Add Longest Alternating Subsequence (#2743)

DynamicProgramming/LongestAlternatingSubsequence.java

@@ -0,0 +1,68 @@
+/*
+
+ * Problem Statement: - 
+ * Find Longest Alternating Subsequence
+
+ * A sequence {x1, x2, .. xn} is alternating sequence if its elements satisfy one of the following relations : 
+
+   x1 < x2 > x3 < x4 > x5 < …. xn or 
+   x1 > x2 < x3 > x4 < x5 > …. xn
+*/
+
+import java.io.*;
+
+public class LongestAlternatingSubsequence {
+
+	/* Function to return longest alternating subsequence length*/
+	static int AlternatingLength(int arr[], int n){
+		/*
+
+		las[i][0] = Length of the longest
+			alternating subsequence ending at
+			index i and last element is
+			greater than its previous element
+
+		las[i][1] = Length of the longest
+			alternating subsequence ending at
+			index i and last element is
+			smaller than its previous
+			element 
+
+		*/
+		int las[][] = new int[n][2]; // las = LongestAlternatingSubsequence
+
+		for (int i = 0; i < n; i++)
+			las[i][0] = las[i][1] = 1;
+
+		int result = 1; // Initialize result
+
+		/* Compute values in bottom up manner */
+		for (int i = 1; i < n; i++){
+
+			/* Consider all elements as previous of arr[i]*/
+			for (int j = 0; j < i; j++){
+
+				/* If arr[i] is greater, then check with las[j][1] */
+				if (arr[j] < arr[i] && las[i][0] < las[j][1] + 1)
+					las[i][0] = las[j][1] + 1;
+
+				/* If arr[i] is smaller, then check with las[j][0]*/
+				if( arr[j] > arr[i] && las[i][1] < las[j][0] + 1)
+					las[i][1] = las[j][0] + 1;
+			}
+
+			/* Pick maximum of both values at index i */
+			if (result < Math.max(las[i][0], las[i][1]))
+				result = Math.max(las[i][0], las[i][1]);
+		}
+
+		return result;
+	}
+
+	public static void main(String[] args)
+	{
+		int arr[] = { 10, 22, 9, 33, 49,50, 31, 60 };
+		int n = arr.length;
+		System.out.println("Length of Longest "+"alternating subsequence is " +AlternatingLength(arr, n));
+	}
+}