solves #300: Longest Increasing Subsequence in java

Author: anishLearnsToCode

Diff for: README.txt

@@ -246,7 +246,7 @@
 | 294  | 🔒 [Flip Game II](https://leetcode.com/problems/flip-game-ii)                                                                                                          |                                                                                                                                                                                                                                  |                                                                                                                                   |
 | 298  | 🔒 [Binary Tree Longest Consecutive Sequence](https://leetcode.com/problems/binary-tree-longest-consecutive-sequence)                                                  |                                                                                                                                                                                                                                  |                                                                                                                                   |
 | 299  | [Bulls and Cows](https://leetcode.com/problems/bulls-and-cows)                                                                                                         |                                                            [![Java](assets/java.png)](src/BullsAndCows.java) [![Python](assets/python.png)](python/bulls_and_cows.py)                                                            |                                                                                                                                   |
-| 300  | [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence)                                                                         |                                                                                                                                                                                                                                  |                                                                                                                                   |
+| 300  | [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence)                                                                         |                                                                                                             [![Java](assets/java.png)](src/LongestIncreasingSubsequence.java)                                                                                                                     |                                                                                                                                   |
 | 303  | [Range Sum Query - Immutable](https://leetcode.com/problems/range-sum-query-immutable)                                                                                 |                                                 [![Java](assets/java.png)](src/RangeSumQueryImmutable.java) [![Python](assets/python.png)](python/range_sum_query_immutable.py)                                                  |                                                                                                                                   |
 | 304  | [Range Sum Query 2D - Immutable](https://leetcode.com/problems/range-sum-query-2d-immutable)                                                                           |                                                                                                                                                                                                                                  |                                                                                                                                   |
 | 306  | [Additive Number](https://leetcode.com/problems/additive-number)                                                                                                       |                                                                                                                                                                                                                                  |                                                                                                                                   |

Diff for: src/LongestIncreasingSubsequence.java

@@ -0,0 +1,43 @@
+// https://leetcode.com/problems/longest-increasing-subsequence
+// T: O(NlogN)
+// S: O(N)
+
+import java.util.ArrayList;
+import java.util.List;
+
+public class LongestIncreasingSubsequence {
+    public static int lengthOfLIS(int[] nums) {
+        final List<Integer> tail = new ArrayList<>();
+        int maxLength = 1;
+        tail.add(nums[0]);
+
+        for (int i = 1 ; i < nums.length ; i++) {
+            if (nums[i] > tail.get(maxLength - 1)) {
+                tail.add(nums[i]);
+                maxLength++;
+            } else if (nums[i] < tail.get(0)) {
+                tail.set(0, nums[i]);
+            } else {
+                int insertionIndex = binarySearch(tail, nums[i]);
+                tail.set(insertionIndex, nums[i]);
+            }
+        }
+
+        return maxLength;
+    }
+
+    private static int binarySearch(List<Integer> array, int x) {
+        int left = 0, right = array.size(), middle;
+        while (left <= right) {
+            middle = left + (right - left) / 2;
+            if (array.get(middle) == x) return middle;
+            else if (array.get(middle) < x) left = middle + 1;
+            else right = middle - 1;
+        }
+        return left;
+    }
+
+    public static void main(String[] args) {
+        System.out.println(lengthOfLIS(new int[] {1,3,6,7,9,4,10,5,6}));
+    }
+}