Insert Interval into Sorted List in DSA C# - Build from Scratch

Insert Interval into Sorted List

📖 Scenario: You are managing a schedule of booked time slots represented as intervals. Each interval has a start and end time. The schedule is sorted by start times and intervals do not overlap.Now, you receive a new time slot request. You want to insert this new interval into the schedule, merging it with existing intervals if they overlap, so the schedule remains sorted and without overlaps.

🎯 Goal: Build a program that inserts a new interval into a sorted list of non-overlapping intervals and merges any overlapping intervals.

📋 What You'll Learn

Create a list of intervals represented as integer arrays with start and end times.

Create a new interval to insert into the list.

Write logic to insert and merge the new interval correctly.

Print the final list of merged intervals.

💡 Why This Matters

🌍 Real World

Scheduling systems, calendar apps, and booking platforms often need to insert and merge time intervals to avoid conflicts.

💼 Career

Understanding interval insertion and merging is useful for software engineers working on calendar features, resource allocation, and time management tools.

1

Create the initial list of intervals

Create a list of integer arrays called intervals with these exact intervals: [1, 3], [6, 9].

DSA C#

// Your code here

Hint

Use List<int[]> and initialize it with two arrays: new int[] {1, 3} and new int[] {6, 9}.

2

Create the new interval to insert

Create an integer array called newInterval with the exact values [2, 5].

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List intervals = new List { new int[] {1, 3}, new int[] {6, 9} };
        // Your code here
    }
}

Hint

Use int[] newInterval = new int[] {2, 5}; to create the new interval.

3

Insert and merge the new interval

Write code to insert newInterval into intervals and merge overlapping intervals. Use a new list called merged to store the result. Iterate over intervals with foreach (int[] interval in intervals). Merge intervals that overlap with newInterval. Add non-overlapping intervals directly to merged. After the loop, add the last newInterval to merged. Finally, assign intervals = merged.

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List intervals = new List { new int[] {1, 3}, new int[] {6, 9} };
        int[] newInterval = new int[] {2, 5};
        // Insert and merge intervals here
    }
}

Hint

Use the standard interval insertion and merging logic with comparisons of start and end times. Update newInterval when merging.

4

Print the merged intervals

Use a foreach loop with int[] interval in intervals to print each interval in the format [start, end] on its own line using Console.WriteLine.

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List intervals = new List { new int[] {1, 3}, new int[] {6, 9} };
        int[] newInterval = new int[] {2, 5};

        List merged = new List();

        foreach (int[] interval in intervals)
        {
            if (interval[1]  newInterval[1])
            {
                merged.Add(newInterval);
                newInterval = interval;
            }
            else
            {
                newInterval[0] = Math.Min(newInterval[0], interval[0]);
                newInterval[1] = Math.Max(newInterval[1], interval[1]);
            }
        }

        merged.Add(newInterval);
        intervals = merged;

        // Print intervals here
    }
}

Hint

Use Console.WriteLine($"[{interval[0]}, {interval[1]}]"); inside a foreach loop to print each interval.

Practice

1. What is the main goal when inserting a new interval into a sorted list of non-overlapping intervals?

easy

A. To sort the intervals again after insertion without merging

B. To add the new interval at the end without checking overlaps

C. To remove all intervals that come before the new interval

D. To merge overlapping intervals and keep the list sorted without overlaps

Solution

1. Step 1: Understand the problem context

   The list contains sorted, non-overlapping intervals. Inserting a new interval may cause overlaps.

2. Step 2: Identify the required action

   We must merge any overlapping intervals with the new one and keep the list sorted without overlaps.

3. Final Answer:

   To merge overlapping intervals and keep the list sorted without overlaps -> Option D

4. Quick Check:

   Insert and merge intervals = To merge overlapping intervals and keep the list sorted without overlaps [OK]

Hint: Merge overlapping intervals to keep list sorted and non-overlapping [OK]

Common Mistakes:

• Inserting without merging overlaps
• Appending without sorting
• Removing unrelated intervals

2. Which of the following C# code snippets correctly declares a list of intervals as List intervals?

easy

A. var intervals = new List { [1, 3], [6, 9] };

B. var intervals = new List { new int[] {1, 3}, new int[] {6, 9} };

C. List intervals = new List { (1, 3), (6, 9) };

D. List<int> intervals = new List<int> { {1, 3}, {6, 9} };

Solution

1. Step 1: Check correct syntax for List of int arrays

   List requires elements as int arrays, declared with new int[] {start, end}.

