diff --git a/DynamicProgramming/LongestAlternatingSubsequence.java b/DynamicProgramming/LongestAlternatingSubsequence.java new file mode 100644 index 000000000..3551edf02 --- /dev/null +++ b/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)); + } +}