# Interval Union - Amazon Top Interview Questions

### Problem Statement :

```Given a two-dimensional integer list intervals representing unsorted inclusive intervals, return their union in sorted order.

Constraints

n ≤ 100,000 where n is the length of intervals

Example 1

Input

intervals = [
[0, 5],
[4, 6]
]

Output

[
[0, 6]
]

Example 2

Input

intervals = [
[1, 2],
[3, 4]
]

Output

[
[1, 2],
[3, 4]
]

Example 3

Input

intervals = [
[5, 6],
[1, 2]
]

Output

[
[1, 2],
[5, 6]
]```

### Solution :

```                        ```Solution in C++ :

vector<vector<int>> solve(vector<vector<int>>& intervals) {
sort(intervals.begin(), intervals.end());
vector<vector<int>> ans;
if (intervals.size() == 0) {
return {};
}
int mini = intervals, maxi = intervals;
for (int i = 1; i < intervals.size(); i++) {
if (intervals[i] > maxi) {
ans.push_back({mini, maxi});
mini = intervals[i];
maxi = intervals[i];
} else {
if (intervals[i] > maxi) {
maxi = intervals[i];
}
}
}
ans.push_back({mini, maxi});
return ans;
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, intervals):
events = []
OPEN, CLOSE = 0, 1

for start, end in intervals:
events.append((start, OPEN))
events.append((end, CLOSE))

events.sort()

ans = []
prev = 0
balance = 0

for time, event_type in events:
if balance == 0:
prev = time

if event_type == OPEN:
balance += 1
else:
balance -= 1

if balance == 0:
ans.append((prev, time))

return ans```
```

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