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DSA Visualizations /

Overview of TechniquesOverview of Techniques14
❯

  1. 1Overview of DSA Problem Solving Techniques
  2. 2Brute Force Technique in DSA
  3. 3Greedy Algorithm Technique in DSA
  4. 4Divide and Conquer Technique in DSA
  5. 5Dynamic Programming Technique in DSA
  6. 6Backtracking Technique in DSA
  7. 7Recursion Technique in DSA
  8. 8Sliding Window Technique in DSA
  9. 9Two Pointers Technique
  10. 10Binary Search Technique
  11. 11Tree / Graph Traversal Technique in DSA
  12. 12Bit Manipulation Technique in DSA
  13. 13Hashing Technique
  14. 14Heaps Technique in DSA

SortingSorting10
❯

  1. 1Bubble Sort
  2. 2Selection Sort
  3. 3Insertion Sort
  4. 4Merge Sort
  5. 5Quick Sort
  6. 6Heap Sort
  7. 7Radix Sort
  8. 8Counting Sort
  9. 9Bucket Sort
  10. 10Shell Sort

ArraysArrays32
❯

  1. 1Find Maximum and Minimum in Array using Loop
  2. 2Find Second Largest in Array
  3. 3Find Second Smallest in Array
  4. 4Reverse Array using Two Pointers
  5. 5Check if Array is Sorted
  6. 6Remove Duplicates from Sorted Array
  7. 7Left Rotate an Array by One Place
  8. 8Left Rotate an Array by K Places
  9. 9Move Zeroes in Array to End
  10. 10Linear Search in Array
  11. 11Union of Two Arrays
  12. 12Find Missing Number in Array
  13. 13Max Consecutive Ones in Array
  14. 14Find Kth Smallest Element
  15. 15Longest Subarray with Given Sum (Positives)
  16. 16Longest Subarray with Given Sum (Positives and Negatives)
  17. 17Find Majority Element in Array (more than n/2 times)
  18. 18Find Majority Element in Array (more than n/3 times)
  19. 19Maximum Subarray Sum using Kadane's Algorithm
  20. 20Print Subarray with Maximum Sum
  21. 21Stock Buy and Sell
  22. 22Rearrange Array Alternating Positive and Negative Elements
  23. 23Next Permutation of Array
  24. 24Leaders in an Array
  25. 25Longest Consecutive Sequence in Array
  26. 26Count Subarrays with Given Sum
  27. 27Sort an Array of 0s, 1s, and 2s
  28. 28Two Sum Problem
  29. 29Three Sum Problem
  30. 304 Sum Problem
  31. 31Find Length of Largest Subarray with 0 Sum
  32. 32Find Maximum Product Subarray

Arrays - Binary SearchArrays - Binary Search28
❯

  1. 1Binary Search in Array using Iteration
  2. 2Find Lower Bound in Sorted Array
  3. 3Find Upper Bound in Sorted Array
  4. 4Search Insert Position in Sorted Array (Lower Bound Approach)
  5. 5Floor and Ceil in Sorted Array
  6. 6First Occurrence in a Sorted Array
  7. 7Last Occurrence in a Sorted Array
  8. 8Count Occurrences in Sorted Array
  9. 9Search Element in a Rotated Sorted Array
  10. 10Search in Rotated Sorted Array with Duplicates
  11. 11Minimum in Rotated Sorted Array
  12. 12Find Rotation Count in Sorted Array
  13. 13Search Single Element in Sorted Array
  14. 14Find Peak Element in Array
  15. 15Square Root using Binary Search
  16. 16Nth Root of a Number using Binary Search
  17. 17Koko Eating Bananas
  18. 18Minimum Days to Make M Bouquets
  19. 19Find the Smallest Divisor Given a Threshold
  20. 20Capacity to Ship Packages within D Days
  21. 21Kth Missing Positive Number
  22. 22Aggressive Cows Problem
  23. 23Allocate Minimum Number of Pages
  24. 24Split Array - Minimize Largest Sum
  25. 25Painter's Partition Problem
  26. 26Minimize Maximum Distance Between Gas Stations
  27. 27Median of Two Sorted Arrays of Different Sizes
  28. 28K-th Element of Two Sorted Arrays

