Why Intervals Are a Common Problem Pattern in DSA Python - Why It Works

Concept Flow - Why Intervals Are a Common Problem Pattern

Identify intervals

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Sort intervals by start

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Compare current interval with previous

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If overlapping: merge intervals

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Update merged interval

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If no overlap: add interval to result

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Repeat for all intervals

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Return merged intervals

Intervals problems usually start by sorting intervals, then comparing and merging overlapping ones step-by-step.

Execution Sample

DSA Python

intervals = [[1,3],[2,6],[8,10],[15,18]]
intervals.sort(key=lambda x: x[0])
merged = []
for interval in intervals:
    if not merged or merged[-1][1] < interval[0]:
        merged.append(interval)
    else:
        merged[-1][1] = max(merged[-1][1], interval[1])

This code merges overlapping intervals from a list.

Execution Table

Step	Operation	Current Interval	Merged List Before	Action	Merged List After	Visual State
1	Sort intervals	[1,3]	[ ]	Sort by start	[ ]	[1,3] -> [2,6] -> [8,10] -> [15,18] -> null
2	Process interval	[1,3]	[ ]	merged empty, append	[[1,3]]	[1,3] -> null
3	Process interval	[2,6]	[[1,3]]	Overlap with [1,3], merge	[[1,6]]	[1,6] -> null
4	Process interval	[8,10]	[[1,6]]	No overlap, append	[[1,6],[8,10]]	[1,6] -> [8,10] -> null
5	Process interval	[15,18]	[[1,6],[8,10]]	No overlap, append	[[1,6],[8,10],[15,18]]	[1,6] -> [8,10] -> [15,18] -> null
6	End	N/A	[[1,6],[8,10],[15,18]]	All intervals processed	[[1,6],[8,10],[15,18]]	[1,6] -> [8,10] -> [15,18] -> null

💡 All intervals processed and merged where overlapping.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
intervals	[[1,3],[2,6],[8,10],[15,18]]	[[1,3],[2,6],[8,10],[15,18]]	[[1,3],[2,6],[8,10],[15,18]]	[[1,3],[2,6],[8,10],[15,18]]	[[1,3],[2,6],[8,10],[15,18]]	[[1,3],[2,6],[8,10],[15,18]]
merged	[]	[[1,3]]	[[1,6]]	[[1,6],[8,10]]	[[1,6],[8,10],[15,18]]	[[1,6],[8,10],[15,18]]
current interval	N/A	[1,3]	[2,6]	[8,10]	[15,18]	N/A

Key Moments - 3 Insights

Why do we sort intervals before merging?

Sorting ensures intervals are in order by start time, so we can easily check overlap with the last merged interval (see Step 1 in execution_table). Without sorting, merging would be incorrect.

Why do we compare merged[-1][1] with interval[0]?

merged[-1][1] is the end of the last merged interval; interval[0] is the start of the current. If merged[-1][1] < interval[0], intervals do not overlap (see Step 4 and 5). Otherwise, they overlap and must be merged (Step 3).

How does merging update the last interval?

When intervals overlap, we update the end of the last merged interval to the max end of both intervals (Step 3). This extends the merged interval to cover both.

Visual Quiz - 3 Questions

Look at the execution_table at Step 3. What is the merged list after processing the interval [2,6]?

A [[1,3],[2,6]]

B [[1,6]]

C [[2,6]]

D [[1,3]]

💡 Hint

Check the 'Merged List After' column at Step 3 in execution_table.

At which step does the condition 'merged[-1][1] < interval[0]' become false, causing a merge?

A Step 2

B Step 4

C Step 3

D Step 5

💡 Hint

Look at the 'Action' column in execution_table where merging happens.

If the intervals were not sorted first, what would likely happen to the merged list?

A It might miss some overlaps and produce incorrect merges.

B It would still merge correctly.

C It would produce an empty list.

D It would merge all intervals into one.

💡 Hint

Refer to the importance of sorting in the concept_flow and key_moments.

Concept Snapshot

Intervals problems often require sorting intervals by start time.
Then, iterate through intervals, merging overlapping ones by comparing current start with last merged end.
If no overlap, append interval to result.
This pattern helps solve many interval-related problems efficiently.

Full Transcript

Intervals are common in problems like scheduling or merging ranges. The key step is to sort intervals by their start times. Then, we go through each interval and compare it with the last merged interval. If they overlap, we merge by extending the end time. If not, we add the new interval to the merged list. This approach ensures all overlapping intervals are combined correctly. Sorting is crucial because it puts intervals in order, making it easy to detect overlaps. Without sorting, the merging logic can fail. This pattern is a foundation for many interval problems in data structures and algorithms.