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

Speedrun the LinkedIn Coding Interview: Top Problems in Go

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` $\leq$ `nums.length` $\leq 10^3$

* $-10^4 \leq$ `nums[i]` $\leq 10^4$

# 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:


What is the 4th largest element in the following unsorted array?

[5, 12, 9, 0, 6, 7, 1, 8, 4, 9]

What is the 4th largest element in the following unsorted array?
[5, 12, 9, 0, 6, 7, 1, 8, 4, 9]

What is the 6th largest element in the following unsorted array?

[122, 67, 89, 34, 23, 156, 132, 99, 94, 67, 72, 107, 103, 83, 125, 54, 48, 58]

What is the 6th largest element in the following unsorted array?
[122, 67, 89, 34, 23, 156, 132, 99, 94, 67, 72, 107, 103, 83, 125, 54, 48, 58]

What is the 5th largest element in the following unsorted array?

[-8, -11, -7, -9, -12, -10, -20, -33]

What is the 5th largest element in the following unsorted array?
[-8, -11, -7, -9, -12, -10, -20, -33]

What is the 6th largest element in the following unsorted array?

[-2, 8, 0, -5, 7, -1, 3, -3, -4, 1, 4]

What is the 6th largest element in the following unsorted array?
[-2, 8, 0, -5, 7, -1, 3, -3, -4, 1, 4]

Kth Largest Element in an Array

Kth Largest Element in an Array

# 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:

// Template for the min heap

package main

import (
	"container/heap"
)

// MinHeap structure initialization
type MinHeap []int

// newMinHeap function initializes an instance of MinHeap
func newMinHeap() *MinHeap {
	min := &MinHeap{}
	heap.Init(min)
	return min
}

// Len function returns the length of MinHeap
func (h MinHeap) Len() int {
 return len(h)
}

// Empty function returns true if empty, false otherwise
func (h MinHeap) Empty() bool {
 return len(h) == 0
}

// Less function compares two elements of the MinHeap given their indexes
func (h MinHeap) Less(i, j int) bool {
 return h[i] < h[j]
}

// Swap function swaps the values of the elements whose indices are given
func (h MinHeap) Swap(i, j int) {
 h[i], h[j] = h[j], h[i]
}

// Top function returns the element at the top of the MinHeap
func (h MinHeap) Top() int {
 if h.Empty() {
		return 0
	} else {
		return h[0]
	}
}

// Push function pushes an element into the MinHeap
func (h *MinHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}

// Pop function pops the element at the top of the MinHeap
func (h *MinHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

# 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: `findKthLargest`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Go`\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 `findKthLargest` 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 `findKthLargest`.\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) `findKthLargest`. \n- While calculating time complexity, include the time complexity of built-in Go 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) `findKthLargest`. \n- While calculating space complexity, include the space complexity of built-in Go 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.

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 


        def find_kth_largest(nums, k):
            k_numbers_min_heap = []
            for i in range(k):
                k_numbers_min_heap.append(nums[i])
            
            heapq.heapify(k_numbers_min_heap)

            for i in range(k, len(nums)):
                if nums[i] > k_numbers_min_heap[0]:
                    heapq.heappop(k_numbers_min_heap)
                    heapq.heappush(k_numbers_min_heap, nums[i])

            return k_numbers_min_heap[0]


        expected_outputs = [] 
        expected = find_kth_largest(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

package main

func findKthLargest(nums []int, k int) int {
	
	// Replace this placeholder return statement with your code
	return -1
}

kth_largest_element_in_an_array (1).yaml

testcases:
  - name: "testcase 1 - smallest k"
    inputs:
    - 1: [5, 2, 9, -3, 7]
    - 2: 1
    output:
    - 1: 9
  - name: "testcase 2 - largest k"
    inputs:
    - 1: [5, 2, 9, -3, 7]
    - 2: 5
    output:
    - 1: -3
  - name: "testcase 3 - negative values"
    inputs:
    - 1: [10, -5, 0, -8, 4]
    - 2: 3
    output:
    - 1: 0
  - name: "testcase 4 - maximum values"
    inputs:
    - 1: [10000, -10000, 5000, 8000, -9000]
    - 2: 4
    output:
    - 1: -9000
  - name: "testcase 5 - small array"
    inputs:
    - 1: [3, 1, 2]
    - 2: 2
    output:
    - 1: 1

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 # Not a valid 1D array if it's not a list
 
 return all(isinstance(elem, int) and not isinstance(elem, bool) for elem in arr)

 def is_sorted(arr):
 if all(arr[i] < arr[i + 1] for i in range(len(arr) - 1)):
 return False
 if all(arr[i] > arr[i + 1] for i in range(len(arr) - 1)):
 return False

 return True
 

 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 nums = self.__inputs[0]
 k = self.__inputs[1]
 
 if not is_valid_1d_array(nums):
 self.store_result ("'nums' should be a valid 1D array of integers", ValidationFunction.FAIL)
 elif not (1 <= len(nums) <= 1000):
 self.store_result ("'nums' length should be in the range [1,1000]", ValidationFunction.FAIL)
 elif not (1 <= k <= len(nums)):
 self.store_result ("'k' should be in the range [1,"+str(len(nums))+"]", ValidationFunction.FAIL)
 elif not all(-10000 <= num <= 10000 for num in nums):
 self.store_result ("'nums[i]' should be in the range [-10000,10000]", ValidationFunction.FAIL)
 else: 
 self.store_result("", ValidationFunction.PASS)

Try to solve the Kth Largest Element in an Array problem.

Top K Elements

Heaps

Conclusion

Kth Largest Element in an Array

Statement

Examples

Understand the problem

Figure it out!

Try it yourself