🧩 Python DSA Patterns — Interval Patterns ⏱️🐍

Interval problems deal with ranges like [start, end] and focus on how these ranges overlap, merge, or conflict with each other.

They are extremely common in:

• Scheduling
• Calendars
• Resource allocation
• Timeline-based problems

✨ What Is an Interval?

An interval is usually represented as:

[start, end]

Examples:

• Meetings: [9, 11]
• Events: [2, 5]
• Time slots, ranges, bookings

The core challenge is understanding how two intervals relate:

• Do they overlap?
• Can they be merged?
• Do they conflict?

⚡ Golden Rule (Very Important)

Almost all interval problems start by sorting intervals by start time.

Once sorted, decisions become local and predictable.

🧠 Common Interval Patterns

1️⃣ Merge Overlapping Intervals

• Combine intervals that overlap
• Output a condensed list

2️⃣ Detect Overlap / Conflict

• Check if two intervals clash
• Used in scheduling & meeting rooms

3️⃣ Insert a New Interval

• Insert and merge efficiently

4️⃣ Minimum Resources Required

• Find how many rooms/resources are needed
• Track overlaps using pointers or heaps

📝 Example 1 — Merge Intervals (Core Pattern)

Merge all overlapping intervals into one.

def merge_intervals(intervals):
    intervals.sort(key=lambda x: x[0])
    merged = []

    for start, end in intervals:
        if not merged or merged[-1][1] < start:
            merged.append([start, end])
        else:
            merged[-1][1] = max(merged[-1][1], end)

    print("Merged Intervals:", merged)

📝 Example 2 — Check If Intervals Overlap

Two intervals overlap if the start of one is before the end of the other.

def is_overlap(a, b):
    return a[0] < b[1] and b[0] < a[1]

print(is_overlap([1, 3], [2, 4]))  # True
print(is_overlap([1, 2], [3, 4]))  # False

📝 Example 3 — Meeting Rooms (Conceptual)

Find minimum rooms needed so meetings don’t overlap.

Idea:

• Sort start times and end times separately
• Use two pointers to track overlaps

(No full code here — this is a pattern note, not a script.)

🧠 Where Interval Patterns Help

• 📅 Calendar & scheduling systems
• 🏢 Meeting room allocation
• 🚦 Time conflict detection
• 📊 Resource usage over time
• 🧩 Greedy scheduling problems

❗ Common Mistakes

• Forgetting to sort intervals first
• Confusing inclusive vs exclusive ends
• Overcomplicating overlap logic
• Trying brute-force comparisons (O(n²))

✅ Takeaways

• Sort by start time first — always
• Most interval problems are greedy
• Merge when current start ≤ previous end
• Interval patterns appear far more often than expected

🏋️ Practice Problems

1. Merge Intervals
2. Insert Interval
3. Meeting Rooms I & II
4. Non-overlapping Intervals
5. Minimum Number of Arrows to Burst Balloons