Why Intervals Are a Common Problem Pattern in DSA C - Challenge Your Understanding

Challenge - 5 Problems

🧠 Conceptual

intermediate

Why are intervals important in algorithm problems?

Intervals often represent ranges of values or time. Why do many algorithm problems use intervals as a core concept?

A Because intervals always have fixed lengths, simplifying calculations.

B Because intervals are easier to sort than individual numbers.

C Because intervals help model continuous ranges and overlapping conditions in real-world scenarios.

D Because intervals never overlap, making problems simpler.

💡 Hint

Think about how intervals represent real-world things like meeting times or ranges.

Intervals represent continuous ranges and often overlap, which models many real-world problems like scheduling or resource allocation.

❓ Predict Output

intermediate

Output of merging overlapping intervals

What is the output of merging these intervals?

DSA C

intervals = [[1,3],[2,6],[8,10],[15,18]]

# After merging overlapping intervals, what is the resulting list?

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

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

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

D [[2,6],[8,10],[15,18]]

💡 Hint

Look for intervals that overlap and combine their ranges.

The intervals [1,3] and [2,6] overlap, so they merge into [1,6]. The others remain separate.

🔧 Debug

advanced

Identify the error in interval insertion code

What error does this code produce when inserting a new interval?

DSA C

def insert_interval(intervals, new_interval):
    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)
    result.extend(intervals[i:])
    return result

intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]]
new_interval = [4,8]
print(insert_interval(intervals, new_interval))

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

B Raises IndexError

C Outputs [[1,2],[3,8],[12,16]]

D Outputs [[1,2],[3,10],[12,16]]

💡 Hint

Check how overlapping intervals are merged and appended.

The code merges intervals overlapping with [4,8] into [3,10], then appends the rest. So output is [[1,2],[3,10],[12,16]].

📝 Syntax

advanced

Which option causes a syntax error in interval comprehension?

Which of these dictionary comprehensions for intervals causes a syntax error?

DSA C

intervals = [(1,3),(2,4),(5,7)]

A {i: (start, end) if start < 4 for i, (start, end) in enumerate(intervals)}

B {i: (start, end) for i, (start, end) in enumerate(intervals)}

C {i: (start, end) for i, (start, end) in enumerate(intervals) if start < 4}

D {i: (start, end) for i, (start, end) in enumerate(intervals) if end > 3}

💡 Hint

Check the placement of the if condition in the comprehension syntax.

Option A places the if condition incorrectly inside the value expression, causing a syntax error.

🚀 Application

expert

Maximum number of overlapping intervals

Given intervals [[1,4],[2,5],[7,9],[3,6]], what is the maximum number of intervals overlapping at any point?

A 1

B 3

C 4

D 2

💡 Hint

Visualize the intervals on a number line and count overlaps.

Intervals [1,4], [2,5], and [3,6] overlap between 3 and 4, so maximum overlap is 3.