#%RAML 1.0
title: book api
version: v1
baseUri: http://localhost:6061/{version}
protocols:
  - HTTP
  - HTTPS
mediaType: 
- application/json
- application/xml
/book:
  get:
    description: retrives all books.
    responses:
      200:
        body:
            example: |
              []
  post:
    description: adds a product to the database.
    body:
        example: |
          []
    responses:
      201:
        body:
            example: |
              []
  /{bookTitle}:
    get:
      queryParameters:
        author:
          displayName: Author
          type: string
          description: An Author's full name.
          example: yonas
          required: false
        publicationYear:
          displayName: publicationYear
          type: number
          description: The year when the book is released.
          example: 1984
          required: false
        rating:
          displayName: Rating
          type: number
          description: The average rating(1-5) submitted by the user.
          example: 3
          required: false
      responses:
        200:
          body:
            application/json:
              example: |
                []

class Solution:
    def heightChecker(self, heights: List[int]) -> int:
        n = len(heights)
        max_ele = max(heights)
        
        # initialize count array
        count = [0] * (max_ele + 1)
        # store freq of ele in count array
        for h in heights:
            count[h] += 1
        # build the cumulative count sum
        for i in range(1,max_ele + 1):
            count[i] += count[i-1]
        # build the output array
        sortedHeights = [0] * n
        
        for i in range(n - 1,-1,-1):
            position = count[heights[i]] - 1
            sortedHeights[position] = heights[i]
            count[heights[i]] -= 1
        # checking for the correct order
        numOfUnequalIndices = 0
        for i in range(n):
            if heights[i] != sortedHeights[i]:
                numOfUnequalIndices += 1
        return numOfUnequalIndices

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