StringsStrings18
❯

  1. 1Reverse Words in a String
  2. 2Find the Largest Odd Number in a Numeric String
  3. 3Find Longest Common Prefix in Array of Strings
  4. 4Check If Two Strings Are Isomorphic - Optimal HashMap Solution
  5. 5Check String Rotation using Concatenation - Optimal Approach
  6. 6Check if Two Strings Are Anagrams - Optimal Approach
  7. 7Sort Characters by Frequency - Optimal HashMap and Heap Approach
  8. 8Find Longest Palindromic Substring - Dynamic Programming Approach
  9. 9Find Longest Palindromic Substring Without Dynamic Programming
  10. 10Remove Outermost Parentheses in String
  11. 11Find Maximum Nesting Depth of Parentheses - Optimal Stack-Free Solution
  12. 12Convert Roman Numerals to Integer - Efficient Approach
  13. 13Convert Integer to Roman Numeral - Step-by-Step for Beginners
  14. 14Implement Atoi - Convert String to Integer in Java
  15. 15Count Number of Substrings in a String - Explanation with Formula
  16. 16Edit Distance Problem
  17. 17Calculate Sum of Beauty of All Substrings - Optimal Approach
  18. 18Reverse Each Word in a String - Optimal Approach

MatrixMatrix3
❯

  1. 1Set Matrix Zeroes
  2. 2Rotate Matrix by 90 Degrees Clockwise
  3. 3Print Matrix in Spiral Manner

Matrix - Binary SearchMatrix - Binary Search5
❯

  1. 1Row with Maximum Number of 1's
  2. 2Search in a Sorted 2D Matrix
  3. 3Search in Row and Column-wise Sorted Matrix
  4. 4Find Target in 2D Matrix
  5. 5Matrix Median

Binary TreesBinary Trees36
❯

  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Postorder Traversal of a Binary Tree Using Recursion
  4. 4Postorder Traversal of a Binary Tree using Iteration
  5. 5Level Order Traversal of a Binary Tree using Recursion
  6. 6Level Order Traversal of a Binary Tree using Iteration
  7. 7Reverse Level Order Traversal of a Binary Tree using Iteration
  8. 8Reverse Level Order Traversal of a Binary Tree using Recursion
  9. 9Find Height of a Binary Tree
  10. 10Find Diameter of a Binary Tree
  11. 11Find Mirror of a Binary Tree - Todo
  12. 12Inorder Traversal of a Binary Tree using Recursion
  13. 13Inorder Traversal of a Binary Tree using Iteration
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree

Binary Search TreesBinary Search Trees14
❯

  1. 1Find a Value in a Binary Search Tree
  2. 2Delete a Node in a Binary Search Tree
  3. 3Find the Minimum Value in a Binary Search Tree
  4. 4Find the Maximum Value in a Binary Search Tree
  5. 5Find the Inorder Successor in a Binary Search Tree
  6. 6Find the Inorder Predecessor in a Binary Search Tree
  7. 7Check if a Binary Tree is a Binary Search Tree
  8. 8Find the Lowest Common Ancestor of Two Nodes in a Binary Search Tree
  9. 9Convert a Binary Tree into a Binary Search Tree
  10. 10Balance a Binary Search Tree
  11. 11Merge Two Binary Search Trees
  12. 12Find the kth Largest Element in a Binary Search Tree
  13. 13Find the kth Smallest Element in a Binary Search Tree
  14. 14Flatten a Binary Search Tree into a Sorted List

Find Longest Consecutive Sequence in an Array
Optimal HashSet Solution

Topic Contents

ProblemExamplesSolutionVisualizationAlgorithmCodeTimeSpace

Problem Statement

Given an unsorted array of integers, your task is to find the length of the longest sequence of consecutive numbers that appear in the array.

