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

Find Peak Element in Array - Optimal Binary Search Approach



Problem Statement

Given an array of integers, your task is to find the index of any peak element in the array.

A peak element is defined as an element that is not smaller than its neighbors. For the edge elements (first or last), we only compare with their one existing neighbor.

If there are multiple peaks, return the index of any one of them. If the array is empty, return -1.

Examples

Input ArrayPeak IndexPeak ValueDescription
[1, 3, 20, 4, 1]22020 is greater than both 3 and 4, so it's a peak
[10, 20, 15, 2, 23, 90, 67]1 or 520 or 90Both 20 and 90 are peaks; either is valid
[5, 10, 20]220Last element is greater than its left neighbor
[20, 10, 5]020First element is greater than its right neighbor
[10]010Single element is always a peak
[1, 2]12Last element is greater than its only neighbor
[2, 1]02First element is greater than its only neighbor
[]-1-Empty array, no peak exists

Solution

To solve the problem of finding a peak element in an array, we need to understand what a peak means. A peak is simply an element that is not smaller than its neighbors. That means for any index i, arr[i] is a peak if:

  • It is the first element and arr[i] ≥ arr[i+1]
  • It is the last element and arr[i] ≥ arr[i-1]
  • It is in the middle and arr[i] ≥ arr[i-1] and arr[i] ≥ arr[i+1]

So how do we find such an element efficiently? Let's walk through different scenarios:

📍 Case 1: The array has only one element

Any single element is trivially a peak because it has no neighbors to compare with. So, the only element is the peak.

📍 Case 2: The peak is at the beginning or end

If the first element is greater than the second, it's a peak. Similarly, if the last element is greater than the second last, it's also a peak.

📍 Case 3: The peak is somewhere in the middle

We can use a binary search approach. At each step, we look at the middle element arr[mid] and compare it with its neighbors:

  • If arr[mid] is greater than or equal to both neighbors, then it is a peak.
  • If arr[mid] is smaller than its right neighbor, then there must be a peak on the right side (because the values are increasing).
  • If arr[mid] is smaller than its left neighbor, then there must be a peak on the left side (because the values are increasing in that direction).

By following this process, we can efficiently reach a peak without scanning every element. The time complexity is O(log n), which is optimal for this problem.

📍 Case 4: The array is empty

If the array is empty, there are no elements to evaluate, so we return -1 to indicate that no peak exists.

Since the problem only asks for any one peak, and not necessarily the greatest one, we can stop as soon as we find a valid peak index using this logic.

Visualization

Algorithm Steps

  1. Initialize low = 0 and high = n - 1.
  2. While low ≤ high, calculate mid = (low + high) / 2.
  3. Check if arr[mid] is a peak:
    • It is greater than or equal to its neighbors (consider edge conditions).
  4. If it is a peak, return mid.
  5. If arr[mid] < arr[mid + 1], move to right half: low = mid + 1.
  6. Else, move to left half: high = mid - 1.

Code

Java
Python
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
public class PeakElementFinder {
  public static int findPeakElement(int[] arr) {
    int low = 0, high = arr.length - 1;

    while (low <= high) {
      int mid = low + (high - low) / 2;

      boolean leftOK = (mid == 0 || arr[mid] >= arr[mid - 1]);
      boolean rightOK = (mid == arr.length - 1 || arr[mid] >= arr[mid + 1]);

      if (leftOK && rightOK) return mid;
      else if (mid < arr.length - 1 && arr[mid] < arr[mid + 1]) low = mid + 1;
      else high = mid - 1;
    }

    return -1; // Should never reach here if at least one peak exists
  }

  public static void main(String[] args) {
    int[] arr = {1, 3, 20, 4, 1, 0};
    int peakIndex = findPeakElement(arr);
    System.out.println("Peak Index: " + peakIndex + ", Peak Element: " + arr[peakIndex]);
  }
}

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)The middle element is a peak in the first check.
Average CaseO(log n)At each step, the search space is halved, similar to binary search.
Average CaseO(log n)In the worst case, binary search continues until the peak is found at the edge.

Space Complexity

O(1)

Explanation: The algorithm uses constant extra space regardless of input size.



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