Merge Overlapping Intervals in DSA Javascript - 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 in the result overlap.

beginner

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

Sorting helps to easily find overlapping intervals by comparing each interval with the previous one in order.

intermediate

In merging intervals, what do you do when the current interval's start is less than or equal to the last merged interval's end?

You merge them by updating the last merged interval's end to the maximum of both ends.

beginner

What happens if the current interval does not overlap with the last merged interval?

You add the current interval as a new separate interval in the merged list.

beginner

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

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 Sort intervals by start time

C Reverse the intervals

D Remove duplicates

Sorting by start time helps to process intervals in order and easily find overlaps.

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

A [1,5]

B [3,4]

C [1,4]

D [4,5]

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

What do you do if the current interval starts after the last merged interval ends?

A Discard current interval

B Merge them

C Add current interval as new

D Swap intervals

No overlap means the current interval is separate and added as is.

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

A List/Array

B Queue

C Hash Map

D Stack

A list or array is used to keep track of merged intervals in order.

What is the time complexity of merging intervals after sorting?

A O(n^2)

B O(log n)

C O(n)

D O(n log n)

Sorting takes O(n log n), merging intervals is O(n), so total is O(n log n).

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 how sorting intervals helps in merging overlapping intervals efficiently.

Consider how order simplifies overlap detection.

Practice

1. What is the main purpose of the Merge Overlapping Intervals algorithm?

easy

A. To sort intervals by their length

B. To combine all intervals that overlap into one continuous interval

C. To find the maximum number of intervals

D. To split intervals into smaller parts

Solution

1. Step 1: Understand the problem goal

   The algorithm aims to merge intervals that share any overlapping range into a single interval.

2. Step 2: Identify the correct purpose

   Among the options, only combining overlapping intervals matches the goal.

3. Final Answer:

   To combine all intervals that overlap into one continuous interval -> Option B

4. Quick Check:

   Merge overlapping intervals = combine overlaps [OK]

Hint: Think about joining intervals that touch or overlap [OK]

Common Mistakes:

• Confusing merging with sorting intervals
• Thinking it splits intervals instead of merging
• Assuming it counts intervals instead of merging

2. Which of the following is the correct way to sort intervals by their start time in JavaScript before merging?

easy

A. intervals.sort((a, b) => a[0] - b[0])

B. intervals.sort((a, b) => b[1] - a[1])

C. intervals.sort((a, b) => b[0] - a[0])

D. intervals.sort((a, b) => a[1] - b[1])

Solution

1. Step 1: Identify sorting key for merging

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

2. Step 2: Choose correct sort function

   The correct syntax is intervals.sort((a, b) => a[0] - b[0]) to sort ascending by start time.

3. Final Answer:

   intervals.sort((a, b) => a[0] - b[0]) -> Option A

4. Quick Check:

   Sort by start time = a[0] - b[0] [OK]

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

Common Mistakes:

• Sorting by end time instead of start time
• Sorting in descending order
• Using wrong array indices for sorting

3. What is the output of the following code?

const intervals = [[1,3],[2,6],[8,10],[15,18]];
function merge(intervals) {
  intervals.sort((a,b) => a[0] - b[0]);
  const merged = [];
  for (const interval of intervals) {
    if (!merged.length || merged[merged.length-1][1] < interval[0]) {
      merged.push(interval);
    } else {
      merged[merged.length-1][1] = Math.max(merged[merged.length-1][1], interval[1]);
    }
  }
  return merged;
}
console.log(merge(intervals));

medium

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

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

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

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

Solution

1. Step 1: Sort intervals by start time

   Sorted intervals: [[1,3],[2,6],[8,10],[15,18]] (already sorted)

2. Step 2: Merge overlapping intervals

   Merge [1,3] and [2,6] into [1,6]. Others remain separate.

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 by comparing end of last merged with start of current [OK]

Common Mistakes:

• Not merging overlapping intervals
• Merging intervals incorrectly by extending wrong boundaries
• Returning original intervals without merging

4. The following code is intended to merge overlapping intervals but has a bug. What is the bug?

function merge(intervals) {
  intervals.sort((a,b) => a[0] - b[0]);
  const merged = [];
  for (const interval of intervals) {
    if (merged.length === 0 || merged[merged.length-1][1] <= interval[0]) {
      merged.push(interval);
    } else {
      merged[merged.length-1][1] = Math.max(merged[merged.length-1][1], interval[1]);
    }
  }
  return merged;
}

medium

A. The merged array is not initialized correctly

B. The intervals are not sorted before merging

C. The condition should use < instead of <= to detect overlap

D. The max function is used incorrectly

Solution

1. Step 1: Analyze the overlap condition

   The condition uses <= which treats touching intervals as non-overlapping.

2. Step 2: Correct the condition for merging

   Using < instead of <= allows intervals that touch at the boundary to merge correctly.

3. Final Answer:

   The condition should use < instead of <= to detect overlap -> Option C

4. Quick Check:

   Overlap check needs <, not <= [OK]

Hint: Use <, not <=, to merge touching intervals [OK]

Common Mistakes:

• Using <= causes missing merges for touching intervals
• Not sorting intervals before merging
• Incorrectly updating merged intervals

5. Given intervals [[1,4],[4,5],[7,9],[8,10]], what is the merged output if intervals that touch at boundaries are considered overlapping?

hard

A. [[1,4],[5,7],[8,10]]

B. [[1,4],[4,5],[7,9],[8,10]]

C. [[1,10]]

D. [[1,5],[7,10]]

Solution

1. Step 1: Sort intervals by start time

   Sorted intervals: [[1,4],[4,5],[7,9],[8,10]] (already sorted)

2. Step 2: Merge touching and overlapping intervals

   [1,4] and [4,5] touch, so merge to [1,5]. [7,9] and [8,10] overlap, merge to [7,10].

3. Final Answer:

   [[1,5],[7,10]] -> Option D

4. Quick Check:

   Touching intervals merge = [[1,5],[7,10]] [OK]

Hint: Treat touching intervals as overlapping to merge boundaries [OK]

Common Mistakes:

• Not merging intervals that only touch at boundaries
• Merging all intervals incorrectly into one
• Leaving intervals separate despite overlap