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 in Array using Iteration



Problem Statement

You are given a sorted array of integers and a target number. Your task is to find the index of the target number using the binary search algorithm, implemented in an iterative way (using loops instead of recursion).

Binary search works only when the array is sorted in ascending order. If the target exists in the array, return its index. Otherwise, return -1.

Examples

Input ArrayTargetOutputDescription
[10, 20, 30, 40, 50]302Target 30 is at index 2
[5, 10, 15, 20, 25]50First element match
[5, 10, 15, 20, 25]254Last element match
[1, 3, 5, 7, 9]6-16 does not exist in the array
[2, 4, 6, 8, 10]11-1Target is greater than all elements
[2, 4, 6, 8, 10]1-1Target is smaller than all elements
[]10-1Empty array, nothing to search
[100]1000Single element match
[100]200-1Single element does not match

Solution

Binary search is a fast and efficient way to find a target element in a sorted array. Instead of scanning every element one-by-one (like linear search), binary search checks the middle of the array and eliminates half of the elements in each step. This makes the algorithm run in O(log n) time complexity.

How It Works

We start with two pointers:

  • low points to the beginning of the array
  • high points to the end of the array

We calculate the mid index using Math.floor((low + high) / 2). Then we compare arr[mid] with the target:

  • If arr[mid] equals the target, we have found the element and return its index.
  • If arr[mid] is less than the target, we ignore the left half by setting low = mid + 1.
  • If arr[mid] is greater than the target, we ignore the right half by setting high = mid - 1.

We repeat this until low becomes greater than high. If we haven’t returned by then, the target is not in the array, and we return -1.

Understanding Different Cases

  • Target in the array: Binary search finds it quickly and returns the index.
  • Target not in the array: The search range shrinks until no possibilities are left, and we return -1.
  • Target smaller than all elements: We never find a valid mid and the loop ends quickly with -1.
  • Target greater than all elements: Similarly, the algorithm eliminates all elements, and returns -1.
  • Empty array: Since there are no elements, the search ends immediately with -1.
  • Single element arrays: Either the element matches the target or it doesn’t—easy to handle.

This iterative version avoids the overhead of recursive calls and is suitable for memory-constrained environments or large input sizes.

Visualization

Algorithm Steps

  1. Given a sorted array arr and a target value.
  2. Initialize two pointers: low = 0 and high = arr.length - 1.
  3. Repeat while low ≤ high:
  4. → Calculate mid = Math.floor((low + high) / 2).
  5. → If arr[mid] == target, return mid (target found).
  6. → If arr[mid] < target, set low = mid + 1.
  7. → Else, set high = mid - 1.
  8. If the loop ends without finding the target, return -1 (not found).

Code

Python
JavaScript
Java
C++
C
def binary_search(arr, target):
    low, high = 0, len(arr) - 1
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

# Sample Input
arr = [1, 3, 5, 7, 9, 11]
target = 7
print("Index:", binary_search(arr, target))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)The target element is found at the middle index on the first comparison.
Average CaseO(log n)The search space is divided in half during each iteration until the target is found or determined to be absent.
Average CaseO(log n)The target is located at the very beginning or end, or is not in the array, requiring the full depth of the binary search process.

Space Complexity

O(1)

Explanation: The algorithm uses constant space. It only maintains a few variables (like low, high, and mid) and does not allocate extra space based on input size.



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