Why Merge Overlapping Intervals in DSA Rust?

The Big Idea

What if you could instantly clean up messy overlapping schedules with just a simple method?

The Scenario

Imagine you have a list of booked meeting times in a day, but some meetings overlap. You want to find the total free time, but first, you need to merge these overlapping meetings into one continuous block.

The Problem

Manually checking each meeting against every other to merge overlaps is slow and confusing. It's easy to miss overlaps or merge incorrectly, especially when many meetings overlap in complex ways.

The Solution

Merge Overlapping Intervals sorts the meetings by start time, then combines any that overlap into one. This way, you get a clean list of non-overlapping intervals, making it easy to see free time or total booked time.

Before vs After

✗ Before

let intervals = vec![(1, 5), (3, 7), (8, 10)];
// Manually check and merge overlaps one by one

✓ After

let intervals = vec![(1, 5), (3, 7), (8, 10)];
let merged = merge_intervals(intervals);

What It Enables

This lets you quickly and correctly combine overlapping time blocks, making scheduling and time management simple and error-free.

Real Life Example

When booking rooms or resources, merging overlapping reservations helps avoid double-booking and shows exactly when the resource is busy.

Key Takeaways

Manual merging is slow and error-prone.

Sorting intervals first simplifies merging.

Merged intervals give a clear, non-overlapping schedule.

Practice

1. What is the main goal when merging overlapping intervals in a list like [[1,3],[2,6],[8,10]]?

easy

A. Remove all intervals that overlap

B. Sort intervals by their end values only

C. Combine intervals that overlap into one continuous interval

D. Split intervals into smaller parts

Solution

1. Step 1: Understand overlapping intervals

   Intervals overlap if one starts before the other ends. For example, [1,3] and [2,6] overlap.

2. Step 2: Merge overlapping intervals

   We combine overlapping intervals into one that covers both, like merging [1,3] and [2,6] into [1,6].

3. Final Answer:

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

4. Quick Check:

   Merging overlapping intervals means combining them [OK]

Hint: Merge intervals by combining overlapping ranges [OK]

Common Mistakes:

• Sorting only by end values misses correct merges
• Removing intervals instead of merging
• Splitting intervals unnecessarily

2. Which Rust code snippet correctly sorts a vector of intervals by their start value before merging?

easy

A. intervals.sort_by_key(|interval| interval[0]);

B. intervals.sort();

C. intervals.sort_by(|a, b| b[0].cmp(&a[0]));

D. intervals.sort_by_key(|interval| interval[1]);

Solution

1. Step 1: Identify sorting by start value

   We want to sort intervals by their first element (start), so we use sort_by_key with interval[0].

2. Step 2: Check sorting direction and key

   intervals.sort_by_key(|interval| interval[0]); sorts ascending by start, which is correct. intervals.sort_by(|a, b| b[0].cmp(&a[0])); sorts descending, which is wrong. intervals.sort_by_key(|interval| interval[1]); sorts by end, not start.

3. Final Answer:

   intervals.sort_by_key(|interval| interval[0]); -> Option A

4. Quick Check:

   Sort by start value using sort_by_key(interval[0]) [OK]

Hint: Use sort_by_key with interval[0] to sort by start [OK]

Common Mistakes:

• Sorting by end instead of start
• Sorting descending instead of ascending
• Using sort() without key for nested vectors

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

let mut intervals = vec![vec![1,4], vec![2,5], vec![7,9]];
intervals.sort_by_key(|x| x[0]);
let mut merged = vec![];
for interval in intervals {
    if merged.is_empty() || merged.last().unwrap()[1] < interval[0] {
        merged.push(interval);
    } else {
        let last = merged.last_mut().unwrap();
        last[1] = last[1].max(interval[1]);
    }
}
println!("{:?}", merged);

medium

A. [[2,5], [7,9]]

B. [[1,4], [2,5], [7,9]]

C. [[1,9]]

D. [[1,5], [7,9]]

Solution

1. Step 1: Sort intervals by start

   Sorted intervals: [[1,4], [2,5], [7,9]] (already sorted).

2. Step 2: Merge overlapping intervals

   [1,4] and [2,5] overlap, merged to [1,5]. [7,9] does not overlap, so added as is.

3. Final Answer:

   [[1,5], [7,9]] -> Option D

4. Quick Check:

   Merged intervals = [[1,5], [7,9]] [OK]

Hint: Merge intervals by extending end if overlapping [OK]

Common Mistakes:

• Not merging overlapping intervals
• Merging non-overlapping intervals
• Incorrectly updating interval ends

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

let mut intervals = vec![vec![1,3], vec![2,4], vec![5,7]];
intervals.sort_by_key(|x| x[1]);
let mut merged = vec![];
for interval in intervals {
    if merged.is_empty() || merged.last().unwrap()[1] < interval[0] {
        merged.push(interval);
    } else {
        let last = merged.last_mut().unwrap();
        last[1] = last[1].max(interval[1]);
    }
}
println!("{:?}", merged);

medium

A. Sorting by end value causes incorrect merging

B. Using last_mut() causes a runtime error

C. The vector intervals is not mutable

D. The condition to check overlap is reversed

Solution

1. Step 1: Check sorting key

   The code sorts intervals by their end value, but merging requires sorting by start value to process intervals in order.

2. Step 2: Effect of wrong sorting

   Sorting by end causes intervals to be processed out of order, leading to missed merges or incorrect merges.

3. Final Answer:

   Sorting by end value causes incorrect merging -> Option A

4. Quick Check:

   Sort by start, not end, for correct merging [OK]

Hint: Always sort intervals by start before merging [OK]

Common Mistakes:

• Sorting by end instead of start
• Misusing mutable references
• Incorrect overlap condition

5. Given a list of intervals [[1,3],[2,4],[5,7],[6,8],[9,10]], write a Rust function to merge all overlapping intervals and return the merged list. What is the correct merged output?

hard

A. [[1,3],[2,4],[5,7],[6,8],[9,10]]

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

C. [[1,8],[9,10]]

D. [[1,4],[5,7],[6,8],[9,10]]

Solution

1. Step 1: Sort intervals by start

   Sorted intervals: [[1,3],[2,4],[5,7],[6,8],[9,10]] (already sorted).

2. Step 2: Merge overlapping intervals step-by-step

   Merge [1,3] and [2,4] to [1,4]. Merge [5,7] and [6,8] to [5,8]. [9,10] stays separate.

3. Final Answer:

   [[1,4],[5,8],[9,10]] -> Option B

4. Quick Check:

   Merge intervals by extending ends where overlapping [OK]

Hint: Merge intervals by sorting and extending ends [OK]

Common Mistakes:

• Not merging all overlapping intervals
• Merging non-overlapping intervals
• Incorrect final intervals after merge