Find Peak Element Using Binary Search in DSA C# - Build from Scratch

Find Peak Element Using Binary Search

📖 Scenario: Imagine you have a list of numbers representing heights of hills along a trail. You want to find a hill that is taller than its neighbors, called a peak. This helps hikers find the highest point nearby quickly.

🎯 Goal: Build a program that finds a peak element in a list of integers using binary search. The program will efficiently find a hill taller than its neighbors without checking every hill.

📋 What You'll Learn

Create an integer array called heights with specific values

Create two integer variables left and right to mark the search range

Use a while loop with binary search logic to find a peak element index

Print the index of the peak element found

💡 Why This Matters

🌍 Real World

Finding peak elements quickly helps in signal processing, stock market analysis, and terrain mapping where local maximum points are important.

💼 Career

Understanding binary search and peak finding algorithms is useful for software engineers working on performance-critical applications and algorithm design.

1

Create the Heights Array

Create an integer array called heights with these exact values: 1, 3, 20, 4, 1, 0, 5

DSA C#

// Create the heights array with given values
// Your code here

Hint

Use int[] heights = { ... }; to create the array with the exact numbers.

2

Set Search Range Variables

Create two integer variables called left and right. Set left to 0 and right to heights.Length - 1

DSA C#

int[] heights = {1, 3, 20, 4, 1, 0, 5};
// Create left and right variables for binary search
// Your code here

Hint

Use int left = 0; and int right = heights.Length - 1; to set the search range.

3

Implement Binary Search to Find Peak

Use a while loop with the condition left < right. Inside the loop, create an integer mid as the middle index between left and right. If heights[mid] is greater than heights[mid + 1], set right to mid. Otherwise, set left to mid + 1. After the loop ends, left will be the peak index.

DSA C#

int[] heights = {1, 3, 20, 4, 1, 0, 5};
int left = 0;
int right = heights.Length - 1;
// Add binary search loop to find peak index
// Your code here

Hint

Use binary search logic comparing heights[mid] and heights[mid + 1] to move left or right.

4

Print the Peak Element Index

Print the value of left, which is the index of the peak element found.

DSA C#

int[] heights = {1, 3, 20, 4, 1, 0, 5};
int left = 0;
int right = heights.Length - 1;

while (left  heights[mid + 1])
    {
        right = mid;
    }
    else
    {
        left = mid + 1;
    }
}
// Print the peak index
// Your code here

Hint

Use System.Console.WriteLine(left); to print the peak index.

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