Added longest increasing subsequence algo.

Algoritms/Longest_increasing_subsequence.cpp

@@ -0,0 +1,55 @@
+/* A Memoization Java Program for LIS Implementation */
+import java.util.Arrays;
+import java.lang.*;
+class LIS {
+
+/* To make use of recursive calls, this function must
+	return two things: 1) Length of LIS ending with element
+	arr[n-1]. We use max_ending_here for this purpose 2)
+	Overall maximum as the LIS may end with an element
+	before arr[n-1] max_ref is used this purpose.
+	The value of LIS of full array of size n is stored in
+	*max_ref which is our final result */
+static int f(int idx, int prev_idx, int n, int a[],
+			int[][] dp)
+{
+	if (idx == n) {
+	return 0;
+	}
+
+	if (dp[idx][prev_idx + 1] != -1) {
+	return dp[idx][prev_idx + 1];
+	}
+
+	int notTake = 0 + f(idx + 1, prev_idx, n, a, dp);
+	int take = Integer.MIN_VALUE;
+	if (prev_idx == -1 || a[idx] > a[prev_idx]) {
+	take = 1 + f(idx + 1, idx, n, a, dp);
+	}
+
+	return dp[idx][prev_idx + 1] = Math.max(take, notTake);
+}
+
+// The wrapper function for _lis()
+static int lis(int arr[], int n)
+{
+
+	// The function _lis() stores its result in max
+	int dp[][] = new int[n+1][n+1];
+	for (int row[] : dp)
+	Arrays.fill(row, -1);
+
+	return f(0, -1, n, arr, dp);
+
+
+}
+
+// driver program to test above functions
+public static void main(String args[])
+{
+	int a[] = { 3, 10, 2, 1, 20 };
+	int n = a.length;
+	System.out.println("Length of lis is " + lis(a, n)
+					+ "\n");
+}
+}