[Dana] Add longest increasing subsequence (#50)

Add longest increasing subsequence program with sample input and result

---------

Co-authored-by: Kostis Sagonas <kostis@cs.ntua.gr>

Author: geokoko

dana/programs/lis.dana

@@ -0,0 +1,63 @@
+(*
+   Finds the length of the Longest Increasing Subsequence.
+   Dynamic Programming solution in O(N^2)
+*)
+
+def main
+	
+	def lis is int: n as int, arr as int[]
+
+		var dp is int [n]
+		var i j maxLen is int
+
+		if n <= 0:
+			return: 0
+
+		(* Initialize dp array *)
+		i := 0
+		loop:
+			if i >= n : break
+			dp[i] := 1
+			i := i + 1
+
+		(* Begin computing values *)
+		i := 1
+  		loop:
+    		if i >= n: break
+    		j := 0
+    		loop:
+      			if j >= i: break
+      			if arr[j] < arr[i] and dp[j] + 1 > dp[i]:
+        			dp[i] := dp[j] + 1
+      			j := j + 1
+    		i := i + 1
+
+  		maxLen := dp[0]
+  		i := 1
+  		loop:
+    		if i >= n: break
+    		if dp[i] > maxLen:
+      			maxLen := dp[i]
+   			i := i + 1
+
+  		return: maxLen
+
+	var n is int
+	n := readInteger()
+
+	var arr is int [n]
+
+	(* Populate array *)
+	var i is int
+	i := 0
+	loop:
+		if i >= n: break
+		arr[i] := readInteger()
+		i := i + 1
+	
+	var len is int
+	len := lis: n, arr
+
+	writeString: "longest inreasing subsequence has length "
+	writeInteger: len
+	writeString: "\n"

dana/programs/lis.input

@@ -0,0 +1,2 @@
+8
+10 9 2 5 3 7 101 18

dana/programs/lis.output

@@ -0,0 +1 @@
+longest inreasing subsequence has length 4