What is the Maximum Sum of Subsequence with No Nineteen Consecutive Elements problem and how can it be solved using Dynamic Programming?

What is the Maximum Sum of Subsequence with No Nineteen Consecutive Elements problem and how can it be solved using Dynamic Programming?

The Maximum Sum of Subsequence with No Nineteen Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, where no consecutive elements in the subsequence can be the number 19.

To solve this problem using dynamic programming, we can use an array to store the maximum sum of subsequences up to a certain index. Let's call this array "dp".

The dynamic programming approach involves iterating through the given sequence and updating the "dp" array at each index. At each index, we have two options:

1. Include the current element in the subsequence: In this case, we cannot include the previous element if it is 19. Therefore, the maximum sum up to the current index would be the sum of the current element and the maximum sum up to the previous non-19 element.

2. Exclude the current element from the subsequence: In this case, the maximum sum up to the current index would be the same as the maximum sum up to the previous index.

We can then update the "dp" array at each index by taking the maximum value between the two options mentioned above.

Finally, the maximum sum of the subsequence with no nineteen consecutive elements would be the maximum value in the "dp" array.

By using this dynamic programming approach, we can efficiently solve the Maximum Sum of Subsequence with No Nineteen Consecutive Elements problem.