DSA With AI
Week 9 ยท Intervals

Merge Intervals

Solve Merge Intervals by recognizing the Intervals pattern and turning the prompt into a small invariant before coding.

Medium Intervals Week 9 Practice runner

Frame the problem

  • Implement merge_intervals with the exact signature used by the interactive runner.
  • Use the visible tests to confirm the input and output shape before reading the final solution.
  • Treat challenge tests as edge-case pressure: empty inputs, repeated values, boundary shapes, or impossible states.
  • State the invariant before code, then dry-run one passing case and one failing-looking case.
1. Reveal example inputs and outputs

Example 1

Input:

merge_intervals([
  [
    1,
    3
  ],
  [
    2,
    6
  ],
  [
    8,
    10
  ],
  [
    15,
    18
  ]
])

Output:

[
  [
    1,
    6
  ],
  [
    8,
    10
  ],
  [
    15,
    18
  ]
]
2. Brute force first

What direct brute force would be correct for a tiny input? Name the exact repeated work that the target pattern removes.

3. Reveal the insight ladder
  1. Map the prompt to the Intervals pattern instead of starting from syntax.
  2. Sort by start time first.
  3. Touching endpoints count as overlapping here.
  4. Only reveal the final code after you can explain why each state update is safe.
4. Dry run before code
  1. merge-overlap: input [[[1,3],[2,6],[8,10],[15,18]]] should produce [[1,6],[8,10],[15,18]]. Hint to check your state: Sort by start time first.
  2. merge-touching: input [[[1,4],[4,5]]] should produce [[1,5]]. Hint to check your state: Touching endpoints count as overlapping here.
5. Reveal final Python solution 
def merge_intervals(intervals: list[list[int]]) -> list[list[int]]:
    intervals = sorted(intervals)
    merged: list[list[int]] = []
    for start, end in intervals:
        if not merged or start > merged[-1][1]:
            merged.append([start, end])
        else:
            merged[-1][1] = max(merged[-1][1], end)
    return merged

Complexity: Derive the exact bounds from merge_intervals: count how often each input item is visited and the maximum size of the main state structure.

Interview narration

  • I will first describe the invariant in plain language.
  • Then I will explain what data structure carries that invariant across the traversal, loop, recursion, or DP transition.
  • Finally I will walk one edge case before writing the optimized version.

Common traps

  • Solving only the visible example instead of the invariant.
  • Forgetting empty input, singleton input, duplicate values, or impossible-state cases.
  • Revealing the solution before doing a dry run from the starter signature.

Follow-up drills

1. How do you turn this into a timed interview answer?

Start with the invariant, give the brute force in one sentence, name the optimized state, code the core loop or recursion, and run one visible test aloud before mentioning complexity.

2. How do you scale the same pattern to a larger input?

Track which state grows with the input: hash maps and sets grow with distinct values, queues grow with frontier width, recursion grows with depth, heaps grow with active candidates, and DP tables grow with state count.

3. What should you practice from blank tomorrow?

Rewrite merge_intervals without looking at the solution, then compare only the invariant and state updates before checking syntax.

Interactive runner

Write the required Python function. Your code runs locally in this browser. Hints reveal one failing case at a time.