The “Check if All the Integers in a Range Are Covered” problem on Leetcode is a fascinating problem that deals with array manipulation and interval coverage. This problem not only tests your ability to manipulate arrays effectively but also your understanding of ranges and intervals. This article will take you through different methods of tackling this problem, understanding edge cases, and optimizing for speed and efficiency.

## 1. Problem Statement

The problem asks you to determine if all integers from `left`

to `right`

(inclusive) are covered by some range `[a, b]`

in `ranges`

. You are to return `True`

if all integers in the range `[left, right]`

are covered by at least one interval in `ranges`

, otherwise return `False`

.

## 2. Naive Approach: The Iterative Method

The simplest approach to solving this problem is to loop through the numbers from `left`

to `right`

and for each number, check whether it falls within any of the ranges in `ranges`

.

Python Code:

```
def isCovered(ranges, left, right):
for i in range(left, right + 1):
if all(i < a or i > b for a, b in ranges):
return False
return True
```

## 3. Sorting and Merging Intervals

Another technique is to first sort the ranges, and then merge overlapping or adjacent intervals. After merging, you can check whether `[left, right]`

is covered by any of the merged intervals.

Python Code:

```
def isCovered(ranges, left, right):
ranges.sort()
for a, b in ranges:
if a <= left <= b:
left = b + 1
return left > right
```

## 4. Interval Coverage: The Constant Space Technique

This method involves iterating through the `ranges`

once and updating `left`

and `right`

based on whether or not they’re covered by the ranges in `ranges`

. This is a constant space method.

Python Code:

```
def isCovered(ranges, left, right):
for i in range(left, right + 1):
covered = False
for l, r in ranges:
if l <= i <= r:
covered = True
break
if not covered:
return False
return True
```

## 5. Dealing with Edge Cases

#### 5.1 When `ranges`

has a single interval

In this case, it’s easy to check whether `[left, right]`

is covered by this single interval.

#### 5.2 When `left == right`

When `left`

and `right`

are the same, you only need to check if this single value is covered by any interval.

## 6. Complexity Analysis

#### Naive Approach

**Time Complexity**: O((right – left) * n), where n is the length of`ranges`

**Space Complexity**: O(1)

#### Sorting and Merging Intervals

**Time Complexity**: O(n log n) for sorting**Space Complexity**: O(1)

#### Interval Coverage: Constant Space Technique

**Time Complexity**: O((right – left) * n)**Space Complexity**: O(1)

## 7. Conclusion

The “Check if All the Integers in a Range Are Covered” problem on LeetCode tests your understanding of array manipulation and intervals. There are multiple ways to solve it, ranging from naive methods to more optimized techniques.