Merge Overlapping Intervals in DSA C - Execution Trace

Concept Flow - Merge Overlapping Intervals

Sort intervals by start

↓

Initialize merged list empty

↓

For each interval

↓

Check overlap with last merged

↓

Merge intervals

↓

Repeat

↓

Done

Sort intervals first, then go through each interval to merge if overlapping or add if not.

Execution Sample

DSA C

int intervals[][2] = {{1,3},{2,6},{8,10},{15,18}};
// Sort by start
// Merge overlapping intervals
// Result: {{1,6},{8,10},{15,18}}

This code merges overlapping intervals from a list of intervals.

Execution Table

Step	Operation	Current Interval	Merged List Before	Action	Merged List After	Visual State
1	Sort intervals	[1,3],[2,6],[8,10],[15,18]	[]	Sort by start	[1,3],[2,6],[8,10],[15,18]	[1,3] -> [2,6] -> [8,10] -> [15,18] -> null
2	Initialize merged list	[1,3]	[]	Add first interval	[1,3]	[1,3] -> null
3	Check overlap	[2,6]	[1,3]	2 <= 3 overlap	Merge to [1,6]	[1,6] -> null
4	Check overlap	[8,10]	[1,6]	8 > 6 no overlap	Add [8,10]	[1,6] -> [8,10] -> null
5	Check overlap	[15,18]	[1,6],[8,10]	15 > 10 no overlap	Add [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 merge intervals when current start <= last merged end?

Because intervals overlap if the current interval starts before or exactly when the last merged interval ends. See step 3 in execution_table where [2,6] overlaps with [1,3].

Why do we add the current interval to merged list when no overlap?

Because intervals do not overlap if current start is greater than last merged end, so we keep them separate. See step 4 and 5 where [8,10] and [15,18] are added separately.

Why do we sort intervals first?

Sorting ensures intervals are in order by start time, so merging can be done in one pass. Without sorting, overlapping intervals might be missed.

Visual Quiz - 3 Questions

Look at the execution_table, what is the merged list after step 3?

A [[1,3]]

B [[1,6]]

C [[2,6]]

D [[1,3],[2,6]]

💡 Hint

Check the 'Merged List After' column in step 3 of execution_table.

At which step does the condition for no overlap first occur?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at the 'Action' column in execution_table where it says 'no overlap'.

If intervals were not sorted, what would change in the execution_table?

A Merging might miss overlapping intervals

B Intervals would be merged correctly anyway

C Merged list would be empty

D Sorting step would be skipped but no effect

💡 Hint

Refer to the key_moments explanation about sorting importance.

Concept Snapshot

Merge Overlapping Intervals:
1. Sort intervals by start time.
2. Initialize merged list with first interval.
3. For each next interval, if it overlaps with last merged, merge them.
4. Else, add interval to merged list.
5. Result is merged intervals without overlap.

Full Transcript

To merge overlapping intervals, first sort the intervals by their start times. Then start with an empty merged list and add the first interval. For each next interval, check if it overlaps with the last interval in the merged list. Overlap means the current interval's start is less than or equal to the last merged interval's end. If overlapping, merge by updating the end of the last merged interval to the maximum end of both. If no overlap, add the current interval as a new entry in the merged list. Continue until all intervals are processed. The final merged list contains intervals without overlaps.