Learn and practice the Sliding Window, and Union Find patterns to solve coding interview problems.

Speedrun the Apple Coding Interview: Top Problems in C++

Each pattern in this module exemplifies the power of dissecting a problem in detail and figuring out the least expensive operations required to solve it. In the Sliding Window pattern, we’ll gain practice in various techniques to ensure that a solution that seems to require nested loops actually executes in linear time. Using the Union Find pattern, we’ll learn to solve a diverse set of problems using the disjoint-set data structure.

Elegant by Design

# Statement
Given an unsorted array, `nums`, your task is to return the length of the longest consecutive sequence of elements. The consecutive sequence of elements is such that there are no missing elements in the sequence. The consecutive elements can be present anywhere in the input array.

> **Note:** Two elements, $x$ and $y$, are called **consecutive** if the difference between them is equal to $1$.

**Constraints:**
- $0 \leq$ `nums.lengths` $\leq 10^{3}$
- $-10^{6} \leq$ `nums[i]` $\leq 10^{6}$

# 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 output if the following numbers array is given as input?

nums = $[1, 3, 2]$


What is the output if the following numbers array is given as input?
nums = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1, 3, 2]</annotation></semantics></math>[1,3,2]

What is the output if the following numbers array is given as input?

nums = $[10, 1, 12, 9, 8, 15, 11, 17, 16]$


What is the output if the following numbers array is given as input?
nums = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>10</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>12</mn><mo separator="true">,</mo><mn>9</mn><mo separator="true">,</mo><mn>8</mn><mo separator="true">,</mo><mn>15</mn><mo separator="true">,</mo><mn>11</mn><mo separator="true">,</mo><mn>17</mn><mo separator="true">,</mo><mn>16</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[10, 1, 12, 9, 8, 15, 11, 17, 16]</annotation></semantics></math>[10,1,12,9,8,15,11,17,16]

What is the output if the following numbers array is given as input?

nums = $[99, 2, 100, 1, 101, 4, 102, 3]$


What is the output if the following numbers array is given as input?
nums = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>99</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>100</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>101</mn><mo separator="true">,</mo><mn>4</mn><mo separator="true">,</mo><mn>102</mn><mo separator="true">,</mo><mn>3</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[99, 2, 100, 1, 101, 4, 102, 3]</annotation></semantics></math>[99,2,100,1,101,4,102,3]

What is the output if the following numbers array is given as input?

nums = $[15, 100, 200, 50, 1]$


What is the output if the following numbers array is given as input?
nums = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>15</mn><mo separator="true">,</mo><mn>100</mn><mo separator="true">,</mo><mn>200</mn><mo separator="true">,</mo><mn>50</mn><mo separator="true">,</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[15, 100, 200, 50, 1]</annotation></semantics></math>[15,100,200,50,1]

Longest Consecutive Sequence

Longest Consecutive Sequence

# 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 `main.cpp` in the following coding playground. The supporting code template provided in `UnionFind.cpp` is meant to assist in developing your solution to the problem.

#include <unordered_map>
#include <vector>

class UnionFind {
public:
 std::unordered_map<int, int> parent;
 std::unordered_map<int, int> size;
 int maxLength;

 // Constructor
 UnionFind(std::vector<int>& nums) {
 for (int num : nums) {
 parent[num] = num;
 size[num] = 1;
 }
 maxLength = 1;
 }

 // Function to find the root of a sequence to which num1 belongs
 int Find(int num) {
 if (parent[num] != num) {
 parent[num] = Find(parent[num]);
 }
 return parent[num];
 }

 // Function to merge the two sequences and updating lengths
 void Union(int num1, int num2) {
 int xRoot = Find(num1);
 int yRoot = Find(num2);
 if (xRoot != yRoot) {
 if (size[xRoot] < size[yRoot]) {
 std::swap(xRoot, yRoot);
 }
 parent[yRoot] = xRoot;
 size[xRoot] += size[yRoot];
 maxLength = std::max(maxLength, size[xRoot]);
 }
 }
};

# Helper class for making connected components 
class UnionFind:
 # Constructor
 def __init__(self, nums):
 self.parent = {num: num for num in nums}
 self.size = {num: 1 for num in nums}
 self.max_length = 1

 # Function to find the root of a sequence to which num1 belongs
 def find(self, num):
 if self.parent[num] != num:
 self.parent[num] = self.find(self.parent[num])
 return self.parent[num]

