Find Peak Element Using Binary Search in DSA Typescript - 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 useful for finding a peak element?

Binary search helps find a peak element in O(log n) time by comparing middle elements with neighbors and deciding which half to search next.

beginner

In the binary search for a peak element, if the middle element is less than its right neighbor, which side do we search next?

We search the right half because a peak must exist there since the right neighbor is greater.

beginner

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

The time complexity is O(log n) because the search space is halved in each step.

beginner

Show the TypeScript function signature for finding a peak element using binary search.

function findPeakElement(nums: number[]): number

What is a peak element in an array?

A An element greater than its neighbors

B The smallest element in the array

C The first element of the array

D An element equal to its neighbors

A peak element is defined as an element greater than its neighbors.

If nums[mid] < nums[mid + 1], which half should we search next to find a peak?

A Right half

B Neither half

C Both halves

D Left half

If the middle element is less than its right neighbor, a peak must exist in the right half.

What is the time complexity of the binary search approach to find a peak element?

A O(n)

B O(log n)

C O(n log n)

D O(1)

Binary search reduces the search space by half each time, resulting in O(log n) time.

Which of these is a valid base case for the peak element search?

A Array length is infinite

B Array length is zero

C Array length is negative

D Array length is one

If the array has one element, that element is the peak by definition.

What does the function findPeakElement return?

A The peak element value

B The number of peak elements

C The index of a peak element

D The sum of peak elements

The function returns the index of any one peak element found.

Explain how binary search is used to find a peak element in an array.

Think about how the array is divided and how the peak is guaranteed in one half.

Describe the conditions that determine if the middle element is a peak or which side to search next.

Focus on comparisons between middle element and its neighbors.

Practice

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

easy

A. An element that is greater than its neighbors

B. The smallest element in the array

C. The first element of 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: Apply this to binary search context

   Binary search finds such an element by comparing mid element with neighbors to decide which half to search next.

3. Final Answer:

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

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 TypeScript syntax to start a binary search loop for finding a peak element in array nums?

easy

A. while(left < right) { ... }

B. if(nums[mid] > nums[mid+1]) { ... }

C. for(let i = 0; i < nums.length; i++)

D. switch(nums[mid]) { ... }

Solution

1. Step 1: Identify the loop type for binary search

   Binary search uses a while loop with condition left < right to narrow down the search range.

2. Step 2: Check options for correct binary search syntax

   while(left < right) { ... } shows the correct while loop structure for binary search.

3. Final Answer:

   while(left < right) { ... } -> Option A

4. Quick Check:

   Binary search uses while loop [OK]

Hint: Binary search uses while(left < right) loop [OK]

Common Mistakes:

• Using for loop instead of while
• Using if instead of loop for search
• Using switch incorrectly for binary search

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

medium

A. 3

B. 1

C. 2

D. 0

Solution

1. Step 1: Identify peak elements in the array

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

2. Step 2: Binary search will find index 2 as peak

   Binary search compares mid with neighbors and narrows to index 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Peak at index 2 = 20 [OK]

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

Common Mistakes:

• Choosing first or last element incorrectly
• Confusing peak with global max always
• Ignoring neighbors in peak definition

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

let left = 0;
let right = nums.length - 1;
while (left < right) {
  let mid = Math.floor((left + right) / 2);
  if (nums[mid] < nums[mid + 1]) {
    left = mid + 1;
  } else {
    right = mid - 1;
  }
}
return left;

medium

A. Return should be right instead of left

B. The loop condition should be while(left <= right)

C. The mid calculation is incorrect

D. The else branch should set right = mid, not mid - 1

Solution

1. Step 1: Analyze the else branch update of right pointer

   Setting right = mid - 1 skips the mid element, possibly missing peak.

2. Step 2: Correct approach is right = mid to keep mid in range

   To ensure peak is not skipped, right should be set to mid, not mid - 1.

3. Final Answer:

   The else branch should set right = mid, not mid - 1 -> Option D

4. Quick Check:

   Keep mid in range by right = mid [OK]

Hint: Use right = mid to avoid skipping mid element [OK]

Common Mistakes:

• Setting right = mid - 1 causing missed peaks
• Changing loop condition unnecessarily
• Miscomputing mid index

5. You have an array nums = [10, 20, 15, 2, 23, 90, 67]. Using binary search to find a peak element, which index could be returned as a valid peak?

hard

A. 2

B. 5

C. 6

D. 3

Solution

1. Step 1: Identify all peak elements in the array

   Peaks are elements greater than neighbors: 20 at index 1 and 90 at index 5.

2. Step 2: Binary search can return any peak; index 5 (value 90) is a valid peak

   90 is greater than 23 and 67, so index 5 is a valid peak.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   90 at index 5 is peak [OK]

Hint: Binary search may return any peak, here index 5 is valid [OK]

Common Mistakes:

• Assuming only one peak exists
• Choosing non-peak elements
• Ignoring neighbors when checking peak