Dynamic Programming Questions
The Maximum Sum of Subsequence with No Thirty-Five Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, with the constraint that no subsequence should contain thirty-five consecutive elements.
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 denote this array as dp, where dp[i] represents the maximum sum of subsequences ending at index i.
We can initialize the dp array with the first element of the given sequence, i.e., dp[0] = sequence[0]. Then, we iterate through the remaining elements of the sequence, updating the dp array as follows:
1. For each index i, if the previous element (i-1) is not included in the subsequence, then we can include the current element and update dp[i] as dp[i-1] + sequence[i].
2. If the previous element (i-1) is included in the subsequence, then we cannot include the current element. In this case, we update dp[i] as dp[i-2] + sequence[i] to ensure that there are no thirty-five consecutive elements.
After iterating through all the elements, the maximum sum of subsequences with no thirty-five consecutive elements will be the maximum value in the dp array.
In summary, the problem can be solved using dynamic programming by maintaining an array to store the maximum sum of subsequences up to a certain index, considering the constraints of not including thirty-five consecutive elements.