Problem Description
Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input.
Examples
Example 1: Input: intervals = [[1,3],[2,6],[8,10],[15,18]] Output: [[1,6],[8,10],[15,18]] Explanation: Since intervals [1,3] and [2,6] overlap, merge them into [1,6]. Example 2: Input: intervals = [[1,4],[4,5]] Output: [[1,5]] Explanation: Intervals [1,4] and [4,5] are considered overlapping.
Python Solution
def merge(intervals: List[List[int]]) -> List[List[int]]:
if not intervals:
return []
# Sort intervals based on start time
intervals.sort(key=lambda x: x[0])
merged = [intervals[0]]
for interval in intervals[1:]:
if interval[0] <= merged[-1][1]:
# Overlapping intervals, update end time
merged[-1][1] = max(merged[-1][1], interval[1])
else:
# Non-overlapping interval, add to result
merged.append(interval)
return merged
Java Solution
class Solution {
public int[][] merge(int[][] intervals) {
if (intervals == null || intervals.length <= 1) {
return intervals;
}
// Sort intervals based on start time
Arrays.sort(intervals, (a, b) -> Integer.compare(a[0], b[0]));
List merged = new ArrayList<>();
merged.add(intervals[0]);
for (int i = 1; i < intervals.length; i++) {
if (intervals[i][0] <= merged.get(merged.size() - 1)[1]) {
// Overlapping intervals, update end time
merged.get(merged.size() - 1)[1] =
Math.max(merged.get(merged.size() - 1)[1], intervals[i][1]);
} else {
// Non-overlapping interval, add to result
merged.add(intervals[i]);
}
}
return merged.toArray(new int[merged.size()][]);
}
}
C++ Solution
class Solution {
public:
vector> merge(vector>& intervals) {
if (intervals.empty()) {
return {};
}
// Sort intervals based on start time
sort(intervals.begin(), intervals.end());
vector> merged;
merged.push_back(intervals[0]);
for (int i = 1; i < intervals.size(); i++) {
if (intervals[i][0] <= merged.back()[1]) {
// Overlapping intervals, update end time
merged.back()[1] = max(merged.back()[1], intervals[i][1]);
} else {
// Non-overlapping interval, add to result
merged.push_back(intervals[i]);
}
}
return merged;
}
};
JavaScript Solution
/**
* @param {number[][]} intervals
* @return {number[][]}
*/
var merge = function(intervals) {
if (!intervals.length) {
return [];
}
// Sort intervals based on start time
intervals.sort((a, b) => a[0] - b[0]);
const merged = [intervals[0]];
for (let i = 1; i < intervals.length; i++) {
if (intervals[i][0] <= merged[merged.length - 1][1]) {
// Overlapping intervals, update end time
merged[merged.length - 1][1] =
Math.max(merged[merged.length - 1][1], intervals[i][1]);
} else {
// Non-overlapping interval, add to result
merged.push(intervals[i]);
}
}
return merged;
};
C# Solution
public class Solution {
public int[][] Merge(int[][] intervals) {
if (intervals == null || intervals.Length <= 1) {
return intervals;
}
// Sort intervals based on start time
Array.Sort(intervals, (a, b) => a[0].CompareTo(b[0]));
var merged = new List();
merged.Add(intervals[0]);
for (int i = 1; i < intervals.Length; i++) {
if (intervals[i][0] <= merged[merged.Count - 1][1]) {
// Overlapping intervals, update end time
merged[merged.Count - 1][1] =
Math.Max(merged[merged.Count - 1][1], intervals[i][1]);
} else {
// Non-overlapping interval, add to result
merged.Add(intervals[i]);
}
}
return merged.ToArray();
}
}
Complexity Analysis
- Time Complexity: O(n log n) due to sorting, where n is the number of intervals
- Space Complexity: O(n) to store the merged intervals
Solution Explanation
This solution uses a sorting-based approach to merge overlapping intervals:
- Algorithm steps:
- Sort intervals by start time
- Initialize result with first interval
- For each remaining interval:
- If it overlaps with last merged interval, update end time
- Otherwise, add it as a new interval
Key points:
- Sorting ensures efficient merging
- Single pass through sorted intervals
- Handles all edge cases
- In-place merging possible