2. Step 2: Validate each option

   var intervals = new List { new int[] {1, 3}, new int[] {6, 9} }; uses new int[] correctly; others use invalid syntax like braces or tuples.

3. Final Answer:

   var intervals = new List { new int[] {1, 3}, new int[] {6, 9} }; -> Option B

4. Quick Check:

   List of int arrays syntax = var intervals = new List { new int[] {1, 3}, new int[] {6, 9} }; [OK]

Hint: Use new int[] {start, end} inside List initialization [OK]

Common Mistakes:

• Using curly braces instead of new int[]
• Using tuples instead of arrays
• Incorrect variable type declaration

3. Given the intervals [[1, 3], [6, 9]] and a new interval [2, 5], what is the resulting list after inserting and merging?

medium

A. [[2, 5], [6, 9]]

B. [[1, 3], [2, 5], [6, 9]]

C. [[1, 5], [6, 9]]

D. [[1, 9]]

Solution

1. Step 1: Identify overlapping intervals

   The new interval [2, 5] overlaps with [1, 3] because 2 ≤ 3.

2. Step 2: Merge overlapping intervals

   Merge [1, 3] and [2, 5] into [1, 5]. The interval [6, 9] remains unchanged.

3. Final Answer:

   [[1, 5], [6, 9]] -> Option C

4. Quick Check:

   Merged intervals = [[1, 5], [6, 9]] [OK]

Hint: Merge intervals if new start ≤ existing end [OK]

Common Mistakes:

• Not merging overlapping intervals
• Inserting new interval without merging
• Merging all intervals incorrectly

4. Consider this C# code snippet to insert an interval into a sorted list. What is the bug?

var intervals = new List { new int[] {1, 2}, new int[] {3, 5} };
var newInterval = new int[] {4, 7};

foreach(var interval in intervals) {
    if(interval[1] >= newInterval[0]) {
        interval[1] = Math.Max(interval[1], newInterval[1]);
        break;
    }
}

medium

A. It modifies only the first overlapping interval but misses merging subsequent overlaps

B. It throws a runtime exception due to invalid index access

C. It inserts the new interval at the wrong position

D. It does not check for any overlaps before merging

Solution

1. Step 1: Analyze the loop behavior

   The loop breaks after merging with the first overlapping interval, ignoring others.

2. Step 2: Identify the bug impact

   Intervals after the first overlap are not merged, causing incorrect final intervals.

3. Final Answer:

   It modifies only the first overlapping interval but misses merging subsequent overlaps -> Option A

4. Quick Check:

   Loop breaks early, missing merges = It modifies only the first overlapping interval but misses merging subsequent overlaps [OK]

Hint: Do not break loop early; merge all overlapping intervals [OK]

Common Mistakes:

• Breaking loop too soon
• Not merging all overlaps
• Assuming single overlap only

5. You have intervals [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]] and a new interval [4, 8]. After inserting and merging, what is the final list?

hard

A. [[1, 2], [3, 10], [12, 16]]

B. [[1, 2], [4, 8], [12, 16]]

C. [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]

D. [[1, 2], [3, 8], [12, 16]]

Solution

1. Step 1: Find intervals overlapping with [4, 8]

   Intervals [3, 5], [6, 7], and [8, 10] overlap with [4, 8].

2. Step 2: Merge all overlapping intervals

   Merge [3, 5], [6, 7], [8, 10], and [4, 8] into [3, 10].

3. Step 3: Keep non-overlapping intervals unchanged

   Intervals [1, 2] and [12, 16] remain as is.

4. Final Answer:

   [[1, 2], [3, 10], [12, 16]] -> Option A

5. Quick Check:

   Merged overlapping intervals correctly = [[1, 2], [3, 10], [12, 16]] [OK]

Hint: Merge all intervals overlapping new interval into one [OK]

Common Mistakes:

• Merging only some overlapping intervals
• Not merging intervals that touch at boundaries
• Replacing intervals instead of merging