Insert Interval into Sorted List in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal when inserting an interval into a sorted list of intervals?

To add the new interval into the list so that the list remains sorted and any overlapping intervals are merged into one.

beginner

How do you know if two intervals overlap?

Two intervals overlap if the start of one interval is less than or equal to the end of the other interval, and the start of the other interval is less than or equal to the end of the first interval.

intermediate

Why do we add all intervals that end before the new interval starts without merging?

Because these intervals do not overlap with the new interval and can be kept as they are to maintain order.

intermediate

What is the process to merge overlapping intervals after inserting a new interval?

We update the start of the new interval to the minimum start of overlapping intervals and the end to the maximum end, then skip those intervals in the list.

intermediate

What is the time complexity of inserting an interval into a sorted list of intervals?

O(n), where n is the number of intervals, because we may need to scan through the list once to find the correct position and merge overlaps.

What should you do with intervals that end before the new interval starts?

A Merge them with the new interval

B Ignore them

C Remove them from the list

D Add them directly to the result list

Intervals that end before the new interval starts do not overlap, so they can be added directly to the result.

When merging intervals, how do you update the new interval's boundaries?

A Start = max of starts, End = min of ends

B Start and End remain unchanged

C Start = min of starts, End = max of ends

D Start = average of starts, End = average of ends

To merge overlapping intervals, take the smallest start and largest end among them.

What is the first step when inserting a new interval into a sorted list?

A Add the new interval at the end

B Add all intervals that end before the new interval starts

C Merge all intervals

D Remove overlapping intervals first

We first add all intervals that come before the new interval without overlap.

If the new interval does not overlap with any existing intervals, what happens?

A It is added as a separate interval in the correct position

B It is merged with the last interval

C It replaces all intervals

D It is ignored

If no overlap, the new interval is inserted in order without merging.

What data structure is typically used to represent intervals in this problem?

A Array or list of pairs

B Queue

C Stack

D Linked list

Intervals are usually stored as a list or array of pairs representing start and end.

Explain step-by-step how to insert a new interval into a sorted list of intervals and merge overlaps.

Think about scanning the list once and handling three parts: before, overlapping, after.

Describe how to check if two intervals overlap and how to merge them.

Focus on comparing starts and ends of intervals.

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