If the array is empty, return 0.

Examples❯

Input ArrayLongest Consecutive SequenceLengthDescription
[100, 4, 200, 1, 3, 2][1, 2, 3, 4]4Longest consecutive sequence starts at 1 and ends at 4
[0, 3, 7, 2, 5, 8, 4, 6, 0, 1][0, 1, 2, 3, 4, 5, 6, 7, 8]9All elements from 0 to 8 form the longest consecutive sequence
[10, 30, 20][10]1No two numbers are consecutive, so each number alone is a sequence
[1, 9, 3, 10, 2, 20][1, 2, 3]3Consecutive sequence from 1 to 3
[5, 5, 5, 5][5]1All elements are duplicates, so only one unique number exists
[][]0Empty array, no sequence exists

Solution❯

The goal is to find the longest chain of consecutive numbers that appear in the array, even though the array itself might be completely unsorted.

A consecutive sequence means a series of numbers like [3, 4, 5, 6] — where each number is 1 more than the previous one. We are not concerned with the order of elements in the original array, just whether the numbers exist to form a sequence.

Understanding the Problem Through Cases

Case 1: Normal case with random numbers
In an array like [100, 4, 200, 1, 3, 2], even though the numbers are jumbled, there's a consecutive sequence [1, 2, 3, 4]. We return 4, the length of that sequence.

Case 2: All numbers already in order
If the array is like [1, 2, 3, 4, 5], then the whole array forms one big sequence. We return the array’s length.

Case 3: Duplicates in the array
For arrays like [5, 5, 5], duplicates don’t help us. We only care about unique numbers. So, we ignore repeats and count the length of the sequence among distinct values.

Case 4: Disconnected numbers
If the numbers have big gaps between them like [10, 30, 50], then each number is its own sequence. The answer will be 1.

Case 5: Empty array
If no numbers are given, then there’s no sequence. So the answer is simply 0.

How We Efficiently Solve It

We put all numbers into a HashSet to remove duplicates and allow fast lookups. Then for each number, we check whether it could be the start of a new sequence (i.e., num - 1 is not in the set). If it is a valid start, we keep checking num + 1, num + 2, ... to count how long the sequence continues.

This way, we avoid re-checking numbers that are part of earlier sequences and ensure we process each number only once. The result is a very fast and scalable solution that works even for large arrays.

⏱️ Time Complexity

Since we use a set and visit each number once, the time complexity is O(n), where n is the number of elements in the array.

Visualization

Algorithm Steps

  1. Given an unsorted array arr of integers.
  2. Insert all elements into a HashSet for constant-time lookups.
  3. Initialize max_length = 0.
  4. For each element num in arr:
  5. → Check if num - 1 is not in the set (meaning num is the start of a new sequence).
  6. → If so, initialize current_length = 1 and incrementally check for num + 1, num + 2, ... while they exist in the set, incrementing current_length.
  7. → Update max_length with the maximum of max_length and current_length.
  8. Return max_length.

Code

Python
JavaScript
Java
C++
C
def longest_consecutive_sequence(arr):
    num_set = set(arr)
    max_length = 0
    
    for num in arr:
        if num - 1 not in num_set:
            current = num
            length = 1
            while current + 1 in num_set:
                current += 1
                length += 1
            max_length = max(max_length, length)

    return max_length

# Sample Input
arr = [100, 4, 200, 1, 3, 2]
print("Longest Consecutive Sequence Length:", longest_consecutive_sequence(arr))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, each element is checked only once, and very few sequences are formed. The HashSet operations are constant time on average.
Average CaseO(n)Each number is visited once when building the set and at most once again when scanning for sequence starts, resulting in linear time.
Average CaseO(n)Even in the worst case, each element is processed at most twice—once during insertion and once during sequence scanning. So time remains linear.

Space Complexity

O(n)

Explanation: A HashSet is used to store all unique elements of the array for quick lookups, which requires linear space in terms of the input size.

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