Insert Interval
Detailed guide and Python implementation for the 'Insert Interval' problem.
1. Concept Overview
The 'Insert Interval' problem is a key challenge in the Intervals section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Insert Interval.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Insert Interval carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the ith interval and intervals is sorted in ascending order by starti. You are also given an interval newInterval = [start, end] that represents the start and end of another interval. Insert newInterval into intervals such that intervals is still sorted in ascending order by starti and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary).
Return intervals after the insertion.
Write a function insert(intervals: List[List[int]], newInterval: List[int]) -> List[List[int]].
- •0 <= len(intervals) <= 10^4
- •intervals[i].length == 2
- •0 <= starti <= endi <= 10^5
- •intervals is sorted by starti in ascending order
- •newInterval.length == 2
- •0 <= start <= end <= 10^5
Examples
intervals = [[1,3],[6,9]], newInterval = [2,5]
[[1,5],[6,9]]
The new interval [2,5] overlaps with [1,3], so they are merged into [1,5].
intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
[[1,2],[3,10],[12,16]]
Because [4,8] overlaps with [3,5],[6,7],[8,10], they merge to [3,10].
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def insert_opt(intervals, newInterval):
res = []
for i in range(len(intervals)):
if newInterval[1] < intervals[i][0]:
res.append(newInterval); return res + intervals[i:]
elif newInterval[0] > intervals[i][1]:
res.append(intervals[i])
else:
newInterval = [min(newInterval[0], intervals[i][0]), max(newInterval[1], intervals[i][1])]
res.append(newInterval); return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def insert_brute(intervals, newInterval):
intervals.append(newInterval); intervals.sort()
res = []
for i in intervals:
if not res or i[0] > res[-1][1]: res.append(i)
else: res[-1][1] = max(res[-1][1], i[1])
return resAlgorithm Pattern Checklist
When dealing with Intervals data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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