Merge Overlapping Intervals in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Merge Overlapping Intervals problem?

To combine all intervals that overlap into a single continuous interval, so that the final list has no overlapping intervals.

beginner

Why do we sort intervals by their start time before merging?

Sorting by start time helps us easily find overlapping intervals by comparing each interval with the previous merged one in order.

intermediate

In merging intervals, what do we do when the current interval overlaps with the last merged interval?

We update the end of the last merged interval to the maximum end between the two overlapping intervals.

intermediate

What is the time complexity of the Merge Overlapping Intervals algorithm?

O(n log n) because sorting the intervals takes O(n log n) time, and merging them takes O(n) time.

beginner

Given intervals [[1,3],[2,6],[8,10],[15,18]], what is the merged output?

The merged intervals are [[1,6],[8,10],[15,18]] because [1,3] and [2,6] overlap and combine into [1,6].

What is the first step in merging overlapping intervals?

A Sort intervals by end time

B Reverse the intervals

C Sort intervals by start time

D Remove duplicates

Sorting intervals by their start time helps to easily find and merge overlapping intervals.

If two intervals [1,4] and [3,5] overlap, what is their merged interval?

A [1,3]

B [1,5]

C [4,5]

D [3,5]

The merged interval covers from the earliest start (1) to the latest end (5).

What do you do if the current interval does NOT overlap with the last merged interval?

A Add the current interval as a new merged interval

B Merge them anyway

C Discard the current interval

D Sort intervals again

If there is no overlap, the current interval is added as a separate interval.

What is the output of merging [[1,2],[3,4],[5,6]]?

A [[1,2],[3,6]]

B [[1,6]]

C [[1,4],[5,6]]

D [[1,2],[3,4],[5,6]]

None of the intervals overlap, so the output is the same as input.

What data structure is commonly used to store the merged intervals during the process?

A List/Array

B Queue

C Stack

D Hash Map

A list or array is used to store merged intervals in order.

Explain step-by-step how to merge overlapping intervals given a list of intervals.

Think about sorting first and then checking overlaps one by one.

Describe why sorting intervals is important before merging them.

Consider how unordered intervals would complicate merging.

Practice

1. What is the main purpose of merging overlapping intervals in a list of intervals?

easy

A. To remove all intervals that have the same start and end points

B. To sort intervals by their start time only

C. To combine intervals that overlap into a single continuous interval

D. To split intervals into smaller parts

Solution

1. Step 1: Understand overlapping intervals

   Overlapping intervals share some common range, so merging combines them into one continuous interval.

2. Step 2: Purpose of merging

   Merging reduces multiple overlapping intervals into fewer intervals without overlaps.

3. Final Answer:

   To combine intervals that overlap into a single continuous interval -> Option C

4. Quick Check:

   Merging = Combining overlaps [OK]

Hint: Merging means joining overlapping intervals into one [OK]

Common Mistakes:

• Thinking merging means sorting only
• Confusing merging with removing duplicates
• Assuming intervals are split instead of combined

2. Which of the following Python code snippets correctly sorts a list of intervals by their start time before merging?

easy

A. intervals.sort(key=lambda x: x[0], reverse=True)

B. intervals.sort(key=lambda x: x[0])

C. sorted(intervals)

D. intervals.sort(key=lambda x: x[1])

Solution

1. Step 1: Identify sorting key for intervals

   We sort intervals by their start time, which is the first element in each interval.

2. Step 2: Check code correctness

   Using intervals.sort(key=lambda x: x[0]) sorts by start time ascending, which is correct.

