How do you solve Count Ways to Group Overlapping Ranges on LeetCode?

Count Ways to Group Overlapping Ranges (LeetCode #2580) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Merging overlapping ranges reduces complexity.

What is the time complexity of Count Ways to Group Overlapping Ranges?

The optimal solution for Count Ways to Group Overlapping Ranges runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the ranges, and the space complexity is O(n) for storing the merged ranges.

What is the brute force solution for Count Ways to Group Overlapping Ranges?

The brute force approach for Count Ways to Group Overlapping Ranges is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we can check every possible way to group the ranges and count valid configurations. This is straightforward but inefficient due to the high number of combinations. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Count Ways to Group Overlapping Ranges?

Count Ways to Group Overlapping Ranges uses the following concepts: Array, Sorting. The recommended patterns to study are: Sorting, Greedy Algorithms.

What are the interview tips for Count Ways to Group Overlapping Ranges?

Explain your thought process clearly. Discuss the time complexity of your approach. Be prepared to optimize your solution.

What are common mistakes when solving Count Ways to Group Overlapping Ranges?

Failing to merge overlapping ranges correctly. Not considering edge cases with single ranges.

#2580

Count Ways to Group Overlapping Ranges

Medium

ArraySortingSortingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n)Space O(n)

The optimal solution involves merging overlapping ranges and counting the number of distinct groups formed. This reduces the problem to a linear scan after sorting, making it efficient.

⚙️

Algorithm

3 steps

1Step 1: Sort the ranges based on the start time.
2Step 2: Merge overlapping ranges into groups.
3Step 3: The number of ways to split the groups is 2 raised to the power of the number of merged groups.

solution.py15 lines

1# Full working Python code
2
3def countWays(ranges):
4    MOD = 10**9 + 7
5    ranges.sort(key=lambda x: x[0])
6    merged = []
7
8    for start, end in ranges:
9        if not merged or merged[-1][1] < start:
10            merged.append([start, end])
11        else:
12            merged[-1][1] = max(merged[-1][1], end)
13
14    return pow(2, len(merged), MOD)
15

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the ranges, and the space complexity is O(n) for storing the merged ranges.

1Merging overlapping ranges reduces complexity.
2The number of ways to split is based on the number of merged groups.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.