Merge pull request TheAlgorithms#109 from icalF/master

Add longest increasing subsequence

Author: AnupKumarPanwar

Dynamic Programming/LongestIncreasingSubsequence.java

@@ -0,0 +1,62 @@
+import java.util.Scanner;
+
+/**
+ *
+ * @author Afrizal Fikri (https://github.com/icalF)
+ *
+ */
+public class LongestIncreasingSubsequence {
+    public static void main(String[] args) throws Exception {
+
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+
+        int ar[] = new int[n];
+        for (int i = 0; i < n; i++) {
+            ar[i] = sc.nextInt();
+        }
+
+        System.out.println(LIS(ar));
+    }
+
+    private static int upperBound(int[] ar, int l, int r, int key) {
+        while (l < r-1) {
+            int m = (l + r) / 2;
+            if (ar[m] >= key)
+                r = m;
+            else
+                l = m;
+        }
+
+        return r;
+    }
+
+    public static int LIS(int[] array) {
+        int N = array.length;
+        if (N == 0)
+            return 0;
+ 
+        int[] tail = new int[N];
+        int length = 1; // always points empty slot in tail
+     
+        tail[0] = array[0];
+        for (int i = 1; i < N; i++) {
+
+            // new smallest value
+            if (array[i] < tail[0])
+                tail[0] = array[i];
+
+            // array[i] extends largest subsequence
+            else if (array[i] > tail[length-1])
+                tail[length++] = array[i];
+
+            // array[i] will become end candidate of an existing subsequence or
+            // Throw away larger elements in all LIS, to make room for upcoming grater elements than array[i]
+            // (and also, array[i] would have already appeared in one of LIS, identify the location and replace it)
+            else
+                tail[upperBound(tail, -1, length-1, array[i])] = array[i];
+        }
+     
+        return length;
+    }
+}