Hi Team,
I have coded the problem in the following fashion. I was able to test it out for some of the scenarios and it worked. Is this approach fine or will break for some other testing scenarios.
Also I was not able to get the Tabulation Version (Bottom Up) for this way of coding. Could you help me on this 
public class JLongestBitonicSubsequence {
public static void main(String[] args) {
JLongestBitonicSubsequence game = new JLongestBitonicSubsequence();
int[] input = {4, 2, 3, 6, 10, 1, 12};
Arrays.stream(input).forEach(x -> System.out.print(x + " "));
System.out.println();
game.solveWithBruteForce(input);
game.solveWithMemoization(input);
game.solveWithTabulation(input);
input = new int[]{4, 2, 5, 9, 7, 6, 10, 3, 1};
System.out.println();
Arrays.stream(input).forEach(x -> System.out.print(x + " "));
System.out.println();
game.solveWithBruteForce(input);
game.solveWithMemoization(input);
game.solveWithTabulation(input);
input = new int[]{1, 2, 12, 15, 9, 11, 6, 10, 7, 1};
System.out.println();
Arrays.stream(input).forEach(x -> System.out.print(x + " "));
System.out.println();
game.solveWithBruteForce(input);
game.solveWithMemoization(input);
game.solveWithTabulation(input);
}
private void solveWithBruteForce(int[] input) {
int longest = solve(input, 0, -1, false);
/ Since we are initially checking for the increasing we are making the turnTaken as false /
System.out.println("(Brute Force) longest bitonic subsequence: " + longest);
}
private int solve(int[] input, int currentIndex, int previousIndex, boolean turnTaken) {
if (currentIndex == input.length) return 0;
if (!turnTaken) {
int increasing = 0;
if (previousIndex == -1 || input[ currentIndex ] > input[ previousIndex ]) {//Increasing Check
increasing = 1 + solve(input, currentIndex + 1, currentIndex, turnTaken);
}
/ If it is not increasing then we can take two kinds of decisions “skip the current element” and check the rest
or take a turn (change the flag value from false to true) with the “current element” and check if it returning
a max value /
int skippingCurrent = solve(input, currentIndex + 1, previousIndex, turnTaken);
int takingTurn = solve(input, currentIndex, previousIndex, true);
return Math.max(Math.max(increasing, skippingCurrent), takingTurn);
} else {
int decreasing = 0;
if (previousIndex == -1 || input[ currentIndex ] < input[ previousIndex ]) {//Decreasing Check
decreasing = 1 + solve(input, currentIndex + 1, currentIndex, turnTaken);
}
/ Here we are not taking a turn like we did before in the Increasing Check’s takingTurn scenario since we are
checking only for a bitonic and so only one turn is allowed */
int skippingCurrent = solve(input, currentIndex + 1, previousIndex, turnTaken);
return Math.max(decreasing, skippingCurrent);
}
}
private void solveWithMemoization(int[] input) {
Integer[][][] memo = new Integer[ input.length ][ input.length ][ 2 ];
int longest = solve(input, 0, -1, false, memo);
System.out.println("(Memoization) longest bitonic subsequence: " + longest);
}
private int solve(int[] input, int currentIndex, int previousIndex, boolean turnTaken, Integer[][][] memo) {
if (currentIndex == input.length) return 0;
int turnIndex = turnTaken ? 1 : 0; / turnTaken if false we save in 0th index of the third dimension of the memo matrix /
if (memo[ currentIndex ][ previousIndex + 1 ][ turnIndex ] == null) {
int increase = 0;
int decrease = 0;
if (!turnTaken) {
if (previousIndex == -1 || input[ currentIndex ] > input[ previousIndex ]) {//Increasing Check
increase = 1 + solve(input, currentIndex + 1, currentIndex, turnTaken, memo);
}
int skipping = solve(input, currentIndex + 1, previousIndex, turnTaken, memo);
int takingTurn = solve(input, currentIndex, previousIndex, true, memo);
increase = Math.max(Math.max(increase, takingTurn), skipping);
} else {
if (previousIndex == -1 || input[ currentIndex ] < input[ previousIndex ]) {
decrease = 1 + solve(input, currentIndex + 1, currentIndex, turnTaken, memo);
}
int skipping = solve(input, currentIndex + 1, previousIndex, turnTaken, memo);
decrease = Math.max(decrease, skipping);
}
memo[ currentIndex ][ previousIndex + 1 ][ turnIndex ] = Math.max(increase, decrease);
}
return memo[ currentIndex ][ previousIndex + 1 ][ turnIndex ];
}
private void solveWithTabulation(int[] input) {
int[][] matrix = new int[ input.length + 1 ][ input.length + 1 ];
solve(input, matrix);
}
}