Added solution for Leetcode 0056. Merge Intervals

Author: frankdavid-bp

problems/01. Arrays/Part 02/02. Leetcode Medium 0056. Merge Intervals/Algorithms.md

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+### 1. Sorting Approach
+Sort Intervals:
+* Sort the intervals based on their start times using a comparator.
+Initialize:
+* Create a list to store the merged intervals.
+* Start with the first interval as the current interval to merge.
+
+Loop through Sorted Intervals:
+* For each interval, check if it overlaps with the current interval:
+  * If it overlaps, merge them by updating the end of the current interval to the maximum end of both intervals.
+  * If it doesn't overlap, add the current interval to the list of merged intervals and update the current interval to the next interval.
+Add Last Interval:
+* After the loop, add the last current interval to the list of merged intervals.
+Return Result:
+* Convert the list of merged intervals to an array and return it.
+
+Time Complexity: O(n log n)
+Space Complexity: O(n)
+
+### 2. Optimized Sorting Approach Using LinkedList
+Sort Intervals:
+* Sort the intervals based on their start times using a comparator.
+
+Initialize:
+* Create a LinkedList to store the merged intervals.
+
+Loop through Sorted Intervals:
+* For each interval, check if it overlaps with the last interval in the LinkedList:
+  * If it overlaps, merge them by updating the end of the last interval in the LinkedList to the maximum end of both intervals.
+  * If it doesn't overlap, add the interval to the LinkedList.
+Return Result:
+* Convert the LinkedList of merged intervals to an array and return it.
+Time Complexity: O(n log n)
+Space Complexity: O(n)

problems/01. Arrays/Part 02/02. Leetcode Medium 0056. Merge Intervals/java/OptimizedSortingApproachUsingLinkedList.java

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+import java.util.Arrays;
+import java.util.LinkedList;
+
+public class Solution {
+    public static void main(String[] args) {
+        int[][] intervals = {{1,3},{2,6},{8,10},{15,18}};
+        Arrays.sort(intervals, (a, b) -> Integer.compare(a[0], b[0]));
+
+        LinkedList<int[]> mergedIntervals = new LinkedList<int[]>();
+
+        for(int[]interval : intervals) {
+            if(mergedIntervals.isEmpty() || mergedIntervals.getLast()[1] < interval[0]){
+                mergedIntervals.add(interval);
+            }else{
+                mergedIntervals.getLast()[1] = Math.max(mergedIntervals.getLast()[1], interval[1]);
+            }
+        }
+
+        int[][] arrayMergedIntervals = mergedIntervals.toArray(new int[mergedIntervals.size()][]);
+        System.out.println(Arrays.deepToString(arrayMergedIntervals));
+    }
+}