Learn and practice the Top K Elements and the Heaps patterns to solve coding interview problems.

Educative-99 in Python: Accelerate Your Coding Interview Prep

This module will teach you the underlying concepts and equip you with the techniques needed to use heaps to efficiently solve a diverse range of problems. In many problems, we need to find the k most/least frequent or k largest/smallest elements in a given set of elements. Such problems, common in data analysis, natural language processing, online algorithms, as well as in recommendation systems, may be solved using the Top K Elements pattern. The fast insertion and deletion operations possible with heaps make them ideal to implement efficient algorithms for such problems. Further, we can use two heaps when we need to simultaneously keep track of the k largest elements in a set, as well as the k smallest elements in the same set. Extending this idea, each heap may be based on a separate dataset. These techniques are used to solve problems categorized under the Heaps pattern.

Heaps



**Constraints:**
- $1 \leq k \leq 10^3$
- $0  \leq$ `nums.length`  $\leq  10^3$
- $-10^3 \leq$ `nums[i]` $\leq 10^3$
- $-10^3 \leq$ `value` $\leq 10^3$
- At most, $10^3$ calls will be made to add.
- It is guaranteed that there will be at least $k$ elements in the array when you search for the $k^{th}$ element.


# Examples


# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

KthLargest (2, [10, 7, 11, 5])

What does the call add(12) return?

KthLargest (2, [10, 7, 11, 5])
What does the call add(12) return?

KthLargest (3, [4, 4, 4])

What does the call add(5) return?

KthLargest (3, [4, 4, 4])
What does the call add(5) return?

KthLargest (4, [1, 2, 3])

What does the call add(10) return?

KthLargest (4, [1, 2, 3])
What does the call add(10) return?

Kth Largest Element in a Stream

Kth Largest Element in a Stream

# Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

# Try it yourself

Implement your solution in the following coding playground:

import heapq

class KthLargest:
    # Constructor to initialize heap and add values in it
    def __init__(self, k, nums):
        pass

    # Adds element in the heap and return the Kth largest
    def add(self, val):

        # Replace this placeholder return statement with your code

        return -1


# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `__init__, add`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Python`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `__init__, add` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `__init__, add`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `__init__, add`. \n- While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `__init__, add`. \n- While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

TwoDArray

import sys
import json

sys.path.append("../ds_v1")
from data_structure import DataStructure

# throw parsing errors for incorrect test case format
def parsingError(element_string, error_message):
    sys.stderr.write(f"Parsing Error: {element_string} {error_message}")
    exit()


# className: MyCustomDS
class TwoDArray(DataStructure):
    def __init__(self):
        # constructor
        pass

    def __str__(self):
        # override print() for your data structure
        pass

    # return value will be passed to user program
    def construct(self, value: str, type_of_arr: int) -> any:
        # parse test case in json string 'value' to your desired data structure
        parse_list = json.loads(value)
        return parse_list

    # input param contains return value of user program
    def traverse(self, input: any, type_of_arr: int) -> str:
        # convert your data structure 'input' to a json string representing a test case output
        return input


def evaluate_results(self) -> object:
        """
        self.__inputs is the list of inputs that are passed as input to function
        self.__actual_output is a list of outputs that is produced by the learner's code
        return : self.__edu__result object
        """

        import heapq


        class KthLargest:
            def __init__(self, k, nums):
                self.k = k
                self.top_k_heap = nums
                heapq.heapify(self.top_k_heap)
                while len(self.top_k_heap) > k:
                    heapq.heappop(self.top_k_heap)

            def add(self, val):
                heapq.heappush(self.top_k_heap, val)
                if len(self.top_k_heap) > self.k:
                    heapq.heappop(self.top_k_heap)

                return self.top_k_heap[0]

            def return_Kth_largest(self):
                return self.top_k_heap[0]
        
        
        def main(input_1, input_2):
            result = []
            kth_largest_element = KthLargest(input_2[0][0], input_2[0][1])
            result.append(None)
            for i in range(1, len(input_1)):
                if input_1[i] == "add":
                    kth_largest_element.add(input_2[i][0])
                    res = kth_largest_element.return_Kth_largest()
                    result.append(res)

            return result 
        

        expected_outputs = [] 
        expected = main(self.__inputs[0],self.__inputs[1])
        actual_output = self.__actual_outputs[0]
        

        if expected == actual_output:
            expected_outputs.append(expected)
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            expected_outputs.append(expected)
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

from Kth_largest import KthLargest

def main(input_1, input_2):
    result = []
    kth_largest_element = KthLargest(input_2[0][0], input_2[0][1])
    result.append(None)
    for i in range(1, len(input_1)):
        if input_1[i] == "add":
            res = kth_largest_element.add(input_2[i][0])
            result.append(res)

    return result

kth largest element in a stream.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : ["KthLargest", "add", "add", "add", "add", "add"]
    - 2 : [[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]]
    output: 
    - 1 : [null, 4, 5, 5, 8, 8]