 # Function to merge the two sequences and updating lengths
 def union(self, num1, num2):
 num1_root = self.find(num1)
 num2_root = self.find(num2)
 if num1_root != num2_root:
 if self.size[num1_root] < self.size[num2_root]:
 num1_root, num2_root = num2_root, num1_root
 self.parent[num2_root] = num1_root
 self.size[num1_root] += self.size[num2_root]
 self.max_length = max(self.max_length, self.size[num1_root])

# 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: `LongestConsecutiveSequence`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `C++`\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 `LongestConsecutiveSequence` 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 `LongestConsecutiveSequence`.\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) `LongestConsecutiveSequence`. \n- While calculating time complexity, include the time complexity of built-in C++ 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) `LongestConsecutiveSequence`. \n- While calculating space complexity, include the space complexity of built-in C++ 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
 """
 
 # Union Find class
 class UnionFind:
 # Constructor
 def __init__(self, nums):
 self.parent = {num: num for num in nums}
 self.size = {num: 1 for num in nums}
 self.max_length = 1

 # Function to find the root of a sequence to which num1 belongs
 def find(self, num):
 if self.parent[num] != num:
 self.parent[num] = self.find(self.parent[num])
 return self.parent[num]

 # Function to merge the two sequences and updating lengths
 def union(self, num1, num2):
 x_root = self.find(num1)
 y_root = self.find(num2)
 if x_root != y_root:
 if self.size[x_root] < self.size[y_root]:
 x_root, y_root = y_root, x_root
 self.parent[y_root] = x_root
 self.size[x_root] += self.size[y_root]
 self.max_length = max(self.max_length, self.size[x_root])

 # Solution
 def longest_consecutive_sequence(nums):
 if len(nums) == 0:
 return 0
 ds = UnionFind(nums)

 for num in nums:
 if num + 1 in ds.parent:
 ds.union(num, num + 1)

 return ds.max_length

 # Expected output
 expected = longest_consecutive_sequence(self.__inputs[0])

 # Actual output
 actual = self.__actual_outputs[0]

 # multiple outputs will be added at each index respectively for a single test_case
 expected_outputs = [] 

 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(expected)

 if json.dumps(expected) == json.dumps(actual):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

/*
⬅️ We have provided a UnionFind.cpp file under the "Files" tab 
of this widget. You can use this file to build your solution.
*/
#include "UnionFind.cpp"

int LongestConsecutiveSequence(std::vector<int>& nums) {
 
 // Replace this placeholder return statement with your code

 return 0; 
}

longest-consecutive-sequence.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [19, 34, 76]
    output: 
    - 1 : 1
  - name: "testcase 2"
    inputs:
    - 1: [21, 22, 1, 2, 4, 3]
    output:
    - 1 : 4
  - name: "testcase 3"
    inputs:
    - 1: [99, 2, 100, 3, 5, 4, 1, 101]
    output:
    - 1 : 5
  - name: "testcase 4"
    inputs:
    - 1: [100, 102, 78, 99, 98, 101, 105, 201]
    output:
    - 1 : 5
  - name: "testcase 5"
    inputs:
    - 1: [987, 783, 864, 988, 986]
    output:
    - 1 : 3

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
 """
 nums = self.__inputs[0]

 nums_length_lower_bound = 0
 nums_length_upper_bound = 10**3

 nums_value_lower_bound = -10**6
 nums_value_upper_bound = 10**6

 
 def check_overflow(nums):
 for num in nums:
 if not (-2**31 <= num <= ((2**31) - 1)):
 return num
 return True

 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)

 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 if not is_valid_1d_array(nums):
 self.store_result ("Not a valid test case", ValidationFunction.FAIL)

 elif len(nums) < nums_length_lower_bound or len(nums) > nums_length_upper_bound:
 self.store_result ("expected 'nums' to have " + str(nums_length_lower_bound) + " <= size <= " + str(nums_length_upper_bound) + " but got " + str(len(nums)), ValidationFunction.FAIL)

 elif check_overflow(nums) != True:
 self.store_result (str(check_overflow(nums)) + " is not a valid value of type integer", ValidationFunction.FAIL)

 elif not all (nums_value_lower_bound <= value <= nums_value_upper_bound for value in nums):
 self.store_result("'nums' must consist of values from " + str(nums_value_lower_bound) + " to " + str(nums_value_upper_bound) + " only", ValidationFunction.FAIL)

 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Longest Consecutive Sequence problem.

Sliding Window

Union Find

Conclusion

Longest Consecutive Sequence

Statement

Examples

Understand the problem

Figure it out!

Try it yourself