Why Intervals Are a Common Problem Pattern in DSA Typescript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create an interval object with start and end properties.

DSA Typescript

const interval = { start: 1, end: [1] };

Drag options to blanks, or click blank then click option'

A5

Bstart

Cinterval

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using the variable name 'start' instead of a number for end.

Setting end to 0 which is less than start.

The interval ends at 5, so the end property should be 5.

2fill in blank

medium

Complete the code to check if two intervals overlap.

DSA Typescript

function isOverlap(a: {start: number, end: number}, b: {start: number, end: number}): boolean {
  return a.start <= b.end && b.start [1] a.end;
}

Drag options to blanks, or click blank then click option'

A==

B>

C!=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > which would miss overlapping intervals.

Using == which only checks exact matches.

Two intervals overlap if a.start <= b.end and b.start <= a.end.

3fill in blank

hard

Fix the error in the function that merges two overlapping intervals.

DSA Typescript

function mergeIntervals(a: {start: number, end: number}, b: {start: number, end: number}): {start: number, end: number} {
  return { start: Math.min(a.start, b.start), end: Math.max(a.end, [1]) };
}

Drag options to blanks, or click blank then click option'

Aa.end

Ba.start

Cb.end

Db.start

Attempts:

3 left

💡 Hint

Common Mistakes

Using a.start or b.start instead of end values.

Using Math.min instead of Math.max for end.

To merge intervals, take the maximum end value between a.end and b.end.

4fill in blank

hard

Fill both blanks to create a function that sorts intervals by their start time.

DSA Typescript

function sortIntervals(intervals: {start: number, end: number}[]): {start: number, end: number}[] {
  return intervals.sort((a, b) => a.[1] - b.[2]);
}

Drag options to blanks, or click blank then click option'

Astart

Bend

Clength

Dvalue

Attempts:

3 left

💡 Hint

Common Mistakes

Sorting by end which may not order intervals correctly.

Using properties that do not exist like length or value.

Intervals should be sorted by their start property to process them in order.

5fill in blank

hard

Fill all three blanks to create a function that filters intervals longer than 5 units.

DSA Typescript

function filterLongIntervals(intervals: {start: number, end: number}[]): {start: number, end: number}[] {
  return intervals.filter(interval => (interval.[1] - interval.[2]) [3] 5);
}

Drag options to blanks, or click blank then click option'

Aend

Bstart

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Subtracting start - end which gives negative length.

Using <= instead of > which filters wrong intervals.

Interval length is end - start; filter intervals where length > 5.

Practice

1. Why are interval problems common in data structures and algorithms?

easy

A. Because they help solve scheduling and merging tasks efficiently

B. Because they only involve sorting numbers

C. Because they require complex graph traversal

D. Because they always use recursion

Solution

1. Step 1: Understand the nature of interval problems

   Interval problems often involve ranges of values, like time slots or numeric ranges, which are common in real-world tasks such as scheduling.

2. Step 2: Identify why intervals are useful

   Intervals allow efficient merging and checking overlaps, which are key in many applications like calendar events or resource allocation.

3. Final Answer:

   Because they help solve scheduling and merging tasks efficiently -> Option A

4. Quick Check:

   Intervals = scheduling and merging [OK]

Hint: Think about real-life tasks like booking or meetings [OK]

Common Mistakes:

• Assuming intervals only involve sorting
• Confusing intervals with graph problems
• Thinking recursion is always needed

2. Which TypeScript syntax correctly declares an interval as a tuple of two numbers?

easy

A. let interval: tuple = [5, 10];

B. let interval = (5, 10);

C. let interval: number[] = (5, 10);

D. let interval: [number, number] = [5, 10];

Solution

1. Step 1: Recall TypeScript tuple syntax

   Tuples in TypeScript are declared with square brackets and types inside, like [number, number].

2. Step 2: Check each option

   let interval: [number, number] = [5, 10]; correctly uses tuple syntax. let interval = (5, 10); uses parentheses which is invalid. let interval: number[] = (5, 10); uses array type but assigns parentheses. let interval: tuple = [5, 10]; uses 'tuple' which is not a TypeScript type.

3. Final Answer:

   let interval: [number, number] = [5, 10]; -> Option D

4. Quick Check:

   Tuple syntax = [number, number] [OK]

Hint: Tuples use square brackets with types inside [OK]

Common Mistakes:

• Using parentheses instead of square brackets
• Using 'tuple' as a type keyword
• Confusing arrays with tuples

3. What is the output of this TypeScript code that merges overlapping intervals?

function mergeIntervals(intervals: [number, number][]): [number, number][] {
  intervals.sort((a, b) => a[0] - b[0]);
  const merged: [number, number][] = [];
  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(mergeIntervals([[1,3],[2,6],[8,10],[15,18]]));

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

   The intervals become [[1,3],[2,6],[8,10],[15,18]].

2. Step 2: Merge overlapping intervals

   First interval [1,3] is added. Next [2,6] overlaps with [1,3], so merge to [1,6]. Then [8,10] and [15,18] do not overlap, so added as is.

3. Final Answer:

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

4. Quick Check:

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

Hint: Sort intervals first, then merge overlapping ones [OK]

Common Mistakes:

• Not sorting intervals before merging
• Overwriting intervals incorrectly
• Missing to merge overlapping intervals

4. Find the error in this TypeScript function that checks if two intervals overlap:

function isOverlap(a: [number, number], b: [number, number]): boolean {
  return a[1] > b[0] && b[1] > a[0];
}

medium

A. The function should return a number, not boolean

B. The intervals should be arrays of strings, not numbers

C. The comparison should use >= instead of > to include touching intervals

D. The function is correct as is

Solution

1. Step 1: Understand interval overlap condition

   Two intervals overlap if they share any point, including touching at edges.

2. Step 2: Check the comparison operators

   Using > excludes intervals that just touch (like [1,2] and [2,3]). Using >= includes touching intervals as overlapping.

3. Final Answer:

   The comparison should use >= instead of > to include touching intervals -> Option C

4. Quick Check:

   Use >= for touching intervals overlap [OK]

Hint: Use >= to count touching intervals as overlapping [OK]

Common Mistakes:

• Using > excludes touching intervals
• Returning wrong data type
• Wrong interval data types

5. Given a list of intervals representing booked meeting times, how would you find the minimum number of meeting rooms required?
Choose the best approach.

hard

A. Count intervals and divide by two

B. Sort intervals by start time, use a min-heap to track end times, count rooms needed

C. Use recursion to check all combinations of intervals

D. Sort intervals by end time, merge all intervals into one

Solution

1. Step 1: Understand the problem of meeting rooms

   We need to find how many meetings overlap at the same time to know rooms needed.

2. Step 2: Use sorting and a min-heap

   Sort intervals by start time. Use a min-heap to track earliest ending meeting. If a meeting starts after the earliest ends, reuse room; else add a new room.

3. Step 3: Count the maximum size of the heap

   The heap size at any time is the number of rooms needed.

4. Final Answer:

   Sort intervals by start time, use a min-heap to track end times, count rooms needed -> Option B

5. Quick Check:

   Min rooms = max overlapping intervals [OK]

Hint: Track earliest end times with min-heap to count rooms [OK]

Common Mistakes:

• Merging intervals loses overlap info
• Using recursion causes inefficiency
• Simple division ignores overlaps