refer to: https://www.algoexpert.io/questions/Merge%20Overlapping%20Intervals

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Problem Statement

Sample example

Analysis

step 1: sort the intervals by their start value

step 2: check if the end value of the previous interval is larger than the start value of the latter interval

Code

def mergeOverlappingIntervals(intervals):
    # sort the intervals by startinf value.  O(nlogn)
    sortedIntervals = sorted(intervals, key = lambda x: x[0])
    
    mergedIntervals = []# space: O(n)
    currentInterval = sortedIntervals[0]#initialize the currentInterval as the first interval of the intervals
    mergedIntervals.append(currentInterval)#initialize the mergedIntervals as the first interval of the intervals
    
    for nextInterval in sortedIntervals:# for the first iteration, no update
        _, currentIntervalEnd = currentInterval
        nextIntervalStart, nextIntervalEnd = nextInterval
        
        if currentIntervalEnd >= nextIntervalStart: # overlap found, update the end value of interval
            currentInterval[1] = max(currentIntervalEnd, nextIntervalEnd)
        else: # no overlap, add the current(nextInterval) into the mergedIntervals array
            currentInterval = nextInterval
            mergedIntervals.append(currentInterval)
    return mergedIntervals

Time and Space complexity

O(nlogn) time complexity for sorting

O(n) space complexity for store the mergedIntervals(upper bound, all intervals kept)