ProgramGuru

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<br><span class="highlight">Using Iteration</span>
  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

StringsStrings2
❯

  1. 1Remove Outermost Parentheses in String
  2. 2Edit Distance Problem

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

Search in Rotated Sorted Array (with Duplicates)
Optimal Binary Search

Topic Contents

ProblemExamplesSolutionVisualizationCodeTime ComplexitySpace Complexity

Problem Statement

You are given a rotated sorted array that may contain duplicate values, and a target number key. Your task is to determine whether the key exists in the array or not.

The array was originally sorted in ascending order but then rotated at some pivot point. Due to rotation and the presence of duplicates, the structure can be irregular.

Your goal: Return true if the key is found, else return false.

Examples❯

Input ArrayKeyOutputDescription
[2, 5, 6, 0, 0, 1, 2]0trueKey is present after rotation with duplicates
[2, 5, 6, 0, 0, 1, 2]3falseKey not present in the array
[1, 0, 1, 1, 1]0trueKey is present, array has many duplicates
[1, 1, 1, 1, 1]2falseAll values are duplicates, key is not present
[1]1trueSingle-element array with match
[1]0falseSingle-element array without match
[]5falseEmpty array, so key cannot be present

Solution❯

To solve this problem, we need to search for a given number in a rotated sorted array that may include duplicate values. At first glance, the problem seems similar to regular binary search, but rotation and duplicates introduce a few complications.

What Makes This Problem Tricky?

  • Rotation breaks the normal order of sorting at some pivot point.
  • Duplicates make it harder to decide which half of the array is sorted.

How Do We Approach It?

We use a variation of binary search that works even when we encounter duplicates. Here's how we handle different situations:

Case 1: Middle element matches the key

If the middle element is equal to the key, we return true. That’s the best-case scenario.

Case 2: Duplicates at the boundaries

If the elements at the start, mid, and end are all equal, we can’t tell which side is sorted. In this case, we safely move the start pointer forward and end pointer backward to reduce the ambiguity.

Case 3: Left half is sorted

If the left half from start to mid is sorted, we check if the key lies in that range. If it does, we search in the left half; otherwise, we move to the right half.

Case 4: Right half is sorted

If the right half from mid to end is sorted, and if the key lies in that part, we shift our search to the right half. Otherwise, we go left.

What If the Array is Empty?

If the array has no elements, the key can’t be found, so we simply return false.

Final Outcome

Using this strategy ensures we consider all scenarios, including:

  • Rotated sorted arrays
  • Completely sorted arrays
  • Arrays with lots of duplicates
  • Edge cases like empty or single-element arrays

This method still works in logarithmic time in the average case but may degrade to O(n) when many duplicates exist.

Visualization

Algorithm Steps

  1. Start with start = 0 and end = n - 1.
  2. While start ≤ end, compute mid = start + (end - start) / 2.
  3. If arr[mid] == key, return true.
  4. If arr[start] == arr[mid] == arr[end], increment start and decrement end.
  5. Else, check if left half is sorted (i.e., arr[start] ≤ arr[mid]).
  6. → If yes, and arr[start] ≤ key < arr[mid], move end = mid - 1.
  7. → Else, move start = mid + 1.
  8. If right half is sorted (i.e., arr[mid] ≤ arr[end]):
  9. → If arr[mid] < key ≤ arr[end], move start = mid + 1.
  10. → Else, move end = mid - 1.
  11. Repeat until found or range becomes invalid.

Code

Java
Python
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
public class RotatedArraySearchWithDuplicates {
  public static boolean search(int[] arr, int key) {
    int start = 0, end = arr.length - 1;

    while (start <= end) {
      int mid = start + (end - start) / 2;
      if (arr[mid] == key) return true;

      // Handle duplicates: shrink window
      if (arr[start] == arr[mid] && arr[mid] == arr[end]) {
        start++;
        end--;
      }
      // Left half is sorted
      else if (arr[start] <= arr[mid]) {
        if (arr[start] <= key && key < arr[mid]) {
          end = mid - 1;
        } else {
          start = mid + 1;
        }
      }
      // Right half is sorted
      else {
        if (arr[mid] < key && key <= arr[end]) {
          start = mid + 1;
        } else {
          end = mid - 1;
        }
      }
    }
    return false;
  }

  public static void main(String[] args) {
    int[] arr = {2, 5, 6, 0, 0, 1, 2};
    int key = 0;
    System.out.println("Is Key Present: " + search(arr, key));
  }
}

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)Key is found at the middle index in the first check.
Average CaseO(log n)Binary search generally divides the array in half at each step.
Average CaseO(n)When duplicates exist everywhere, we might need to linearly shrink the search range.

Space Complexity

O(1)

Explanation: Only a constant number of pointers are used for binary search, without extra space.

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