Program to find total unique duration from a list of intervals in Python

Suppose we have a list of intervals where each interval represents a range [start, end] (inclusive). We need to find the total unique duration covered by all intervals combined, handling any overlaps correctly.

So, if the input is like intervals = [[2, 11],[13, 31],[41, 61]], then the output will be 50, as the total unique covered distance is (11 - 2 + 1) = 10 then (31 - 13 + 1) = 19 and (61 - 41 + 1) = 21, so total is 50.

Algorithm

To solve this, we will follow these steps −

• If intervals list is empty, return 0
• Sort the intervals by start time
• Initialize with the first interval [start, end]
• For each subsequent interval, check if it overlaps with current interval
• If no overlap, add current interval duration to answer and start new interval
• If overlap, merge by extending the end time
• Add the final interval duration to answer

Example

Let us see the following implementation to get better understanding −

class Solution:
    def solve(self, intervals):
        if not intervals:
            return 0
        
        intervals.sort()
        start, end = intervals[0]
        ans = 0
        
        for s, e in intervals:
            if s > end:
                # No overlap, add current interval duration
                ans += end - start + 1
                start = s
                end = e
            else:
                # Overlap, merge intervals
                end = max(end, e)
        
        # Add the last interval duration
        ans += end - start + 1
        return ans

# Test the solution
ob = Solution()
intervals = [[2, 11],[13, 31],[41, 61]]
print(ob.solve(intervals))

50

How It Works

The algorithm works by merging overlapping intervals:

1. Sort intervals: [2,11], [13,31], [41,61]
2. First interval [2,11]: No previous interval to compare
3. Second interval [13,31]: 13 > 11, so no overlap. Add (11-2+1)=10 to answer
4. Third interval [41,61]: 41 > 31, so no overlap. Add (31-13+1)=19 to answer
5. Final interval: Add (61-41+1)=21 to answer
6. Total: 10 + 19 + 21 = 50

Example with Overlapping Intervals

Here's an example showing how overlapping intervals are merged −

# Example with overlapping intervals
ob = Solution()
overlapping_intervals = [[1, 5], [3, 8], [10, 15]]
print(f"Overlapping intervals: {overlapping_intervals}")
print(f"Total unique duration: {ob.solve(overlapping_intervals)}")

# Step by step explanation
print("\nStep by step:")
print("1. [1,5] and [3,8] overlap ? merged to [1,8] ? duration = 8")
print("2. [10,15] is separate ? duration = 6") 
print("3. Total = 8 + 6 = 14")

Overlapping intervals: [[1, 5], [3, 8], [10, 15]]
Total unique duration: 14

Step by step:
1. [1,5] and [3,8] overlap ? merged to [1,8] ? duration = 8
2. [10,15] is separate ? duration = 6
3. Total = 8 + 6 = 14

Conclusion

This algorithm efficiently calculates total unique duration by sorting intervals and merging overlaps. The time complexity is O(n log n) due to sorting, and space complexity is O(1).