Merge Overlapping Intervals in DSA C - 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 no two intervals overlap in the final list.

beginner

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

Sorting by start time helps us easily find overlapping intervals by checking consecutive intervals only, making the merging process simple and efficient.

intermediate

In merging intervals, what does it mean if the current interval's start is less than or equal to the last merged interval's end?

It means the intervals overlap and should be merged by extending the last merged interval's end to the maximum end of both intervals.

beginner

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

A dynamic array or list is used to store merged intervals as we build the final set of non-overlapping intervals.

beginner

Show the result of merging intervals: [[1,3], [2,6], [8,10], [15,18]]

After merging overlapping intervals, the result is [[1,6], [8,10], [15,18]]. The first two intervals overlap and merge into [1,6].

What is the first step in merging overlapping intervals?

A Sort intervals by end time

B Sort intervals by start time

C Reverse the intervals

D Remove duplicates

Sorting intervals by their start time helps to easily identify overlapping intervals in order.

If interval A is [1,5] and interval B is [4,8], what should the merged interval be?

A [1,8]

B [1,5]

C [4,8]

D [5,8]

Since intervals overlap, merge by taking the minimum start (1) and maximum end (8).

When do you add a new interval to the merged list without merging?

A When intervals have the same start

B When current interval starts before last merged interval ends

C Always merge intervals

D When current interval starts after last merged interval ends

If current interval starts after the last merged interval ends, they do not overlap and can be added separately.

What is the time complexity of merging intervals after sorting?

A O(log n)

B O(n^2)

C O(n log n)

D O(n)

Sorting takes O(n log n), and merging intervals in one pass takes O(n), so total is O(n log n).

Which of these intervals overlap with [3,7]?

A [5,10]

B [1,2]

C [8,12]

D [0,1]

Interval [5,10] overlaps with [3,7] because 5 ≤ 7.

Explain the step-by-step process to merge overlapping intervals.

Think about sorting first and then comparing intervals one by one.

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

Focus on start and end points comparison.

Practice

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

easy

A. Find the maximum number of intervals without overlap

B. Sort intervals by their end times only

C. Combine all intervals that overlap into one continuous interval

D. Count how many intervals are in the list

Solution

1. Step 1: Understand the problem goal

   The problem asks to merge intervals that overlap, so they become one continuous interval without gaps.

2. Step 2: Identify the correct description

   Combine all intervals that overlap into one continuous interval correctly describes merging overlapping intervals into one combined interval.

3. Final Answer:

   Combine all intervals that overlap into one continuous interval -> Option C

4. Quick Check:

   Merge overlapping intervals = Combine overlaps [OK]

Hint: Think of joining overlapping time slots into one [OK]

Common Mistakes:

• Confusing merging with sorting only
• Counting intervals instead of merging
• Ignoring overlaps

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

easy

A. qsort(intervals, n, sizeof(Interval), compareStart);

B. qsort(intervals, n, sizeof(Interval), compareLength);

C. sort(intervals.begin(), intervals.end());

D. qsort(intervals, n, sizeof(Interval), compareEnd);

Solution

1. Step 1: Identify sorting criteria for merging

   Intervals must be sorted by their start time to merge correctly.

2. Step 2: Match sorting function

   qsort(intervals, n, sizeof(Interval), compareStart); uses compareStart which sorts by start time, correct for merging.

3. Final Answer:

   qsort(intervals, n, sizeof(Interval), compareStart); -> Option A

4. Quick Check:

   Sort by start time = qsort with compareStart [OK]

Hint: Sort intervals by start time before merging [OK]

Common Mistakes:

• Sorting by end time instead of start time
• Using C++ sort syntax in C code
• Sorting by interval length

3. What is the output of the merged intervals after running this code on input intervals: [[1,3], [2,6], [8,10], [15,18]]?

Intervals = [[1,3], [2,6], [8,10], [15,18]]
// After sorting by start time
// Merge overlapping intervals
// Print merged intervals

medium

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

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

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

D. [[1,6], [8,15], [18,18]]

Solution

1. Step 1: Sort intervals by start time

   Intervals are already sorted: [1,3], [2,6], [8,10], [15,18].

2. Step 2: Merge overlapping intervals

   [1,3] and [2,6] overlap, merge to [1,6]. Others do not overlap.

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 intervals if current start ≤ previous end [OK]

Common Mistakes:

• Not merging overlapping intervals
• Merging non-overlapping intervals
• Incorrectly merging intervals with gaps

4. Identify the bug in this C code snippet for merging intervals:

Interval merged[100];
int m = 0;
merged[0] = intervals[0];
for (int i = 1; i < n; i++) {
  if (intervals[i].start <= merged[m].end) {
    merged[m].end = intervals[i].end;
  } else {
    m++;
    merged[m] = intervals[i];
  }
}

medium

A. Loop starts from 0 instead of 1

B. It incorrectly updates the end of the previous interval without checking max end

C. Uses <= instead of < in the overlap condition

D. It compares start with start instead of end

Solution

1. Step 1: Analyze interval merging logic

   When intervals overlap, end should be max of both ends, not just assigned.

2. Step 2: Identify incorrect update

   Code sets previous end to current end without max check, causing wrong merges.

3. Final Answer:

   It incorrectly updates the end of the previous interval without checking max end -> Option B

4. Quick Check:

   Use max end when merging intervals [OK]

Hint: Always update end to max of overlapping intervals [OK]

Common Mistakes:

• Assigning end without max check
• Using strict < instead of <= for touching intervals
• Wrong loop start index

5. Given intervals [[1,4], [4,5], [5,6], [7,8]], what is the merged output if intervals that touch at boundaries are considered overlapping?

hard

A. [[1,8]]

B. [[1,4], [4,5], [5,6], [7,8]]

C. [[1,5], [5,6], [7,8]]

D. [[1,6], [7,8]]

Solution

1. Step 1: Understand touching intervals as overlapping

   Intervals that share boundary points merge: [1,4] and [4,5] merge to [1,5], then with [5,6] to [1,6].

2. Step 2: Merge intervals accordingly

   After merging first three intervals, [7,8] remains separate.

3. Final Answer:

   [[1,6], [7,8]] -> Option D

4. Quick Check:

   Touching intervals merge into one [OK]

Hint: Treat intervals with end == start as overlapping [OK]

Common Mistakes:

• Not merging touching intervals
• Merging all intervals incorrectly
• Ignoring boundary overlap condition