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

Recall & Review

beginner

What is the main goal when inserting a new 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 vice versa.

intermediate

Why do we merge intervals when inserting a new interval into a sorted list?

Merging prevents overlapping intervals from appearing separately, keeping the list clean and representing continuous ranges correctly.

intermediate

What is the time complexity of inserting an interval into a sorted list and merging overlaps?

The time complexity is O(n), where n is the number of intervals, because we may need to check and merge intervals sequentially.

beginner

In the context of interval insertion, what does it mean for the list to be sorted?

The intervals are sorted by their start times in ascending order, which helps in efficiently finding where to insert and merge the new interval.

What should you do if the new interval does not overlap with any existing intervals?

A Insert it in the correct position to keep the list sorted

B Merge it with the first interval

C Discard the new interval

D Replace the last interval with the new one

If there is no overlap, the new interval should be inserted in the correct sorted position.

Which condition indicates two intervals [a, b] and [c, d] overlap?

A b < c

B a > d

C a > b

D b >= c and a <= d

Intervals overlap if the end of the first is at least the start of the second and the start of the first is at most the end of the second.

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

A Sort the list again

B Merge all intervals first

C Find the position where the new interval fits based on start time

D Remove all intervals

You first find where the new interval fits to keep the list sorted.

After merging overlapping intervals, what is true about the list?

A It may have overlapping intervals

B It remains sorted and has no overlapping intervals

C It is unsorted

D It contains duplicates

Merging ensures the list stays sorted and free of overlapping intervals.

What data structure is commonly used to represent intervals?

A List of two elements [start, end]

B Single integer

C String

D Boolean

Intervals are usually represented as lists or arrays with two elements: start and end.

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

Think about scanning the list and combining intervals that touch or overlap.

Describe the conditions that determine if two intervals overlap and why merging is necessary.

Focus on the start and end points and what happens if intervals overlap.

Practice

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

easy

A. To add the new interval and merge any overlapping intervals to keep the list sorted and non-overlapping

B. To replace the first interval with the new interval regardless of overlap

C. To insert the new interval at the end without checking for overlaps

D. To delete all intervals that come after the new interval

Solution

1. Step 1: Understand the problem requirement

   The goal is to insert a new interval into a sorted list of intervals without overlaps.

2. Step 2: Merge overlapping intervals after insertion

   After inserting, merge any intervals that overlap to maintain the sorted, non-overlapping property.

3. Final Answer:

   To add the new interval and merge any overlapping intervals to keep the list sorted and non-overlapping -> Option A

4. Quick Check:

   Insert and merge intervals = To add the new interval and merge any overlapping intervals to keep the list sorted and non-overlapping [OK]

Hint: Insert then merge overlapping intervals to keep list sorted [OK]

Common Mistakes:

• Ignoring merging after insertion
• Inserting without maintaining order
• Replacing intervals incorrectly

2. Which of the following Python code snippets correctly inserts a new interval into a sorted list of intervals without merging?

easy

A. intervals.remove(new_interval)

B. intervals.append(new_interval)

C. intervals.sort()

D. intervals.insert(2, new_interval)

Solution

1. Step 1: Identify correct insertion method

   Using insert(index, element) places the new interval at the correct position without losing order.

2. Step 2: Understand other options

   append adds at end without order, sort only sorts but doesn't insert, remove deletes an element.

3. Final Answer:

   intervals.insert(2, new_interval) -> Option D

4. Quick Check:

   Use insert() to add at specific position [OK]

Hint: Use insert(index, value) to place interval correctly [OK]

Common Mistakes:

• Using append without sorting
• Using remove instead of insert
• Relying on sort without insertion

3. What is the output of the following code?

intervals = [[1,3],[6,9]]
new_interval = [2,5]

# Insert new_interval and merge
result = []
i = 0
while i < len(intervals) and intervals[i][1] < new_interval[0]:
    result.append(intervals[i])
    i += 1
while i < len(intervals) and intervals[i][0] <= new_interval[1]:
    new_interval[0] = min(new_interval[0], intervals[i][0])
    new_interval[1] = max(new_interval[1], intervals[i][1])
    i += 1
result.append(new_interval)
while i < len(intervals):
    result.append(intervals[i])
    i += 1
print(result)

medium

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

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

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

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

Solution

1. Step 1: Add intervals before new_interval

   The first while loop checks if intervals[i][1] < new_interval[0]. For i=0, 3 < 2 is false, so no intervals added before. result = [].

2. Step 2: Merge overlapping intervals

   Intervals overlapping with new_interval [2,5] are [1,3] and [2,5] merged to [1,5].

3. Step 3: Add remaining intervals

   Remaining interval [6,9] is added after merged interval.

4. Final Answer:

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

5. Quick Check:

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

Hint: Merge intervals overlapping new_interval boundaries [OK]

Common Mistakes:

• Not merging overlapping intervals
• Appending new_interval without merging
• Incorrect loop conditions

4. The following code tries to insert and merge a new interval but produces incorrect output. What is the bug?

def insert_interval(intervals, new_interval):
    result = []
    for interval in intervals:
        if interval[1] < new_interval[0]:
            result.append(interval)
        elif interval[0] > new_interval[1]:
            result.append(new_interval)
        else:
            new_interval[0] = min(new_interval[0], interval[0])
            new_interval[1] = max(new_interval[1], interval[1])
    result.append(new_interval)
    return result

print(insert_interval([[1,3],[6,9]], [2,5]))

medium

A. Appending new_interval inside loop causes duplicates

B. Not updating new_interval correctly during merge

C. Missing return statement

D. Incorrect comparison operators in conditions

Solution

1. Step 1: Analyze loop behavior

   Appending new_interval inside the loop when interval[0] > new_interval[1] causes multiple appends.

2. Step 2: Understand consequences

   This leads to duplicates and incorrect order in the result list.

3. Final Answer:

   Appending new_interval inside loop causes duplicates -> Option A

4. Quick Check:

   Append new_interval once after loop [OK]

Hint: Append merged interval only once after loop ends [OK]

Common Mistakes:

• Appending inside loop multiple times
• Not merging intervals properly
• Confusing interval boundaries

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

hard

A. [[1,2],[3,5],[6,7],[8,10],[4,8],[12,16]]

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

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

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

Solution

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

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

2. Step 2: Merge overlapping intervals

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

3. Step 3: Combine with non-overlapping intervals

   Keep [1,2] and [12,16] as is, final list is [[1,2],[3,10],[12,16]].

4. Final Answer:

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

5. Quick Check:

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

Hint: Merge all intervals overlapping new interval boundaries [OK]

Common Mistakes:

• Not merging all overlapping intervals
• Appending new interval without merging
• Incorrectly splitting intervals