LeetCode 57: Insert Interval

Given a set of non-overlapping intervals, insert a new interval into the intervals (merge if necessary).
You may assume that the intervals were initially sorted according to their start times.
Example 1:
Given intervals [1,3],[6,9], insert and merge [2,5] in as [1,5],[6,9].
Example 2:
Given [1,2],[3,5],[6,7],[8,10],[12,16], insert and merge [4,9] in as [1,2],[3,10],[12,16].
This is because the new interval [4,9] overlaps with [3,5],[6,7],[8,10].

/**
 * Definition for an interval.
 * public class Interval {
 *     int start;
 *     int end;
 *     Interval() { start = 0; end = 0; }
 *     Interval(int s, int e) { start = s; end = e; }
 * }
 */
public class Solution {
    public List<Interval> insert(List<Interval> intervals, Interval newInterval) {
        // http://www.programcreek.com/2012/12/leetcode-insert-interval/
        // Consider 3 cases:
        // Case 1: newInterval is completely on the right of current interval;
        // Case 2: newInterval is completely on the left of current interval;
        // Case 3: newInterval is overlapped with current interval.
        if (newInterval == null)
            return intervals;
        
        List<Interval> result = new LinkedList<>();
 
        for (Interval itv: intervals)
            // Case 1: newInterval is completely on the right of itv.
            // Add left (itv) firstly.
            if (itv.end < newInterval.start)
                result.add(itv);
            // Case 2: newInterval is completely on the left of itv.
            // Add left (newInterval) firstly.
            // Create right (itv) as new 'newInterval'.
            else if (itv.start > newInterval.end)
            {
                result.add(newInterval);
                newInterval = itv;        
            }
            // Case 3: newInterval is overlapped with itv.
            else
                // Merge newInterval and itv as a new 'newInterval'.
                newInterval = new Interval(Math.min(itv.start, newInterval.start), Math.max(newInterval.end, itv.end));
 
        // Don't miss the last one.
        result.add(newInterval); 
 
        return result;
    }
}