  - name: "testcase 2"
    inputs:
    - 1 : ["KthLargest", "add", "add", "add", "add", "add", "add", "add"]
    - 2 : [[5, [1, 2, 3, 4, 5, -1, -5, 50, 80]], [-1], [-5], [50], [80], [100], [123], [38]]
    output: 
    - 1 : [null, 3, 3, 4, 5, 50, 50, 50]

  - name: "testcase 3"
    inputs:
    - 1 : ["KthLargest", "add", "add", "add", "add"]
    - 2 : [[3, [-10, 10, -30, 20]], [40], [10], [70], [5]]
    output: 
    - 1 : [null, 10, 10, 20, 20]

  - name: "testcase 4"
    inputs:
    - 1 : ["KthLargest", "add", "add", "add", "add", "add", "add", "add", "add", "add", "add"]
    - 2 : [[8, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]], [-1], [-2], [-3], [-4], [-5], [-6], [-7], [-8], [-9], [-10]]
    output: 
    - 1 : [null, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

  - name: "testcase 5"
    inputs:
    - 1 : ["KthLargest", "add", "add", "add", "add", "add", "add", "add", "add", "add", "add"]
    - 2 : [[6, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]]
    output: 
    - 1 : [null, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 def is_valid_1d_array(arr):
 if not isinstance(arr, list):
 return False

 if any(elem is None or isinstance(elem, bool) for elem in arr):
 return False
 if not all(isinstance(elem, str) for elem in arr):
 return False

 return True


 def is_valid_2d_array(arr):
 for elem in arr:
 if isinstance(elem, list):
 if not is_valid_2d_array(elem):
 return False
 elif not isinstance(elem, int):
 return False
 elif isinstance(elem,bool):
 return False
 return True

 
 # if not isinstance(arr, list) or not all(isinstance(row, list) for row in arr):
 # return False

 # for row in arr[1:]:
 # if any(elem is None or isinstance(elem, bool) for elem in row):
 # return False
 # if not all(isinstance(elem, int) for elem in row):
 # return False

 # kth = arr[:1]

 # if len(kth[0]) != 2:
 # return False

 # for k in kth:
 # if is_valid_1d_array(k[1]):
 # return False
 # return True


 def check_add(operation):
 for i in operation[1:]:
 if i != "add":
 return False
 return True


 def check_array(calls):
 for call in calls:
 if not is_valid_2d_array(call):
 return False
 return True


 def check_k(calls):
 kth = calls[:1]
 if not 1 <= kth[0][0] <= 1000:
 return False

 return True


 def check_k_nums(calls):
 kth = calls[:1]
 if kth[0][0] > len(kth[0][1]):
 return False

 return True


 def check_nums(calls):
 for call in calls:
 if not -1000 <= call <= 1000:
 return False
 return True


 def check_values(calls):
 call = calls[1:]
 for i in call:
 if len(i)<1:
 return False
 if not -1000 <= i[0] <= 1000:
 return False
 return True

 operation = self.__inputs[0]
 calls = self.__inputs[1]

 if not is_valid_1d_array(operation):
 self.store_result ("'operation' should be a valid 1D array of strings in the following format: ['KthLargest','add','add'...]", ValidationFunction.FAIL)
 elif not is_valid_2d_array(calls):
 self.store_result ("'calls' should be a valid 2D array of integers in the following format: [[k,nums],[call],[call]...]", ValidationFunction.FAIL)
 elif not 0 <= len(calls[0][1]) <= 1000:
 self.store_result ("'nums' length should be in the range [0,1000]", ValidationFunction.FAIL) 
 elif operation[0] != "KthLargest":
 self.store_result ("'operation[0]' should have the value: 'KthLargest'", ValidationFunction.FAIL)
 elif not check_add(operation):
 self.store_result ("'operation[1:]' should have this value: 'add'", ValidationFunction.FAIL)
 elif len(operation) != len(calls):
 self.store_result ("'operation' length should be equal to 'calls' length", ValidationFunction.FAIL)
 elif not check_k(calls):
 self.store_result ("'k' should be in the range [1,1000]", ValidationFunction.FAIL)
 elif not check_k_nums(calls):
 self.store_result ("'k' should be smaller than equal to 'nums' length", ValidationFunction.FAIL)
 elif not check_nums(calls[0][1]):
 self.store_result ("'nums[i]' should be in the range [-1000,1000]", ValidationFunction.FAIL)
 elif not check_values(calls):
 self.store_result ("'call' value should not be empty and in the range [-1000,1000]", ValidationFunction.FAIL)
 elif not 1 <= len(calls[1:]) <= 1000:
 self.store_result ("'calls' length should be in the range [1,1000]", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Kth Largest Element in a Stream problem.

Top K Elements

Heaps

Conclusion

Kth Largest Element in a Stream

Statement

Examples

Understand the problem

Figure it out!

Try it yourself