3. Final Answer:

   intervals.sort(key=lambda x: x[0]) -> Option B

4. Quick Check:

   Sort by start time = key x[0] [OK]

Hint: Sort intervals by first element before merging [OK]

Common Mistakes:

• Sorting by end time instead of start time
• Using sorted(intervals) which returns new list without modifying original
• Sorting in reverse order before merging

3. What is the output of the following Python code?

intervals = [[1,3],[2,6],[8,10],[15,18]]
intervals.sort(key=lambda x: x[0])
merged = []
for interval in intervals:
    if not merged or merged[-1][1] < interval[0]:
        merged.append(interval)
    else:
        merged[-1][1] = max(merged[-1][1], interval[1])
print(merged)

medium

A. [[1, 6], [8, 10], [15, 18]]

B. [[1, 3], [2, 6], [8, 10], [15, 18]]

C. [[1, 6], [2, 6], [8, 10], [15, 18]]

D. [[1, 3], [8, 10], [15, 18]]

Solution

1. Step 1: Sort intervals by start time

   Intervals after sorting: [[1,3],[2,6],[8,10],[15,18]] (already sorted)

2. Step 2: Merge overlapping intervals

   First interval [1,3] added. Next [2,6] overlaps with [1,3], merged to [1,6]. Then [8,10] no overlap, added. Finally [15,18] no overlap, added.

3. Final Answer:

   [[1, 6], [8, 10], [15, 18]] -> Option A

4. Quick Check:

   Merged intervals = [[1,6],[8,10],[15,18]] [OK]

Hint: Merge if current start ≤ last merged end [OK]

Common Mistakes:

• Not updating the end of merged interval
• Appending intervals without merging
• Incorrectly sorting intervals

4. Find the error in the following code that attempts to merge overlapping intervals:

def merge_intervals(intervals):
    intervals.sort()
    merged = []
    for i in range(len(intervals)):
        if not merged or merged[-1][1] < intervals[i][0]:
            merged.append(intervals[i])
        else:
            merged[-1][1] = max(merged[-1][1], intervals[i][1])
    return merged

print(merge_intervals([(1,4),(2,3)]))

medium

A. Not checking if intervals list is empty before sorting

B. Sorting intervals without a key may cause incorrect order

C. Using range(len(intervals)) instead of iterating directly over intervals

D. Modifying merged[-1][1] directly causes an error because tuples are immutable

Solution

1. Step 1: Identify data type of intervals elements

   Intervals are list of tuples like [(1,4),(2,3)], tuples are immutable.

2. Step 2: Trace the merging process

   After sorting, append first tuple (1,4) to merged. Second overlaps, attempt merged[-1][1] = max(4,3) fails: 'tuple' object does not support item assignment.

3. Final Answer:

   Modifying merged[-1][1] directly causes an error because tuples are immutable -> Option D

4. Quick Check:

   Tuples immutable, can't modify [OK]

Hint: Check if intervals are tuples before modifying elements [OK]

Common Mistakes:

• Assuming all intervals are lists when they might be tuples
• Ignoring immutability errors
• Thinking sorting always needs a key

5. Given a list of intervals where some intervals are nested inside others, how would you modify the merge algorithm to handle intervals like [[1,10],[2,5],[6,9],[11,15]] to produce the correct merged output?

hard

A. Sort intervals by start time and merge by extending the end to max of overlapping intervals

B. Sort intervals by end time and merge by extending the start to min of overlapping intervals

C. Remove nested intervals before merging to avoid duplicates

D. Merge only intervals that have exactly the same start or end points

Solution

1. Step 1: Sort intervals by start time

   Sorting ensures intervals are processed in order, e.g. [[1,10],[2,5],[6,9],[11,15]].

2. Step 2: Merge by extending end to max of overlapping intervals

   When intervals overlap or are nested, update the end of merged interval to the maximum end value.

3. Step 3: Result

   Merged intervals become [[1,10],[11,15]] because [2,5] and [6,9] are inside [1,10].

4. Final Answer:

   Sort intervals by start time and merge by extending the end to max of overlapping intervals -> Option A

5. Quick Check:

   Sort + max end merge = correct nested handling [OK]

Hint: Always extend merged end to max overlapping end [OK]

Common Mistakes:

• Sorting by end time instead of start time
• Removing nested intervals instead of merging
• Merging only exact matches, missing nested cases