Find Peak Element Using Binary Search in DSA C# - 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 base condition to stop the binary search when finding a peak element.

When the search space reduces to one element, that element is a peak and the search stops.

What defines a peak element in an array?

A The last element only

B An element smaller than its neighbors

C The first element only

D An element greater than its neighbors

A peak element is greater than its neighbors.

If the middle element is less than its left neighbor, where should the binary search continue?

A Right half

B Left half

C Either half

D Stop search

Search left half because a peak exists there.

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

A O(n)

B O(n log n)

C O(log n)

D O(1)

Binary search halves the search space each step, so O(log n).

What happens if the middle element is greater than both neighbors?

A It is a peak element

B Search left half

C Search right half

D Continue searching both halves

If middle element is greater than neighbors, it is a peak.

Which of these is NOT true about peak elements?

A A peak element is always the maximum element in the array

B The first or last element can be a peak

C There can be multiple peak elements

D Binary search can find a peak efficiently

A peak element is not necessarily the maximum element overall.

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

Think about how to decide which half to search next based on neighbors.

Describe what a peak element is and why it always exists in any array.

Consider edges and local comparisons.

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 smaller than its neighbors

C. An element that is greater than its neighbors

D. The last element of the array

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 the search direction.

3. Final Answer:

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

4. Quick Check:

   Peak element = greater than neighbors [OK]

Hint: Peak element > neighbors, use binary search to find it fast [OK]

Common Mistakes:

• Confusing peak with minimum element
• Thinking peak must be at array ends
• Assuming peak equals maximum element in array

2. Which of the following is the correct C# syntax to calculate the middle index in binary search to avoid overflow?

easy

A. int mid = (low + high) / 2;

B. int mid = (high - low) / 2 + high;

C. int mid = (low - high) / 2;

D. int mid = low + (high - low) / 2;

Solution

1. Step 1: Understand overflow risk in mid calculation

   Using (low + high) / 2 can overflow if low and high are large integers.

2. Step 2: Use safe calculation to avoid overflow

   Calculate mid as low + (high - low) / 2 to prevent overflow.

3. Final Answer:

   int mid = low + (high - low) / 2; -> Option D

4. Quick Check:

   Safe mid calculation = low + (high - low) / 2 [OK]

Hint: Use low + (high - low) / 2 to avoid overflow [OK]

Common Mistakes:

• Using (low + high) / 2 causing overflow
• Subtracting incorrectly in mid calculation
• Mixing up low and high in formula

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

medium

A. 3

B. 2

C. 1

D. 0

Solution

1. Step 1: Identify peak candidates in the array

   Array: [1, 3, 20, 4, 1, 0]. 20 at index 2 is greater than neighbors 3 and 4.

2. Step 2: Binary search finds peak at index 2

   Binary search compares mid elements and narrows down to index 2 as peak.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Peak element index = 2 [OK]

Hint: Peak is local max; check neighbors to confirm [OK]

Common Mistakes:

• Choosing first or last element incorrectly
• Confusing peak with global max
• Not checking both neighbors

4. Identify the error in this C# binary search code snippet for finding a peak element:

int mid = low + (high - low) / 2;
if (arr[mid] < arr[mid + 1])
    low = mid + 1;
else
    high = mid - 1;

medium

A. It may cause index out of range when mid is at the last element

B. The mid calculation can overflow

C. The condition should be arr[mid] > arr[mid + 1]

D. The else block should set low = mid + 1

Solution

1. Step 1: Check boundary conditions for arr[mid + 1]

   If mid is the last index, arr[mid + 1] causes index out of range error.

2. Step 2: Need to ensure mid + 1 is within array bounds

   Code must check or limit mid to avoid accessing beyond array length.

3. Final Answer:

   It may cause index out of range when mid is at the last element -> Option A

4. Quick Check:

   Check array bounds before accessing mid+1 [OK]

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

Common Mistakes:

• Ignoring array boundary causing runtime errors
• Incorrect mid calculation causing overflow
• Wrong comparison direction in if condition

5. Given a mountain array [0, 2, 4, 7, 5, 3, 1], which modification to the binary search algorithm helps find the peak element efficiently?

hard

A. Compare mid with mid+1 and move low or high accordingly

B. Always move low to mid+1 regardless of comparison

C. Use linear search instead of binary search

D. Compare mid with mid-1 and move high to mid-1 always

Solution

1. Step 1: Understand mountain array property

   Mountain array increases then decreases, so peak is where arr[mid] > arr[mid+1].

2. Step 2: Use binary search comparing mid and mid+1

   If arr[mid] < arr[mid+1], move low to mid+1; else move high to mid to find peak.

3. Final Answer:

   Compare mid with mid+1 and move low or high accordingly -> Option A

4. Quick Check:

   Compare mid and mid+1 to find peak [OK]

Hint: Compare mid and mid+1 to decide search direction [OK]

Common Mistakes:

• Moving pointers incorrectly ignoring array shape
• Using linear search losing binary search efficiency
• Comparing mid with mid-1 incorrectly