Merge Overlapping Intervals in DSA Rust - Build from Scratch

Merge Overlapping Intervals

📖 Scenario: You are working on a calendar app that manages meeting times. Sometimes, meetings overlap and you want to combine those overlapping meetings into one longer meeting to avoid confusion.

🎯 Goal: Build a program that takes a list of meeting time intervals and merges all overlapping intervals into one, so the calendar shows clear, non-overlapping meeting times.

📋 What You'll Learn

Create a vector of tuples representing meeting intervals with exact values

Create a variable to hold the merged intervals

Sort the intervals by their start time

Merge overlapping intervals using a loop

Print the merged intervals in the format [(start1, end1), (start2, end2), ...]

💡 Why This Matters

🌍 Real World

Merging overlapping intervals is useful in calendar apps, booking systems, and resource scheduling to avoid conflicts.

💼 Career

Understanding interval merging helps in software roles involving scheduling, data processing, and algorithm design.

1

Create the initial list of meeting intervals

Create a vector called intervals with these exact tuples: (1, 3), (2, 6), (8, 10), (15, 18)

DSA Rust

# Your code here

Hint

Use let mut intervals = vec![(1, 3), (2, 6), (8, 10), (15, 18)]; to create the vector.

2

Create a vector to hold merged intervals

Create an empty vector called merged to store the merged intervals

DSA Rust

fn main() {
    let mut intervals = vec![(1, 3), (2, 6), (8, 10), (15, 18)];
    // Create an empty vector called merged
    // Your code here
}

Hint

Use let mut merged: Vec<(i32, i32)> = Vec::new(); to create an empty vector.

3

Sort and merge overlapping intervals

Sort intervals by the start time using intervals.sort_by_key(|k| k.0). Then use a for loop with variable interval to iterate over intervals. Inside the loop, merge overlapping intervals by comparing with the last interval in merged and update or push accordingly.

DSA Rust

fn main() {
    let mut intervals = vec![(1, 3), (2, 6), (8, 10), (15, 18)];
    let mut merged: Vec = Vec::new();
    // Sort intervals by start time
    // Your code here
    // Use a for loop to merge intervals
    // Your code here
}

Hint

Sort first, then loop through intervals. Use merged.last_mut() to get the last merged interval and update or push new intervals.

4

Print the merged intervals

Print the merged vector using println!("{:?}", merged) to show the merged intervals

DSA Rust

fn main() {
    let mut intervals = vec![(1, 3), (2, 6), (8, 10), (15, 18)];
    let mut merged: Vec = Vec::new();
    intervals.sort_by_key(|k| k.0);
    for interval in intervals {
        if let Some(last) = merged.last_mut() {
            if interval.0  last.1 {
                    last.1 = interval.1;
                }
            } else {
                merged.push(interval);
            }
        } else {
            merged.push(interval);
        }
    }
    // Print the merged intervals
    // Your code here
}

Hint

Use println!("{:?}", merged); to print the vector of tuples.

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