Longest Increasing Subsequence

longest-increasing-subsequence/forest000014.java

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+/*
+Time Complexity: O(nlogn)
+Space Complexity: O(nlogn)
+*/
+class Solution {
+
+    int[] tree;
+    int L = 1;
+
+    public int lengthOfLIS(int[] nums) {
+        init(nums);
+        ArrayList<Tuple> tuples = new ArrayList<>();
+
+        for (int i = 0; i < nums.length; i++) {
+            tuples.add(new Tuple(i, nums[i]));
+        }
+
+        Collections.sort(tuples, (a, b) -> {
+            if (a.val == b.val) {
+                return b.ref - a.ref; // 2순위 : ref 내림차순
+            } else {
+                return a.val - b.val; // 1순위 : val 오름차순
+            }
+        });
+
+        int ans = 0;
+        for (int i = 0; i < nums.length; i++) {
+            int curr = getMax(0, tuples.get(i).ref - 1) + 1;
+            ans = Math.max(ans, curr);
+            insert(tuples.get(i).ref, curr);
+        }
+
+        return ans;
+    }
+
+    public class Tuple {
+        public int ref;
+        public int val;
+
+        public Tuple(int ref, int val) {
+            this.ref = ref;
+            this.val = val;
+        }
+    }
+
+    public void init(int[] nums) {
+        while (L < nums.length) {
+            L *= 2;
+        }
+
+        tree = new int[L * 2];
+
+        for (int i = 1; i < L * 2; i++) {
+            tree[i] = 0;
+        }
+    }
+
+    public void insert(int idx, int v) {
+        int i = idx + L;
+        tree[i] = v;
+        i /= 2;
+        while (i >= 1) {
+            tree[i] = Math.max(tree[i * 2], tree[i * 2 + 1]);
+            i /= 2;
+        }
+    }
+
+    public int getMax(int l, int r) {
+        int i = l + L;
+        int j = r + L;
+        int ret = 0;
+        while (i <= j) {
+            if (i % 2 == 1) {
+                ret = Math.max(ret, tree[i++]);
+            }
+            if (j % 2 == 0) {
+                ret = Math.max(ret, tree[j--]);
+            }
+            i /= 2;
+            j /= 2;
+        }
+
+        return ret;
+    }
+}