Find Peak Element Using Binary Search in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the middle index for binary search.

DSA C#

int mid = low + (high [1] low) / 2;

Drag options to blanks, or click blank then click option'

A*

B/

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' causes incorrect mid calculation.

Using '*' or '/' in place of '-' changes the logic.

The middle index is calculated by subtracting low from high, then dividing by 2, and adding low back.

2fill in blank

medium

Complete the condition to check if mid is a peak element.

DSA C#

if ((mid == 0 || nums[mid] > nums[mid - 1]) && (mid == nums.Length - 1 || nums[mid] > nums[[1]]))

Drag options to blanks, or click blank then click option'

Amid + 1

Bmid - 1

Cmid

Dnums.Length

Attempts:

3 left

💡 Hint

Common Mistakes

Using mid - 1 instead of mid + 1 compares the wrong neighbor.

Using nums.Length as index causes out of range error.

To check if mid is a peak, compare nums[mid] with the next element nums[mid + 1].

3fill in blank

hard

Fix the error in updating the high pointer when the left neighbor is greater.

DSA C#

if (nums[mid] < nums[mid - 1]) {
    high = [1];
} else {
    low = mid + 1;
}

Drag options to blanks, or click blank then click option'

Amid

Bmid - 1

Cmid + 1

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Setting high to mid + 1 searches the wrong side.

Setting high to low causes infinite loop.

If the left neighbor is greater, move high to mid - 1 to search left side.

4fill in blank

hard

Fill both blanks to complete the binary search loop condition and mid calculation.

DSA C#

while (low [1] high) {
    int mid = low + (high [2] low) / 2;

Drag options to blanks, or click blank then click option'

A<=

B<

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<=' causes extra unnecessary iterations.

Using '+' instead of '-' in mid calculation gives wrong index.

The loop runs while low is less than high, and mid is calculated using subtraction.

5fill in blank

hard

Fill in the blank to return the peak element index after the loop.

DSA C#

return [1];

Drag options to blanks, or click blank then click option'

Alow

Bnums.Length - 1

Cmid

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Returning mid may be undefined outside the loop.

Returning nums.Length - 1 is incorrect.

After the loop, low and high converge to the peak index, so return low.

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