FBDS

/ * Given A and B two interval lists, A has no overlap inside A and B has no overlap inside B. Write the function to merge two interval lists, output the result with no overlap.

For example,
A= [1,5], [10,14], [16,18]
B= [2,6], [8,10], [11,20]


output [1,6], [8, 20]

Solve in JavaScript and tell space and time complexity

ChatGPT said:
ChatGPT
To solve the problem of merging two interval lists A and B, where both lists have no overlap within themselves, the approach is to:

Merge both lists into one combined list.
Sort the combined list by the start of each interval.
Iterate over the combined list and merge overlapping intervals as needed.
Approach:
Merge the two lists: Combine both interval lists into one.
Sort the intervals: Sort the intervals based on the start time (if two intervals have the same start time, the interval with the earlier end time comes first).
Merge the intervals: Iterate over the sorted intervals, merging them if they overlap.

Explanation:
Combining the intervals: const intervals = [...A, ...B] merges the two input arrays.
Sorting: intervals.sort((a, b) => a[0] - b[0] || a[1] - b[1]); sorts the intervals by start time, and if two intervals have the same start time, it sorts them by the end time.
Merging: The algorithm iterates through the sorted intervals and checks if the next interval overlaps with the current one. If they overlap, it merges them by updating the end of the current interval to the maximum end of the two. If they do not overlap, it adds the current interval to the result and moves on to the next interval.
Time Complexity:
Sorting the combined list of intervals takes O((m + n) log(m + n)), where m is the number of intervals in list A, and n is the number of intervals in list B.
Merging the intervals takes O(m + n) because each interval is processed once.
Thus, the overall time complexity is O((m + n) log(m + n)).

Space Complexity:
We are using extra space for the combined list of intervals and the result, so the space complexity is O(m + n).
Thus, the space complexity is O(m + n).
*/
function mergeIntervals(A, B) {
    // Combine both lists
    const intervals = [...A, ...B];

    // Sort intervals by start time, if start time is the same, sort by end time
    intervals.sort((a, b) => a[0] - b[0] || a[1] - b[1]);

    const result = [];
    let currentInterval = intervals[0];

    // Iterate over the intervals and merge as needed
    for (let i = 1; i < intervals.length; i++) {
        const [currentStart, currentEnd] = currentInterval;
        const [nextStart, nextEnd] = intervals[i];

        if (nextStart <= currentEnd) {
            // If intervals overlap, merge them
            currentInterval = [currentStart, Math.max(currentEnd, nextEnd)];
        } else {
            // Otherwise, add the current interval to the result and update currentInterval
            result.push(currentInterval);
            currentInterval = intervals[i];
        }
    }

    // Add the last merged interval
    result.push(currentInterval);

    return result;
}

// Example usage:
const A = [[1, 5], [10, 14], [16, 18]];
const B = [[2, 6], [8, 10], [11, 20]];
console.log(mergeIntervals(A, B));  // Output: [ [1, 6], [8, 20] ]