class Solution:
def merge(self, intervals: List[List[int]]) -> List[List[int]]:
"""
Merge all overlapping intervals in a list.
Parameters:
intervals (List[List[int]]): A list of intervals, where each interval is represented as [start, end].
Returns:
List[List[int]]: A list of merged non-overlapping intervals covering all the intervals in the input.
"""
# Sort intervals by the start time.
intervals.sort(key=lambda x: x[0])
# Initialize the list with the first interval.
merged = [intervals[0]]
# Iterate through each interval starting from the second one.
for current in intervals[1:]:
# 'last' holds the last interval in the merged list.
last = merged[-1]
# Check if the current interval overlaps with the last interval in merged.
if current[0] <= last[1]:
# If there is an overlap, update the end of the last interval with the max end.
last[1] = max(last[1], current[1])
else:
# If there is no overlap, add the current interval to merged.
merged.append(current)
return merged
Summary of Techniques and Approaches:
Sorting to Simplify the Problem: The intervals are sorted by their start value. Sorting is a common technique used to bring structure to data, which then makes it simpler to process items sequentially.
Iterative Merging: The solution uses an iterative approach where each interval is compared with the last merged interval. This pattern of sequential processing can be applied to problems involving merging, grouping, or combining overlapping data.
Condition-Driven Update: For overlapping intervals, the update is done by taking the maximum end value. This conditional update technique is valuable when extending or aggregating boundaries or ranges.
In-Place Accumulation: The merged list is built on the fly while iterating through the sorted list. This approach conserves memory and enhances clarity when accumulating results.
These techniques can be identified and applied to various problems that require data grouping, range merging, or interval scheduling, making your solutions not only efficient but also broadly applicable.