Dynamic Programming Questions
The Maximum Sum of Subsequence with No Seventeen 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 have a difference of seventeen.
To solve this problem using dynamic programming, we can use an array to store the maximum sum of subsequences ending at each index. Let's call this array "dp".
We initialize the first two elements of the "dp" array as the first and second elements of the given sequence. Then, for each subsequent element in the sequence, we calculate the maximum sum of subsequences ending at that index by considering two cases:
1. If the previous element is not included in the subsequence, then the maximum sum at the current index is the maximum of the maximum sum at the previous index and the current element itself.
2. If the previous element is included in the subsequence, then the maximum sum at the current index is the maximum of the maximum sum at the previous index (excluding the previous element) and the sum of the current element and the maximum sum at the index two positions before.
Finally, we return the maximum value in the "dp" array as the maximum sum of the subsequence with no seventeen consecutive elements.
Here is the pseudocode for solving this problem using dynamic programming:
1. Initialize dp[0] = sequence[0] and dp[1] = sequence[1].
2. For i = 2 to n-1:
a. dp[i] = max(dp[i-1], sequence[i], sequence[i] + dp[i-2])
3. Return max(dp[0], dp[1], ..., dp[n-1]) as the maximum sum of the subsequence with no seventeen consecutive elements.
By using this dynamic programming approach, we can efficiently solve the Maximum Sum of Subsequence with No Seventeen Consecutive Elements problem.