Find Peak Element Using Binary Search in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a peak element in an array?

A peak element is an element that is greater than its neighbors. For the first or last element, only one neighbor is considered.

intermediate

Why is binary search suitable for finding a peak element?

Because if the middle element is not a peak, we can decide which half to search next based on the slope, reducing the search space efficiently.

intermediate

In the binary search for a peak element, if nums[mid] < nums[mid + 1], which side do we search next?

We search the right half because a peak must exist there due to the increasing slope.

beginner

What is the time complexity of finding a peak element using binary search?

O(log n), where n is the number of elements in the array.

intermediate

Can there be multiple peak elements in an array? If yes, does the binary search always find the first peak?

Yes, there can be multiple peaks. The binary search finds any one peak, not necessarily the first.

What condition indicates that nums[mid] is a peak element?

A nums[mid] > nums[mid - 1] and nums[mid] > nums[mid + 1]

B nums[mid] < nums[mid - 1] and nums[mid] < nums[mid + 1]

C nums[mid] == nums[mid + 1]

D nums[mid] < nums[mid - 1]

A peak element is greater than both neighbors.

If nums[mid] < nums[mid + 1], where should the search continue?

A Right half

B Left half

C At mid

D Search ends

The peak lies in the right half because the slope is rising.

What is the minimum number of elements needed to have a peak element?

A 3

B 1

C 2

D 0

A single element is trivially a peak.

What is the worst-case time complexity of the binary search approach to find a peak?

A O(n)

B O(n log n)

C O(log n)

D O(1)

Binary search reduces the search space by half each time.

Does the binary search for peak element require the array to be sorted?

A Only if array length > 10

B Yes

C Only partially sorted

D No

The array does not need to be sorted to find a peak.

Explain how binary search can be used to find a peak element in an unsorted array.

Think about the slope and which side might contain a peak.

Describe the steps and conditions to move left or right in the binary search for a peak element.

Focus on the relationship between mid and mid+1 elements.

Practice

1. What is a peak element in an array when using binary search to find it?

easy

A. The first element of the array

B. An element that is greater than its neighbors

C. The smallest element in the array

D. An element equal to its neighbors

Solution

1. Step 1: Understand the definition of a peak element

   A peak element is one that is strictly greater than its neighbors on both sides (or just one side if at the boundary).

2. Step 2: Relate to binary search goal

   Binary search finds such an element by comparing middle elements with neighbors to decide search direction.

3. Final Answer:

   An element that is greater than its neighbors -> Option B

4. Quick Check:

   Peak element = greater than neighbors [OK]

Hint: Peak element is bigger than neighbors, not smallest [OK]

Common Mistakes:

• Thinking peak is smallest element
• Confusing peak with first or last element always
• Assuming peak equals neighbors

2. Which of the following is the correct Python syntax to start a binary search loop for finding a peak element in array nums?

easy

A. while left <= right:

B. for i in nums:

C. if left < right:

D. while left < right:

Solution

1. Step 1: Identify binary search loop condition

   Binary search typically uses while left < right: to narrow down the search space until left meets right.

2. Step 2: Compare options

   while left <= right: is common in classic binary search but for peak finding, while left < right: is preferred to avoid infinite loops.

3. Final Answer:

   while left < right: -> Option D

4. Quick Check:

   Binary search loop uses < not <= [OK]

Hint: Use while left < right for peak element binary search [OK]

Common Mistakes:

• Using for loop instead of while
• Using <= which may cause infinite loop
• Using if instead of loop

3. What will be the output index of the peak element for the array nums = [1, 3, 20, 4, 1, 0] using binary search peak finding?

medium

A. 2

B. 1

C. 3

D. 0

Solution

1. Step 1: Identify peak candidates

   Check elements: 20 at index 2 is greater than neighbors 3 and 4, so index 2 is a peak.

2. Step 2: Binary search logic

   Binary search will find index 2 by comparing mid elements and moving left or right accordingly.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Peak at index 2 with value 20 [OK]

Hint: Peak is local max, here 20 at index 2 [OK]

Common Mistakes:

• Choosing first or last element incorrectly
• Confusing index with value
• Not checking both neighbors

4. Given this code snippet to find a peak element, what is the error?

def find_peak(nums):
    left, right = 0, len(nums) - 1
    while left <= right:
        mid = (left + right) // 2
        if nums[mid] < nums[mid + 1]:
            left = mid + 1
        else:
            right = mid - 1
    return left

medium

A. Index mid + 1 may cause out of range error

B. Return should be right instead of left

C. Loop condition should be while left < right

D. Mid calculation is incorrect

Solution

1. Step 1: Check index usage in condition

   The code accesses nums[mid + 1] without checking if mid + 1 is within array bounds.

2. Step 2: Identify potential error

   If mid is at the last index, mid + 1 causes an out of range error.

3. Final Answer:

   Index mid + 1 may cause out of range error -> Option A

4. Quick Check:

   Accessing nums[mid + 1] risks out of range [OK]

Hint: Check array bounds before accessing mid+1 [OK]

Common Mistakes:

• Ignoring array boundary checks
• Using <= in loop causing infinite loop
• Returning wrong index

5. You have an array nums = [10, 20, 15, 2, 23, 90, 67]. Using binary search, which index will be returned as a peak element? Consider multiple peaks exist.

hard

A. 1

B. 4

C. 5

D. 6

Solution

1. Step 1: Identify all peak elements

   Peaks are at index 1 (20 > 10 and 15), index 5 (90 > 23 and 67).

2. Step 2: Understand binary search behavior

   Binary search may return any peak, but typically it finds the one in the middle or right side depending on comparisons.

3. Step 3: Trace binary search on given array

   Mid starts near center; since nums[mid] < nums[mid+1] at some point, search moves right, finally returning index 5.

4. Final Answer:

   5 -> Option C

5. Quick Check:

   Binary search finds peak at index 5 with value 90 [OK]

Hint: Binary search may return any peak; here index 5 is found [OK]

Common Mistakes:

• Assuming only first peak is returned
• Ignoring binary search direction logic
• Confusing index with value