Dynamic Programming Questions
The Maximum Sum of Subsequence with No Fourteen Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, where no four consecutive elements in the subsequence can be the number 14.
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 need to check if the previous element is 14. If it is, we cannot include the current element in the subsequence. Otherwise, we can include it and update the "dp" array at the current index as the sum of the current element and the maximum sum of the subsequence up to the previous index.
2. Exclude the current element from the subsequence: In this case, we simply update the "dp" array at the current index as the maximum sum of the subsequence up to the previous index.
After iterating through the entire sequence, the maximum sum of the subsequence with no fourteen consecutive elements will be the maximum value in the "dp" array.
Here is the pseudocode for the dynamic programming solution:
1. Initialize an array "dp" of size n, where n is the length of the given sequence.
2. Set dp[0] = sequence[0].
3. Set dp[1] = max(sequence[0], sequence[1]).
4. Iterate from i = 2 to n-1:
a. If sequence[i] is 14 and sequence[i-1] is 14, set dp[i] = dp[i-2].
b. Otherwise, set dp[i] = max(dp[i-1], dp[i-2] + sequence[i]).
5. Return the maximum value in the "dp" array.
By following this dynamic programming approach, we can efficiently solve the Maximum Sum of Subsequence with No Fourteen Consecutive Elements problem.