

For example:

```
start:  [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]

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

for loop:
[[7, 0]]
[[7, 0], [7, 1]]
[[7, 0], [6, 1], [7, 1]]
[[5, 0], [7, 0], [6, 1], [7, 1]]
[[5, 0], [7, 0], [5, 2], [6, 1], [7, 1]]
[[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]

output: [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]
```

**Complexity:** O(nlogn + n) time and O(n) space

```python
class Solution:
    def reconstructQueue(self, people):
        """
        :type people: List[List[int]]
        :rtype: List[List[int]]
        """

        sol = []
        sorted_p = sorted(people, key=lambda x: (-x[0], x[1]))
        for person in sorted_p:
            sol.insert(person[1], person)
        return sol
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/406-queue-reconstruction-by-height.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.